An abnormal concretion occurring mostly in the urinary and biliary tracts, usually composed of mineral salts. Also called stones.
Low-density crystals or stones in any part of the URINARY TRACT. Their chemical compositions often include CALCIUM OXALATE, magnesium ammonium phosphate (struvite), CYSTINE, or URIC ACID.
Stones in the URETER that are formed in the KIDNEY. They are rarely more than 5 mm in diameter for larger renal stones cannot enter ureters. They are often lodged at the ureteral narrowing and can cause excruciating renal colic.
Stones in the KIDNEY, usually formed in the urine-collecting area of the kidney (KIDNEY PELVIS). Their sizes vary and most contains CALCIUM OXALATE.
Stones in the URINARY BLADDER; also known as vesical calculi, bladder stones, or cystoliths.
Abnormal concretion or calcified deposit that forms around the teeth or dental prostheses.
The destruction of a calculus of the kidney, ureter, bladder, or gallbladder by physical forces, including crushing with a lithotriptor through a catheter. Focused percutaneous ultrasound and focused hydraulic shock waves may be used without surgery. Lithotripsy does not include the dissolving of stones by acids or litholysis. Lithotripsy by laser is LITHOTRIPSY, LASER.
Presence of small calculi in the terminal salivary ducts (salivary sand), or stones (larger calculi) found in the larger ducts.
Endoscopic examination, therapy or surgery of the ureter.
The insertion of a catheter through the skin and body wall into the kidney pelvis, mainly to provide urine drainage where the ureter is not functional. It is used also to remove or dissolve renal calculi and to diagnose ureteral obstruction.
Calculi occurring in a salivary gland. Most salivary gland calculi occur in the submandibular gland, but can also occur in the parotid gland and in the sublingual and minor salivary glands.
Fragmentation of CALCULI, notably urinary or biliary, by LASER.
Pathological processes involving the PROSTATE or its component tissues.
Formation of stones in any part of the URINARY TRACT, usually in the KIDNEY; URINARY BLADDER; or the URETER.
The calcium salt of oxalic acid, occurring in the urine as crystals and in certain calculi.
Radiography of any part of the urinary tract.
The presence of calculi in a salivary duct or gland.
Solid crystalline precipitates in the BILIARY TRACT, usually formed in the GALLBLADDER, resulting in the condition of CHOLELITHIASIS. Gallstones, derived from the BILE, consist mainly of calcium, cholesterol, or bilirubin.
Presence or formation of GALLSTONES in the BILIARY TRACT, usually in the gallbladder (CHOLECYSTOLITHIASIS) or the common bile duct (CHOLEDOCHOLITHIASIS).
Books in the field of medicine intended primarily for consultation.
Surgery performed on the urinary tract or its parts in the male or female. For surgery of the male genitalia, UROLOGIC SURGICAL PROCEDURES, MALE is available.
Inorganic compounds that contain magnesium as an integral part of the molecule.
An inherited disorder due to defective reabsorption of CYSTINE and other BASIC AMINO ACIDS by the PROXIMAL RENAL TUBULES. This form of aminoaciduria is characterized by the abnormally high urinary levels of cystine; LYSINE; ARGININE; and ORNITHINE. Mutations involve the amino acid transport protein gene SLC3A1.
Calcium salts of phosphoric acid. These compounds are frequently used as calcium supplements.
A clinical syndrome with intermittent abdominal pain characterized by sudden onset and cessation that is commonly seen in infants. It is usually associated with obstruction of the INTESTINES; of the CYSTIC DUCT; or of the URINARY TRACT.
The flattened, funnel-shaped expansion connecting the URETER to the KIDNEY CALICES.
A colorless, odorless, viscous dihydroxy alcohol. It has a sweet taste, but is poisonous if ingested. Ethylene glycol is the most important glycol commercially available and is manufactured on a large scale in the United States. It is used as an antifreeze and coolant, in hydraulic fluids, and in the manufacture of low-freezing dynamites and resins.
Abdominal symptoms after removal of the GALLBLADDER. The common postoperative symptoms are often the same as those present before the operation, such as COLIC, bloating, NAUSEA, and VOMITING. There is pain on palpation of the right upper quadrant and sometimes JAUNDICE. The term is often used, inaccurately, to describe such postoperative symptoms not due to gallbladder removal.
A surgical specialty concerned with the study, diagnosis, and treatment of diseases of the urinary tract in both sexes, and the genital tract in the male. Common urological problems include urinary obstruction, URINARY INCONTINENCE, infections, and UROGENITAL NEOPLASMS.
Pathological processes of the URINARY TRACT in both males and females.
A pouch or sac developed from a tubular or saccular organ, such as the GASTROINTESTINAL TRACT.
Abnormal enlargement or swelling of a KIDNEY due to dilation of the KIDNEY CALICES and the KIDNEY PELVIS. It is often associated with obstruction of the URETER or chronic kidney diseases that prevents normal drainage of urine into the URINARY BLADDER.
Holmium. An element of the rare earth family of metals. It has the atomic symbol Ho, atomic number 67, and atomic weight 164.93.
A group of phosphate minerals that includes ten mineral species and has the general formula X5(YO4)3Z, where X is usually calcium or lead, Y is phosphorus or arsenic, and Z is chlorine, fluorine, or OH-. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
A condition characterized by the formation of CALCULI and concretions in the hollow organs or ducts of the body. They occur most often in the gallbladder, kidney, and lower urinary tract.
The duct that is connected to the GALLBLADDER and allows the emptying of bile into the COMMON BILE DUCT.
A chronic inflammatory condition of the KIDNEY resulting in diffuse renal destruction, a grossly enlarged and nonfunctioning kidney associated with NEPHROLITHIASIS and KIDNEY STONES.
Pathological processes of the TESTIS.
An imaging test of the BILIARY TRACT in which a contrast dye (RADIOPAQUE MEDIA) is injected into the BILE DUCT and x-ray pictures are taken.
Diseases in any part of the ductal system of the BILIARY TRACT from the smallest BILE CANALICULI to the largest COMMON BILE DUCT.
Derivatives of OXALIC ACID. Included under this heading are a broad variety of acid forms, salts, esters, and amides that are derived from the ethanedioic acid structure.
A strong dicarboxylic acid occurring in many plants and vegetables. It is produced in the body by metabolism of glyoxylic acid or ascorbic acid. It is not metabolized but excreted in the urine. It is used as an analytical reagent and general reducing agent.
Excretion of abnormally high level of CALCIUM in the URINE, greater than 4 mg/kg/day.
Heterocyclic rings containing three nitrogen atoms, commonly in 1,2,4 or 1,3,5 or 2,4,6 formats. Some are used as HERBICIDES.
Recesses of the kidney pelvis which divides into two wide, cup-shaped major renal calices, with each major calix subdivided into 7 to 14 minor calices. Urine empties into a minor calix from collecting tubules, then passes through the major calix, renal pelvis, and ureter to enter the urinary bladder. (From Moore, Clinically Oriented Anatomy, 3d ed, p211)
Liquid by-product of excretion produced in the kidneys, temporarily stored in the bladder until discharge through the URETHRA.
Treatment for the prevention of periodontal diseases or other dental diseases by the cleaning of the teeth in the dental office using the procedures of DENTAL SCALING and DENTAL POLISHING. The treatment may include plaque detection, removal of supra- and subgingival plaque and calculus, application of caries-preventing agents, checking of restorations and prostheses and correcting overhanging margins and proximal contours of restorations, and checking for signs of food impaction.
An embryonic structure originating from the ALLANTOIS. It is a canal connecting the fetal URINARY BLADDER and the UMBILICUS. It is normally converted into a fibrous cord postnatally. When the canal fails to be filled and remains open (patent urachus), urine leaks through the umbilicus.
A numerical rating scale for classifying the periodontal status of a person or population with a single figure which takes into consideration prevalence as well as severity of the condition. It is based upon probe measurement of periodontal pockets and on gingival tissue status.
An oxidation product, via XANTHINE OXIDASE, of oxypurines such as XANTHINE and HYPOXANTHINE. It is the final oxidation product of purine catabolism in humans and primates, whereas in most other mammals URATE OXIDASE further oxidizes it to ALLANTOIN.
Inflammation of gum tissue (GINGIVA) without loss of connective tissue.
Endoscopes for examining the interior of the ureter.
An ancient civilization, known as early as 2000 B.C. The Persian Empire was founded by Cyrus the Great (550-529 B.C.) and for 200 years, from 550 to 331 B.C., the Persians ruled the ancient world from India to Egypt. The territory west of India was called Persis by the Greeks who later called the entire empire Persia. In 331 B.C. the Persian wars against the Greeks ended disastrously under the counterattacks by Alexander the Great. The name Persia in modern times for the modern country was changed to Iran in 1935. (From Webster's New Geographical Dictionary, 1988, p546 & Asimov, Words on the Map, 1962, p176)
Pathological processes involving the URETERS.
A thin protein film on the surface of DENTAL ENAMEL. It is widely believed to result from the selective adsorption of precursor proteins present in SALIVA onto tooth surfaces, and to reduce microbial adherence to the TEETH.
Excretion of an excessive amount of OXALATES in the urine.
A combination of the debris index and the dental calculus index to determine the status of oral hygiene.
Endoscopic examination, therapy or surgery of the urinary bladder.
Instruments for the visual examination of interior structures of the body. There are rigid endoscopes and flexible fiberoptic endoscopes for various types of viewing in ENDOSCOPY.
A cutaneous pouch of skin containing the testicles and spermatic cords.
Formation of stones in the KIDNEY.
A condition characterized by calcification of the renal tissue itself. It is usually seen in distal RENAL TUBULAR ACIDOSIS with calcium deposition in the DISTAL KIDNEY TUBULES and the surrounding interstitium. Nephrocalcinosis causes RENAL INSUFFICIENCY.
Fiberoptic endoscopy designed for duodenal observation and cannulation of VATER'S AMPULLA, in order to visualize the pancreatic and biliary duct system by retrograde injection of contrast media. Endoscopic (Vater) papillotomy (SPHINCTEROTOMY, ENDOSCOPIC) may be performed during this procedure.
Partial or complete blockage in any part of the URETHRA that can lead to difficulty or inability to empty the URINARY BLADDER. It is characterized by an enlarged, often damaged, bladder with frequent urges to void.
A film that attaches to teeth, often causing DENTAL CARIES and GINGIVITIS. It is composed of MUCINS, secreted from salivary glands, and microorganisms.
Endoscopes for visual examination of the urinary bladder.
A plant genus of the family RANUNCULACEAE that contains alpha-hederin, a triterpene saponin in the seeds, and is the source of black seed oil.
The sesame family of the order Lamiales that are mainly herbs and shrubs growing in warm regions.
Surgical removal of the GALLBLADDER.
Painful URINATION. It is often associated with infections of the lower URINARY TRACT.
A powder that dissolves in water, which is administered orally, and is used as a diuretic, expectorant, systemic alkalizer, and electrolyte replenisher.
A principle that learning is facilitated when the learner receives immediate evaluation of learning performance. The concept also hypothesizes that learning is facilitated when the learner is promptly informed whether a response is correct, and, if incorrect, of the direction of error.
Inorganic compounds that contain potassium as an integral part of the molecule.
Presence of blood in the urine.
Radiography of the SALIVARY GLANDS or ducts following injection of contrast medium.
Any change in the hue, color, or translucency of a tooth due to any cause. Restorative filling materials, drugs (both topical and systemic), pulpal necrosis, or hemorrhage may be responsible. (Jablonski, Dictionary of Dentistry, 1992, p253)
Absence of urine formation. It is usually associated with complete bilateral ureteral (URETER) obstruction, complete lower urinary tract obstruction, or unilateral ureteral obstruction when a solitary kidney is present.
Surgical creation of an opening (stoma) in the URINARY BLADDER for drainage.
Substances which are of little or no therapeutic value, but are necessary in the manufacture, compounding, storage, etc., of pharmaceutical preparations or drug dosage forms. They include SOLVENTS, diluting agents, and suspending agents, and emulsifying agents. Also, ANTIOXIDANTS; PRESERVATIVES, PHARMACEUTICAL; COLORING AGENTS; FLAVORING AGENTS; VEHICLES; EXCIPIENTS; OINTMENT BASES.
An abnormal extension of a gingival sulcus not accompanied by the apical migration of the epithelial attachment.
The visualization of deep structures of the body by recording the reflections or echoes of ultrasonic pulses directed into the tissues. Use of ultrasound for imaging or diagnostic purposes employs frequencies ranging from 1.6 to 10 megahertz.
Blockage in any part of the URETER causing obstruction of urine flow from the kidney to the URINARY BLADDER. The obstruction may be congenital, acquired, unilateral, bilateral, complete, partial, acute, or chronic. Depending on the degree and duration of the obstruction, clinical features vary greatly such as HYDRONEPHROSIS and obstructive nephropathy.
Pathological processes involving the URETHRA.
Excision of the gallbladder through an abdominal incision using a laparoscope.
Lasers which use a solid, as opposed to a liquid or gas, as the lasing medium. Common materials used are crystals, such as YAG (YTTRIUM aluminum garnet); alexandrite; and CORUNDUM, doped with a rare earth element such as a NEODYMIUM; ERBIUM; or HOLMIUM. The output is sometimes additionally modified by addition of non-linear optical materials such as potassium titanyl phosphate crystal, which for example is used with neodymium YAG lasers to convert the output light to the visible range.
The period of history from the year 500 through 1450 of the common era.
Examination of urine by chemical, physical, or microscopic means. Routine urinalysis usually includes performing chemical screening tests, determining specific gravity, observing any unusual color or odor, screening for bacteriuria, and examining the sediment microscopically.
Spectrophotometry in the infrared region, usually for the purpose of chemical analysis through measurement of absorption spectra associated with rotational and vibrational energy levels of molecules. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
A procedure for smoothing of the roughened root surface or cementum of a tooth after subgingival curettage or scaling, as part of periodontal therapy.
Inflammation of the KIDNEY involving the renal parenchyma (the NEPHRONS); KIDNEY PELVIS; and KIDNEY CALICES. It is characterized by ABDOMINAL PAIN; FEVER; NAUSEA; VOMITING; and occasionally DIARRHEA.
A copper-containing dye used as a gelling agent for lubricants, for staining of bacteria and for the dyeing of histiocytes and fibroblasts in vivo.
Computed tomography where there is continuous X-ray exposure to the patient while being transported in a spiral or helical pattern through the beam of irradiation. This provides improved three-dimensional contrast and spatial resolution compared to conventional computed tomography, where data is obtained and computed from individual sequential exposures.
Pathological processes involving the PERIODONTIUM including the gum (GINGIVA), the alveolar bone (ALVEOLAR PROCESS), the DENTAL CEMENTUM, and the PERIODONTAL LIGAMENT.
Generic term for diseases caused by an abnormal metabolic process. It can be congenital due to inherited enzyme abnormality (METABOLISM, INBORN ERRORS) or acquired due to disease of an endocrine organ or failure of a metabolically important organ such as the liver. (Stedman, 26th ed)
Evaluation undertaken to assess the results or consequences of management and procedures used in combating disease in order to determine the efficacy, effectiveness, safety, and practicability of these interventions in individual cases or series.
Carbonic acid calcium salt (CaCO3). An odorless, tasteless powder or crystal that occurs in nature. It is used therapeutically as a phosphate buffer in hemodialysis patients and as a calcium supplement.
The duration of a surgical procedure in hours and minutes.
A plant genus of the family APIACEAE used for flavoring food.
An index which scores the degree of dental plaque accumulation.
Pathological processes of the PANCREAS.
Removal of dental plaque and dental calculus from the surface of a tooth, from the surface of a tooth apical to the gingival margin accumulated in periodontal pockets, or from the surface coronal to the gingival margin.
Inflammatory responses of the epithelium of the URINARY TRACT to microbial invasions. They are often bacterial infections with associated BACTERIURIA and PYURIA.
Inflammation of the GALLBLADDER; generally caused by impairment of BILE flow, GALLSTONES in the BILIARY TRACT, infections, or other diseases.
A muscarinic antagonist used as an antispasmodic, in rhinitis, in urinary incontinence, and in the treatment of ulcers. At high doses it has nicotinic effects resulting in neuromuscular blocking.
Procedures of applying ENDOSCOPES for disease diagnosis and treatment. Endoscopy involves passing an optical instrument through a small incision in the skin i.e., percutaneous; or through a natural orifice and along natural body pathways such as the digestive tract; and/or through an incision in the wall of a tubular structure or organ, i.e. transluminal, to examine or perform surgery on the interior parts of the body.
Inorganic salts of phosphoric acid.
The formation of crystalline substances from solutions or melts. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
A storage reservoir for BILE secretion. Gallbladder allows the delivery of bile acids at a high concentration and in a controlled manner, via the CYSTIC DUCT to the DUODENUM, for degradation of dietary lipid.
Ducts that collect PANCREATIC JUICE from the PANCREAS and supply it to the DUODENUM.
The flowing of blood from the marginal gingival area, particularly the sulcus, seen in such conditions as GINGIVITIS, marginal PERIODONTITIS, injury, and ASCORBIC ACID DEFICIENCY.
The sphincter of the hepatopancreatic ampulla within the duodenal papilla. The COMMON BILE DUCT and main pancreatic duct pass through this sphincter.
Radiography of the gallbladder after ingestion of a contrast medium.
A monotheistic religion promulgated by the Prophet Mohammed with Allah as the deity.
Non-invasive diagnostic technique for visualizing the PANCREATIC DUCTS and BILE DUCTS without the use of injected CONTRAST MEDIA or x-ray. MRI scans provide excellent sensitivity for duct dilatation, biliary stricture, and intraductal abnormalities.
A musculomembranous sac along the URINARY TRACT. URINE flows from the KIDNEYS into the bladder via the ureters (URETER), and is held there until URINATION.
The largest bile duct. It is formed by the junction of the CYSTIC DUCT and the COMMON HEPATIC DUCT.
Incision of Oddi's sphincter or Vater's ampulla performed by inserting a sphincterotome through an endoscope (DUODENOSCOPE) often following retrograde cholangiography (CHOLANGIOPANCREATOGRAPHY, ENDOSCOPIC RETROGRADE). Endoscopic treatment by sphincterotomy is the preferred method of treatment for patients with retained or recurrent bile duct stones post-cholecystectomy, and for poor-surgical-risk patients that have the gallbladder still present.
Infections with bacteria of the genus PROTEUS.
A key intermediate in metabolism. It is an acid compound found in citrus fruits. The salts of citric acid (citrates) can be used as anticoagulants due to their calcium chelating ability.
Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.
A metallic element that has the atomic symbol Mg, atomic number 12, and atomic weight 24.31. It is important for the activity of many enzymes, especially those involved in OXIDATIVE PHOSPHORYLATION.
Blocked urine flow through the bladder neck, the narrow internal urethral opening at the base of the URINARY BLADDER. Narrowing or strictures of the URETHRA can be congenital or acquired. It is often observed in males with enlarged PROSTATE glands.
An area occupying the most posterior aspect of the ABDOMINAL CAVITY. It is bounded laterally by the borders of the quadratus lumborum muscles and extends from the DIAPHRAGM to the brim of the true PELVIS, where it continues as the pelvic extraperitoneal space.
One of a pair of thick-walled tubes that transports urine from the KIDNEY PELVIS to the URINARY BLADDER.
Radiographic visualization of the body between the thorax and the pelvis, i.e., within the peritoneal cavity.
The mineral component of bones and teeth; it has been used therapeutically as a prosthetic aid and in the prevention and treatment of osteoporosis.
Inability to empty the URINARY BLADDER with voiding (URINATION).
Thin strands of transparent material, usually glass, that are used for transmitting light waves over long distances.
Method of using a polycrystalline powder and Rietveld refinement (LEAST SQUARES ANALYSIS) of X-RAY DIFFRACTION or NEUTRON DIFFRACTION. It circumvents the difficulties of producing single large crystals.
One of the short-acting SULFONAMIDES used in combination with PYRIMETHAMINE to treat toxoplasmosis in patients with acquired immunodeficiency syndrome and in newborns with congenital infections.
A series of steps taken in order to conduct research.
Pathologic deposition of calcium salts in tissues.
The practice of personal hygiene of the mouth. It includes the maintenance of oral cleanliness, tissue tone, and general preservation of oral health.
Pathologic processes that affect patients after a surgical procedure. They may or may not be related to the disease for which the surgery was done, and they may or may not be direct results of the surgery.
Pathological processes of the KIDNEY or its component tissues.
Diseases of the GALLBLADDER. They generally involve the impairment of BILE flow, GALLSTONES in the BILIARY TRACT, infections, neoplasms, or other diseases.
Presence or formation of GALLSTONES in the COMMON BILE DUCT.
Body organ that filters blood for the secretion of URINE and that regulates ion concentrations.
Tomography using x-ray transmission and a computer algorithm to reconstruct the image.
Severe or complete loss of motor function in the lower extremities and lower portions of the trunk. This condition is most often associated with SPINAL CORD DISEASES, although BRAIN DISEASES; PERIPHERAL NERVOUS SYSTEM DISEASES; NEUROMUSCULAR DISEASES; and MUSCULAR DISEASES may also cause bilateral leg weakness.
The duct which coveys URINE from the pelvis of the KIDNEY through the URETERS, BLADDER, and URETHRA.
The optimal state of the mouth and normal functioning of the organs of the mouth without evidence of disease.
Passage of a CATHETER into the URINARY BLADDER or kidney.
A covalently linked dimeric nonessential amino acid formed by the oxidation of CYSTEINE. Two molecules of cysteine are joined together by a disulfide bridge to form cystine.
A dilation of the duodenal papilla that is the opening of the juncture of the COMMON BILE DUCT and the MAIN PANCREATIC DUCT, also known as the hepatopancreatic ampulla.
A trace element that constitutes about 27.6% of the earth's crust in the form of SILICON DIOXIDE. It does not occur free in nature. Silicon has the atomic symbol Si, atomic number 14, and atomic weight [28.084; 28.086].
A non-metal element that has the atomic symbol P, atomic number 15, and atomic weight 31. It is an essential element that takes part in a broad variety of biochemical reactions.
Excision of kidney.
Inorganic salts of phosphoric acid that contain two phosphate groups.
Microscopy in which the object is examined directly by an electron beam scanning the specimen point-by-point. The image is constructed by detecting the products of specimen interactions that are projected above the plane of the sample, such as backscattered electrons. Although SCANNING TRANSMISSION ELECTRON MICROSCOPY also scans the specimen point by point with the electron beam, the image is constructed by detecting the electrons, or their interaction products that are transmitted through the sample plane, so that is a form of TRANSMISSION ELECTRON MICROSCOPY.
An abnormal extension of a gingival sulcus accompanied by the apical migration of the epithelial attachment and bone resorption.
Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.
A basic element found in nearly all organized tissues. It is a member of the alkaline earth family of metals with the atomic symbol Ca, atomic number 20, and atomic weight 40. Calcium is the most abundant mineral in the body and combines with phosphorus to form calcium phosphate in the bones and teeth. It is essential for the normal functioning of nerves and muscles and plays a role in blood coagulation (as factor IV) and in many enzymatic processes.

Dacryolith formation around an eyelash retained in the lacrimal sac. (1/113)

A dacryolith was discovered in the lacrimal sac during a dacryocystorhinostomy for chronic dacryocystitis in which there was mucocele formation. Morphological examination confirmed the presence of an eyelash at the centre of the stone and electron microscopy demonstrated the presence of fungi (Candida sp.) in a matrix which was of markedly vairable morphology. The mechanism by which a hair enters the punctum and passes along the canaliculus may be attributed to the step-like pattern of ridges on the surface of a hair. The directional nature of these ridges dictates preferential movement towards the root end of the hair and prevents movements in the opposite direction.  (+info)

Long term follow up of patients with chronic pancreatitis and pancreatic stones treated with extracorporeal shock wave lithotripsy. (2/113)

BACKGROUND: There have been conflicting reports as to whether pancreatic ductal drainage achieved by endoscopy and lithotripsy improves the clinical outcome of patients with chronic pancreatitis. AIMS: To determine the clinical outcome in patients with chronic pancreatitis who received extracorporeal shock wave lithotripsy (ESWL), and were followed up for two to eight years. METHODS: Eighty patients with severe chronic pancreatitis and endoscopically unretrievable obstructive stones underwent ESWL with a piezoelectric lithotripter between 1989 and 1996. Clinical status, relief of symptoms, further endoscopic or surgical interventions, and mortality were defined. RESULTS: Forty three (54%) patients were treated successfully with ESWL. The only feature associated with treatment success was the presence of a single stone rather than multiple stones. Successfully treated patients tended to experience less pain, although this did not reach statistical significance. A slight increase in weight was noted in our patients; however, there was no notable improvement in anomalous stools and diabetes mellitus. Five patients died due to extrapancreatic reasons. No pancreatic carcinomas developed. CONCLUSIONS: ESWL associated with endoscopic drainage is a safe technique that is particularly successful in patients with a single stone. However, pancreatic drainage by endoscopy and ESWL has almost no effect on pain in chronic pancreatitis. Furthermore, endoscopic management and ESWL does not prevent or postpone the development of glandular insufficiency.  (+info)

Pulmonary alveolar microlithiasis: a rare familial inheritance with report of six cases in a family. Contribution of six new cases to the number of case reports in Turkey. (3/113)

Pulmonary alveolar microlithiasis (PAM) is a lung disease characterized by deposits of calcium within the alveoli. Our aim was to emphasize the familial character and the clinical features of the disease, and to draw attention to the increasing number of Turkish patients reported in the world. We detected 6 cases of PAM. Three cases had been diagnosed 4 years earlier, and 3 new cases were detected during the screening of the family members. All patients were male and the mean age was 11.5 ranging between 5 and 29 years. Five of the patients were cousins and the other one was their uncle. Radiographic studies showed a sand-like appearance in all patients. One case showed small subpleural bullae and bronchiectatic changes in both lower lobes in recent high-resolution CT scans, while his CT performed 4 years ago showed only sand-like appearance. The cases were diagnosed with the demonstration of microliths by bronchoalveolar lavage in 5 patients and transbronchial biopsy in 1. Recently reported cases from Turkey have constituted a considerable percentage among all cases in the world. In conclusion, (1) our patients constitute one of the largest series of cases reported in one family in the world. The disease seems to have familial and racial characteristics. The Turkish race has to be further investigated for genetic transmission. (2) Contrary to female predominance in previous reports, all 6 cases were male and 5 of them were below 12 years of age. (3) The disorder may show rapid progression in some cases probably due to the severity of the genetic disturbance.  (+info)

Histochemical studies of pancreatic calculi. (4/113)

Fourteen pancreatic calculi from the corresponding number of pancreatic lithiasis patients were examined mineralogically and histochemically. The following results were obtained. The main components of calculi were calcium carbonate in 13 of the 14 cases, and calcium phosphate in the remaining one. Calcium carbonate calculi were all so-called intraductal calculi, with acidic glycoprotein apparently enwrapping the component particles. Acidic glycoproteins acted to bridge calcium carbonate particles, as in the cases of gallstone and urinary stone. The calcium phosphate calculus had a histochemical feature of pathologic calcification with degenerated collagen fibrils as the matrix, suggesting the calcification of the fibrotic pancreatic parenchyma after pancreatitis.  (+info)

Urinary stones following renal transplantation. (5/113)

BACKGROUND: The formation of urinary tract stones following renal transplantation is a rare complication. The clinical features of stones after transplantation differ from those of non-transplant patients. Renal colic or pain is usually absent and rarely resembles acute rejection. METHODS: We retrospectively studied 849 consecutive kidney transplant patients in The Rogosin Institute/The Weill-Cornell Medical Center, New York who were transplanted between 1980 and 1997 and had functioning grafts for more than 3 months, to determine the incidence of stone formation, composition, risk factors and patient outcome. RESULTS: At our center, urinary stones were diagnosed in 15 patients (1.8%) of 849 functioning renal grafts for 3 or more months. Of the 15 patients, 10 were males and 5 were females in their third and fourth decade. Eight patients received their transplant from living donors and 7 from cadaveric donors. The stones were first diagnosed between 3 and 109 months after transplantation (mean 17.8 months) and 5 patients had recurrent episodes. The stones were located in the bladder in 11 cases (73.3%), transplanted kidney in 3 cases and in multiple sites in one case. The size of stones varied from 3.4 mm to 40 mm (mean 12 mm). The composition of stones was a mixed form of calcium oxalate and calcium phosphate in 5 cases and 4 patients had infected stones consisting of struvite or mixed form of struvite and calcium phosphate. Factors predisposing to stone formation included tertiary hyperparathyroidism (n = 8), hypercalciuria (n = 5), recurrent urinary tract infection (n = 5), hypocitraturia (n = 4), and obstructive uropathy (n = 2). Many cases had more than one risk factor. Clinically, painless hematuria was observed in 6 patients and dysuria without bacteriuria in 5 patients. None had renal colic or severe pain at any time. There were no changes in graft function at diagnosis and after removal of stones. Five patients passed stones spontaneously and 8 patients underwent cystoscopy for stone removal. CONCLUSION: Urinary stone formation following kidney transplantation is a rare complication (1.8%). Hyperparathyroidism, hypercalciuria, recurrent urinary tract infection and hypocitraturia are the most common risk factors, but often there are multiple factors which predispose to stone formation. To detect stones and determine their location and size, ultrasonography appears to be the most useful diagnostic tool. Prompt diagnosis, the removal of stones and stone-preventive measures can prevent adverse effects on renal graft outcome.  (+info)

Radiological changes in pica. (6/113)

The significance of pica and geophagia as a public health problem is well known. The objective radiographic diagnosis of geophagia depends on the abnormal opacification of the bowel as an immediate manifestitation of the condition. The chance of detectability of geophagia is highest in the colon and can be improved by using low penetration films, particularly for smaller amounts of ingested clay. Other radiologic changes frequently associated with the prolonged practice of geophagic are an atonic pattern of the colon, secondary radiographic changes due to iron-deficiency anemia and bone-age retardation. The occurrences of intestinal obstruction due to pica in the presence of preexisting bowel stricture is demonstrated.  (+info)

Genetic susceptibility to fibrocalculous pancreatic diabetes in Bangladeshi subjects: a family study. (7/113)

Fibrocalculous pancreatic diabetes (FCPD) is an uncommon cause of diabetes, seen mainly in developing countries. A family-based study was carried out in 67 Bangladeshi families, consisting of a proband with FCPD and both parents, to determine whether an association exists between FCPD susceptibility and either the major histocompatiblity complex (MHC) or insulin gene (INS) loci. HLA-DQB1 typing was done using allele-specific primers, and INS was typed using the restriction enzyme HphI. Three microsatellites (TNFa, TNFc and TNFd), from within and flanking the TNF-LT locus, were used for MHC Class IV typing and a PCR-RFLP assay was used to define the -308G/A TNF promoter polymorphism. The extended transmission disequilibrium test (ETDT) was used for statistical analysis. An overall association was observed between FCPD and HLA-DQB1 (P = 0.003), that was largely due to a positive association with HLA-DQB1*0302 and a negative association with HLA-DQB1*0202. Although no association was found between FCPD and TNF-LT microsatellite markers a trend was observed for TNFc (P = 0.037, Pc = 0.15). No association was found between FCPD and INS (P = 0.26). This study confirms an association between FCPD and the MHC using a family-based study design and the stringent ETDT analysis; a novel protective association was found with HLA-DQB1*0202 in Bangladeshi FCPD subjects. The genetic susceptibility to FCPD has features both similar and dissimilar to T1DM.  (+info)

Positional down beating nystagmus in 50 patients: cerebellar disorders and possible anterior semicircular canalithiasis. (8/113)

OBJECTIVES: To clarify the clinical significance of positional down beat nystagmus (pDBN). METHODS: A discussion of the neuro-otological findings in 50 consecutive patients with pDBN. RESULTS: In 38 patients there was evidence of CNS disease (central group) but in 12 there was not (idiopathic group). In the CNS group, presenting symptoms were gait, speech, and autonomic dysfunction whereas in the idiopathic group patients mostly reported positional vertigo. The main neurological and oculomotor signs in the CNS group were explained by cerebellar dysfunction, including 13 patients with multiple system atrophy. In patients with multiple system atrophy with a prominent extrapyramidal component, the presence of pDBN was helpful in the differential diagnosis of atypical parkinsonism. No patient with pDBN had the Arnold-Chiari malformation, a common cause of constant down beat nystagmus (DBN). In the idiopathic group, the pDBN had characteristics which suggested a peripheral labyrinthine disorder: vertigo, adaptation, and habituation. In six patients an additional torsional component was found (concurrently with the pDBN in three). Features unusual for peripheral disorder were: bilateral positive Dix-Hallpike manoeuvre in nine of 12 patients and selective provocation by the straight head-hanging manoeuvre in two. CONCLUSION: It is argued that some patients with idiopathic pDBN have benign paroxysmal positional vertigo (BPPV) with lithiasis of the anterior canal. The torsional component may be weak, because of the predominantly sagittal orientation of the anterior canal, and may not be readily seen clinically. Nystagmus provocation by bilateral Dix-Hallpike and straight head-hanging may be explained by the vertical upwards orientation of the ampullary segment of the anterior canal in the normal upright head position. Such orientation makes right-left specificity with the Dix-Hallpike manoeuvre less important than for posterior canal BPPV. This orientation requires a further downwards movement of the head, often achieved with the straight head-hanging position, to provoke migration of the canaliths. The straight head-hanging manoeuvre should be carried out in all patients with a history of positional vertigo and a negative Dix-Hallpike manoeuvre.  (+info)

TY - JOUR. T1 - Fibrocalculous pancreatic diabetes and obesity. AU - Mohan, Viswanathan. AU - Chari, Suresh T. AU - Ramachandran, Ambady. AU - Jayanthi, Venkatraman. AU - Malathi, Sathyasekaran. AU - Madanagopalan, Nagendram. AU - Viswanathan, Moopil. PY - 1990. Y1 - 1990. N2 - Fibrocalculous pancreatic diabetes (FCPD) is a form of diabetes secondary to chronic pancreatitis that is found in tropical countries. Most patients with FCPD are lean and many are frankly undernourished. Four patients with FCPD who were obese are reported in this paper and this is the first report of obesity in FCPD patients.. AB - Fibrocalculous pancreatic diabetes (FCPD) is a form of diabetes secondary to chronic pancreatitis that is found in tropical countries. Most patients with FCPD are lean and many are frankly undernourished. Four patients with FCPD who were obese are reported in this paper and this is the first report of obesity in FCPD patients.. KW - Fibrocalculous pancreatic diabetes. KW - Malnutrition ...
Our knowledgeable and experienced calculus tutors are available for in-home tutoring, tutoring in a small group on school campus or at the library, or even online. Each Club Z! calculus tutor develops a unique tutoring program and lesson plan, focused on helping students succeed in calculus. Our calculus tutors prepare their students for calculus tests and quizzes, assist them with calculus homework, help improve classroom performance, and increase their understanding and confidence level in calculus. Whether it is graphing linear functions or solving differential equations, our calculus tutors are able to help you to excel at every level, including: Pre-Calculus, High School Calculus, AP Calculus, Honors Calculus, College Level Calculus.. Our calculus tutors in will focus on teaching the best methods for how to learn calculus. We understand that excelling in calculus leads to success in all future math classes, which is why our calculus tutors thoroughly go over each subject to ensure the ...
Our knowledgeable and experienced calculus tutors are available for in-home tutoring, tutoring in a small group on school campus or at the library, or even online. Each Club Z! calculus tutor develops a unique tutoring program and lesson plan, focused on helping students succeed in calculus. Our calculus tutors prepare their students for calculus tests and quizzes, assist them with calculus homework, help improve classroom performance, and increase their understanding and confidence level in calculus. Whether it is graphing linear functions or solving differential equations, our calculus tutors are able to help you to excel at every level, including: Pre-Calculus, High School Calculus, AP Calculus, Honors Calculus, College Level Calculus.. Our calculus tutors in will focus on teaching the best methods for how to learn calculus. We understand that excelling in calculus leads to success in all future math classes, which is why our calculus tutors thoroughly go over each subject to ensure the ...
Synonyms for enterolith in Free Thesaurus. Antonyms for enterolith. 2 words related to enterolith: calculus, concretion. What are synonyms for enterolith?
Many young students wonder why they need to learn calculus if they dont intend to take higher level math classes or work in a field that requires advanced math skills. While many individuals may only use math in high school and college, they may end up using some of the concepts based in calculus later on in life without realizing it.. Calculus can tell you a lot about how values change in a given scenario, particularly values that change at a non-consistent rate. Being able to calculate these values and understand what they mean can also help you to understand other concepts, and anticipate outcomes based on previous data.. Calculus is also used in a wide variety of industries, although it may not be called calculus in each case. Economists, for example, can use calculus to figure out how to achieve maximum profits based on revenue and known future costs. Calculus is also frequently used by scientists to better understand particle physics.. Population dynamics and change also makes use of ...
2. Calculus made Easy 2 Calculus made Easy is an ... students wanting to master Calculus the easy way. Using ... you will find learning calculus a breeze. Calculus made Easy has tutored ... by step worked examples. Calculus Made Easy is designed to help you understand... Details - Download - Screenshot ...
Although it is possible to construct an abstract formal calculus that has no immediate practical use and next to nothing in the way of obvious applications, the very name calculus indicates that this species of formal system owes its origin to the utility of its prototypical members in practical calculation. Generally speaking, any mathematical calculus is designed with the intention of representing a given domain of formal objects, and typically with the aim of facilitating the computations and inferences that need to be carried out in this representation. Thus some idea of the intended denotation, the formal objects that the formulas of the calculus are intended to denote, is given in advance of developing the calculus itself.. ...
Define Barycentric calculus. Barycentric calculus synonyms, Barycentric calculus pronunciation, Barycentric calculus translation, English dictionary definition of Barycentric calculus. a method of treating geometry by defining a point as the center of gravity of certain other points to which coëfficients or weights are ascribed.
Define silica calculi. silica calculi synonyms, silica calculi pronunciation, silica calculi translation, English dictionary definition of silica calculi. n. A white or colorless crystalline compound, SiO2, which in the form of quartz and certain other minerals is a chief component of the earths crust.
A calculus (plural calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ or duct of the body. Formation of calculi is known as lithiasis (/ˌlɪˈθaɪəsɪs/). Stones can cause a number of medical conditions. Some common principles (below) apply to stones at any location, but for specifics see the particular stone type in question. Calculi are not to be confused with gastroliths. ...
Offered by Universidad de Sidney. The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. Students taking Introduction to Calculus will: • gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks), • develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week), • develop and practice methods of differential calculus with applications (fourth week), • develop and practice methods of the integral calculus (fifth week).
Commentary. Calculus is fundamentally different from the mathematics that you have studied previously. Calculus is less static and more dynamic. It is concerned with the change and motion; it deals with quantities that approach other quantities.. The origins of calculus go back at least 2500 years to the ancient Greeks, who found areas using the method of exhaustion. They knew how to find the area A of any polygon by dividing it into triangles. The more triangles they used the better the approximation. By indirect reasoning, Eudoxus (fifth century B.C.) uses exhaustion to prove the familiar formula for the area of a circle: A = π r2. This method of exhaustion was the beginning of the idea of limit by answering the question: What value does the area approach as the number of triangles increases without bound? The area problem is the central problem in the branch of calculus called integral calculus.. Consider the problem of trying to find an equation of the tangent to a curve at any point on ...
Calculus Late Transcendentals Combined, Ninth Edition Countless people have relied on Anton to learn difficult concepts of calculus. The new ninth edition continues the tradition of offering accessible introduction to the field. Improvement in the particular problems and accurate to increase understanding. New applied exercises demonstrate the usefulness of mathematics. Summary tables and multiple step synthesis is included to provide additional support for learning concepts.Calculus Anton 9th Edition And the Quick Check exercises have been revised to give higher priority to the most important ideas. This book will help anyone who needs to learn calculus and build a solid mathematical basis.. Calculus Late Transcendentals Combined, Ninth Edition Review ...
You will see a number of resources. If you think your knowledge of precalculus mathematics might be weak, and particularly if you have been away from mathematics for a while, you should click on Review. There you will find a review, with examples and exercises, of the very basic rules and equations of algebra and analytic geometry that are needed for success in calculus. When I grade calculus exams, I find that the mistakes my students make are often algebra mistakes, not calculus mistakes. So the Algebra Review has warnings about common errors in algebra. Under Projects will find four kinds: Applied Projects involve applying calculus in various ways (designing a roller coaster, piloting a plane, playing baseball, choosing a seat at the movies, explaining rainbows). Laboratory Projects involve technology. Writing Projects ask you to compare present-day methods with those of the founders of calculus. Discovery Projects encourage you to discover patterns in mathematics. You will also see Lies My ...
View Notes - Calculus II Notes 7.2 from M 56495 at University of Texas. Calculus II-Stewart Dr. Berg Spring 2010 7.2 Calculus with Exponential Functions The Exponential Function Bacteria double
New York, NY: Doubleday( 2012). Jiang ZL, Kassab GS, Fung YC. Diameter-defined Strahler download matrix differential calculus with applications and um cheat of the first immiscible JavaScript. Huang W, Yen RT, McLaurine M, Bledsoe G. Morphometry of the other physical download matrix differential calculus with applications in statistics. This download matrix were part still on the University where the schedule were shown download by Works and Development Officer E. The Blake-Kelly Plan was the equality of downloads I( once suggested as the Burns Building), a Free wide policy use viewing the arena of Leith Street and learning to Albany Street. University College, a download matrix differential calculus with applications of adequate heat forces behind a such V carcass was magnetic on the Preparation between Clyde and Leith Streets. Eight Retroviruses arrived organized as the multiple download matrix differential calculus four-generation under the Blake-Kelly demon but this was gained by University ...
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations.The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of
Course List MA35 Labs 1 Single Variable Calculus 2 » Two Variable Calculus 3 Three Variable Calculus Polar Coordinate Labs Two Variable Functions Contents. 2.1 Functions of Two Variables 2.2 Differentiation 2.3 More Derivatives 2.4 Integration 2.4.1 Volume Under a Function Graph 2.4.2 Riemann Integral 2.4.3 Volume between Function Graphs 2.4.4 Change of Order of Integration 2.4.5 Surface Area for Function Graphs 2.4.6 Change of Variables 2.4.7 Total Mass of a Region in the Plane 2.4.8 Center of Mass 2.4.9 Moment of Inertia 2.5 Vector Analysis ...
This course in single-variable calculus is equivalent to one semester of college calculus. This course is designed for those students wishing to take calculus in high school but who are not planning on taking the AP Exam in May. Topics include (I) Functions, Graphs, and Limits (II) Derivatives and (III) Integrals. The focus in this class is a strong understanding of basic calculus principles as well as strenthening college algebra skills. ...
Looking for Calculus of Communicating Systems? Find out information about Calculus of Communicating Systems. A mathematical model for describing processes, mostly used in the study of parallelism. A CCS program, written in behaviour expressions syntax denotes a... Explanation of Calculus of Communicating Systems
MalaCards based summary : Urethral Calculus, also known as calculus in urethra, is related to urethritis and prostatitis. An important gene associated with Urethral Calculus is PLIN1 (Perilipin 1), and among its related pathways/superpathways are Ca, cAMP and Lipid Signaling and Androgen receptor signaling pathway. The drugs Central Nervous System Depressants and Anesthetics have been mentioned in the context of this disorder. Affiliated tissues include kidney, prostate and pancreas, and related phenotype is behavior/neurological ...
This course prepares students for the AP Calculus AB Exam as well as university level calculus courses. The study of calculus is divided into two main branches: differential and integral calculus. Differential calculus is the study of changing quantities, and integral calculus involves techniques for finding sums using infinitesimally small quantities. We will explore the relationship between these two branches and will find many applications as we prepare for the AP exam.. AP Calculus utilizes a culmination of algebraic, geometric, and mathematical reasoning skills gleaned from earlier high school math courses. Many calculus problems require some rigor, but the work is interesting and rewarding. This course is usually the first opportunity for students to use the concept of infinity in a formal, mathematical way, and these new tools confer a gratifying sense of power.. The mathematical and analytical training that students receive in this course will enable them to:. ...
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Description. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time ...
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Vector Calculus is the calculus of vector and scalar fields. It is therefore inherently in multiple dimensions. Just as ordinary calculus can be u...
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BACKGROUND: Pancreatic stone protein/regenerating protein (PSP/reg) serum levels are supposed to be increased in bacterial inflammation. PSP/reg levels also might be useful, therefore, as a predictor of bacterial infection in COPD. METHODS: Two hundred consecutive patients presenting to the ED due to acute exacerbation of COPD were prospectively assessed. Patients were evaluated based on clinical, laboratory, and lung functional parameters at admission (exacerbation) and after short-term follow-up (14-21 days). PSP/reg serum values were measured by a newly developed enzyme-linked immunosorbent assay. RESULTS: PSP/reg levels were elevated in subjects with COPD exacerbation (23.8 ng/mL; 95% CI, 17.1-32.7) when compared with those with stable disease (19.1 ng/mL; 95% CI, 14.1-30.4; P 5 .03) and healthy control subjects (14.0 ng/mL; 95% CI , 12.0-19.0; P , .01). Higher PSP/reg values were observed in exacerbations with positive sputum bacteriology compared with those with negative sputum ...
Serum levels of pancreatic stone protein (PSP)/reg1A as an indicator of beta-cell apoptosis suggest an increased apoptosis rate in hepatocyte nuclear factor 1 alpha (HNF1A-MODY) carriers from the third decade of life onward.
Acute pancreatitis was the most common complication associated with ESWL for pancreatic stones and was treated successfully by endoscopic removal of impacted stone fragments. Physicians performing ESWL should also acquire the technique of interventional endoscopy for pancreatic stones. We have reported a case of purulent pancreatic ductitis successfully treated by endoscopic stenting for the first time.9 We have experienced several similar cases that were caused by obstruction of the pancreatic stent and impaction of pancreatic stone fragments at the orifice of the MPD. All these cases showed abdominal pain, high fever, and occasionally disseminated intravascular coagulation, regardless of antibiotics therapy. Such cases are difficult to be diagnosed because abdominal computed tomography does not show findings suggesting acute pancreatitis, e.g., pancreatic enlargement and inflammatory changes in and around the pancreas, except severe dilation of the MPD. We have called this condition acute ...
A 37-year-old patient was admitted to the hospital with severe dyspnoea and cough. Baseline investigations revealed haemoglobin of 16.2 g/dl, haematocrit of 48.8% and a total leucocyte count of 8800/mm3. Comprehensive metabolic profile and serum and urine protein electrophoresis findings were normal. Arterial blood gas analysis showed type 1 respiratory failure. Spirometry showed restrictive ventilatory disturbances (vital capacity 53%, forced expiratory volume in 1 s 91%). A posterior-anterior chest radiograph showed bilateral diffuse, nodular (sandstorm-like) calcifications in both lungs (figure 1A). A high-resolution CT scan demonstrated multiple bilateral micronodulation of calcific densities throughout both lungs (figure 1B). On transbronchial biopsy, the diagnosis of massive parenchymal and alveolar calcification was confirmed. Echocardiography showed valve calcification with moderate mitral-aortic regurgitation and severe pulmonary hypertension. Abdominal ultrasonography revealed ...
Broncholithiasis is defined as calcified or ossified material in the bronchial lumen. The most frequently seen symptoms are a non-productive cough and hemoptysis. Occasionally, broncholytic expectoration can be seen, which is known as lithoptysis. As this is not a common finding, a case diagnosed with lithoptysis is presented here ...
Looking for online definition of differential calculus in the Medical Dictionary? differential calculus explanation free. What is differential calculus? Meaning of differential calculus medical term. What does differential calculus mean?
Looking for online definition of subgingival calculus in the Medical Dictionary? subgingival calculus explanation free. What is subgingival calculus? Meaning of subgingival calculus medical term. What does subgingival calculus mean?
Boeck L, Graf R, Eggimann P, Pargger H, Raptis DA, Smyrnios N, Thakkar N, Siegemund M, Rakic J, Tamm M, Stolz D. Pancreatic stone protein: a marker of organ failure and outcome in ventilator-associated pneumonia. Chest. 2011 Oct; 140(4):925-32 ...
The invention relates to a calculus crushing device with an endoscope (2). The endoscope (2) comprises a flexible insertion section (4) which can be inserted into a body cavity (28). By inserting the insertion section (4) into the body cavity (28) the interior of the body cavity (28) can be observed. The endoscope (2) also has a clamp orifice (10). An ultrasound wave conductor (16) which is used to conduct an ultrasound wave to a calculus (30) is inserted through this clamp orifice (10). The ultrasound wave conductor (16) is flexible, and its distal end can be inserted into the body cavity (28) via the clamp orifice (10) in such a way that it touches the calculus (30). An ultrasound wave generated by an ultrasound wave generating section (20, 22) is transmitted to the ultrasound wave conductor (16) and then to the calculus (30) in order to crush the latter. |IMAGE|
Many results concerning differential equations carry over quite easily to corresponding results for difference equations, while other results seem to be completely different from their continuous counterparts.[2] The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice-once for differential equations and once again for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale (also known as a time-set), which may be an arbitrary closed subset of the reals. In this way, results apply not only to the set of real numbers or set of integers but to more general time scales such as a Cantor set. The three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus. Dynamic equations on a time scale have a potential for applications, such as in population dynamics. For example, they can model insect ...
single variable calculus edition: university of windsor edition publisher: pearson author: briggs, cochram, gillett isbn-13: 978-1-269-96244-5 used for first year calculus, both semesters, differential calculus, intergral calculus if the ad is still up its still for sale
Pre Calculus Worksheets. Pre Calculus Worksheets Cell Organelles Worksheet. Pre Calculus Worksheets Linear Equations Worksheet. Pre Calculus Worksheets Solving Inequalities Worksheet. - ScriptClub.org
Definition of salivary calculi in the Definitions.net dictionary. Meaning of salivary calculi. What does salivary calculi mean? Information and translations of salivary calculi in the most comprehensive dictionary definitions resource on the web.
Oskar Minkowksi is known for his discovery of pancreatic diabetes. He was nominated for the Nobel Prize six times during his career.
Tonsilloliths are rare concretions found in the tonsillar crypt. They are usually single and unilateral, but occasionally may be multiple or bilateral. This report describes a case of a 47-year-old woman whose radiography revealed one radiopaque image located in the right ramus of the mandible. The patient revealed a history of slight dysphagia, halitosis and swallowing pain with a foreign body sensation. Her medical history revealed a tonsillectomy when she was eight years old and the removal of the uvula because of sleep apnoea six years ago. Computer tomography showed a delimited and calcified oval image measuring 0.6 x 0.6 cm. The tonsillar concretion might have been formed because of a calcification of the lymphoid tissue. On the patients request, surgical excision was not performed and she will be monitored due to the tendency of such lesions to grow ...
Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses.. To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions. As this is an open text, instructors and students are encouraged to interact with the textbook through annotating, revising, and reusing to your advantage. Suggestions for contributions to this growing textbook are welcome. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx providescontent-specific ...
This book was the required text for my two semesters of calculus I had to slough through this past spring and summer. The first semester of calculus would be pretty rough for someone trying to learn it on your own because at times its the concepts that are a little challenging to understand rather than how to do the work. More than likely, some of the material can be confusing without the aid of a teacher or tutor but most chapters you can work independently through without any real problems at all (except the problems themselves, maybe). It will not really take you by the hand and show you all of the little algebra steps in the examples, however. That is YOUR own fault if you dont know whats going on. Do not be expected to be put in a stroller and wheeled around in the land of calculus when you should be walking tall with all the skills you acquired from algebra and trigonometry. As far as the writing goes, it is very well written to get across to most students what exactly you are trying to ...
Well, I cant argue with your beliefs, but I reject them. Application of the calculus to the problems you mention has been quite successful. You assume that atoms behave independently regardless of circumstances. Your assumption that the calculus can deal only with mathematically continuous systems is also faulty. You also have not provided any examples, according to your hypothesis, that application of the calculus has provided faulty results when used to analyze physical phenomena ...
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This question is a bit off topic, but I hope it is of sufficient interest [because of lambda calculus] to this group anyway. I will be teaching our Theory of Computation course this coming fall, again. The topics are the standard: regular sets and finite automata, context-free languages and push-down automata, Turing machines and decidability. I personally find Turing machines to be a very unsatisfying model of computation, and would prefer to rely on other models. My favorites would be lambda calculus, RAMs, and imperative language models (e.g., the LOOP language). My belief is that students would find the three of these easier to relate to than Turing machines. However, I have been unable to find a book for our undergraduate (junior-level) course that covers these models. Occasionally, a book will cover the RAM model as a side-light, but I have been unable to find a book, for example, that covers lambda calculus. Does anyone have any suggestions for books (or even detailed lecture notes) that ...
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics is given in terms of Generalised Semi-Markov Decision Processes. By restricting the distributions to be continuous and by allowing truly concurrent communication we eliminate the non-determinism and arrive at Generalised Semi-Markov Processes (GSMPs); further restriction to exponential distributions gives rise to numerically analysable GSMPs, in particular using techniques from stochastic model checking.
Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management by Morton I Kamien starting at $0.99. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management has 1 available editions to buy at Alibris
Findings of urethral and bilateral renal calyceal calculi. A previous ultrasound 4 months prior had demonstrated a right pelvi-ureteric junction calculus (8 mm), which is not present on this follow-up ultrasound, and bilateral renal calyceal calc...
This study evaluated the ability of clinicians to detect residual calculus following subgingival scaling and root planing and compared the clinical detection to the microscopic presence and surface area occupied by calculus found on teeth extracted after instrumentation. Interexaminer and intraexami …
2008/1/12, Steven Obua ,obua at in.tum.de,: , I have the following question concerning the simply typed , (non-polymorphic) lambda calculus with constants and axioms for those , constants. , The axioms are all of the form p = t, where p is a linear pattern and , all the free variables in t are bound by p. All the axioms are typed. , , Assume that I have two terms A and B, both typed. , , Assume further that I forget now about all types and use beta , eta , conversions and the axioms as if I would do in untyped lambda calculus. , Doing this, I manage to get from A to B. , , My question is, can I therefore also get from A to B if I DO NOT forget , about the types but respect them? In particular, certain eta , abstractions might not be possible that I could use , in the untyped setting but not in the typed setting. Hindley Basic Simple Type Theory 2C1: Subject Reduction Theorem: if Context ,- term1:type and term1 ,, term2 where ,, stands for beta eta reduction then Context ,- term2:type. The ...
This course presents an elementary treatment of topics from differential and integral calculus. It is intended primarily for students in the fields of business and social science. The emphasis is on skill-building and on applications of calculus to the areas of business, economics, and social science. The types of functions studied include polynomials, rational, exponential, and logarithmic. Multivariable content includes applications of partial derivatives ...
A collaborative team of first- and second-year students is generating detailed solutions for Calculus course materials, created during the NSF funded Flipped Calculus project, currently used in our flipped classrooms. The students are working with Associate Professor Mako Haruta and Assistant Professor David Miller on this endeavor. Students are co-writing and co-editing solutions at team meetings, then asynchronously using LaTeX on Overleaf to publish.. ...
Lines. I find this a waste of ink and trees. If we are letting students into our calculus classes that need a review of this basic material, then we have failed in our advising and those students will fail the course. In my opinion, students are there to learn calculus and should already know what a function is. Chapter zero of the Himonas book is devoted to a recapitulation of the categories of functions and chapter one begins the study of limits and continuity. The Anton book follows largely the same path, chapter one contains a review of functions and chapter two begins the study of limits and continuity. Chapter 2 of the Himonas book describes exponential and logarithmic functions. While I agree that some review is probably necessary, once again, I dont believe that such an extensive review is required. With forty pages devoted to these functions, you are spending about as much time on them as is done in a precalculus course and the limit is never mentioned in the chapter. I really dont ...
Calculus With Applications for the Life Sciences was written for the one- or two-semester applied calculus course for life science students with a focus on incorporating interesting, relevant, and realistic applications. This text includes many citations from current data sources. It also offers many opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts ...
ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV) publishes rapidly and efficiently papers and surveys in the areas of control, optimisation and calculus of variations
It was like when I got to college and had to learn to study. Except I didnt, which is why I graduated with a 2.6 GPA. I learned to study ten years later, in graduate school, when I was paying the tuition - after I had worked a series of nightmare jobs and realized that decent grades in grad school were the only way to ensure that I never EVER had to work in insurance again. Mom, if youre reading this, that still doesnt mean I could have passed Calculus if Id just applied myself more. Calculus is hard ...
Almost universally, when Calculus is taught to modern students, we preface the entire subject by introducing those students to a concept known as a limit. The reason for this, historically, was to ensure that mathematics was taught in a rigorous and well-defined manner. When Leibniz (and, independently, Newton) first developed methods for performing calculus, the concept…
Several paradigms exist for distributed computing, this paper tries to provide a sound foundation for autonomous objects communicating in a very structured way. We define ASPfun, a calculus of functional objects, behaving autonomously, and communicating by a request-reply mechanism: requests are method calls handled asynchronously, futures represent awaited results for requests, and replies return the result of a request to an object that holds the corresponding future. This report first presents the ASPfun calculus and its semantics. Secondly we provide a type system for ASPfun, which ensure the ``progress property: while there is a request that is not reduced to a value, the computation can continue. ASPfun and its properties have been formalized and proved using the Isabelle theorem prover.
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Description. UCI Math 2A: Single-Variable Calculus (Fall 2013) Lec 27. Single-Variable Calculus -- Final Exam Review -- View the complete course: http://ocw.uci.edu/courses/math_2a_calculus_i.html Instructor: German A. Enciso, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 2A is the first quarter in Single-Variable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions. Recorded on December 6, 2013 Required attribution: Enciso, German A. Math 2A (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/math_2a_calculus_i.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (http://creativecommons.org/licenses/by-sa/3.0/deed.en_US ...
The complex combination of herbs in TMJ-Ease helps to address the painful issue of TMJ (Temporal Mandibular Joint Pain).. TMJ-Ease corrects vital nutritional imbalances that allow hardened fibrin and also acidic arthritic calculi to buildup in the temporal mandibular joints causing the painful symptoms commonly known as TMJ.. The formula may begin to provide pain relief in as little as two to four weeks as hardened exudated deposits of fibrin and calculi are eliminated through re-absorption.. An easy way to think of TMJ dysfunction would be similar to how a repetitive stress injury would occur. The constant misalignment of the jaw eventually creates a continual state of tissue inflammation. It is this inflammation that sends signals to the body to create and build up microscopic fibers of collagen and fibrinogen that eventually develop as thick layers to attempt to stabilize the TMJ misalignment.. The jaw condyle joints however, are more highly innervated than any other joint in the body. There ...
Compact and sensible book on the most important aspects of calculus. Derivatives of addition, multiplication, division, exponents, sin, cos, tan and more explained in a visual and geometric way.
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A 17-year-old Arcadia High School student earned a perfect score on the Advanced Placement Calculus BC exam in May, making him one of only 11 in the world this year to perform such a feat. Nathan
Surgical ultrasonic instrument for shattering urinary and biliary calculi has the transmitting probe in a probe channel, e.g. a catheter flushed with flowing liquid. The probe, to transmit the ultrasonic energy, has a profiled wire, which leaves cross sectional cavities relative to the probe channel, for passage of the liquid. Pref. the wire has a flat rectangular profile, helically twisted about its longitudinal axis. The wire has a smaller dia. at the nodes of the ultrasonic vibration. The shattered fragments can be sucked out through the channel. The wire can alternatively be shaped to have 3 or more legs in section to define the same number of clearing channels.
... and brane calculi [10]. Computations with mobile membranes can be defined over specific configurations (like process calculi), ... The operations of the two basic brane calculi, pino, exo, phago (PEP) and mate, drip, bud (MBD) are directly inspired by ... The operational semantics of pure ambient safe calculus are defined in terms of a reduction relation ⇒ a m b {\displaystyle \ ... A simulation of the PEP fragment of brane calculus by using mutual membranes with objects on surface is presented. This ...
McMaster, Valentine Munbee (1860). "Urinary calculi". Cite journal requires ,journal= (help) The London Gazette (PDF) http:// ...
... as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus ... Barendregt, H. (1992). "Lambda calculi with types". In Abramsky, S.; Gabbay, D.; Maibaum, T. (eds.). Handbook of Logic in ... just like the untyped lambda calculus[citation needed]. It is a major open problem in the field whether this is always the case ... is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The ...
In mathematical logic, System U and System U− are pure type systems, i.e. special forms of a typed lambda calculus with an ... ISBN 0-444-52077-5. Barendregt, Henk (1992). "Lambda calculi with types". In S. Abramsky; D. Gabbay; T. Maibaum (eds.). ... of polymorphic kinds to generic constructors in analogy to polymorphic types of terms in classical polymorphic lambda calculi, ...
Nonclassical Arithmetics and Calculi. Simon's Rock of Bard College. Ben Goertzel at the Mathematics Genealogy Project Popper, ...
Leonard, Andrew (21 April 2004). "Pirates! Calculus! Banking! Alchemy!". Salon.com. Retrieved November 2, 2019. CS1 maint: ...
Forks are defined as follows: Moreover, (f g p q r) ←→ (f g (p q r)). Thus to write f+g as in calculus, one can write f+g in ... For years, he had struggled to find a way to write f+g as in calculus, from the "scalar operators" in 1978, through the "til" ... Kenneth E. Iverson (J Forum message), retrieved 8 April 2016 March, Herman W.; Wolff, Henry C. (1917). Calculus. McGraw-Hill. ... Orth, Donald L. (1976). Calculus in a New Key. APL Press. ISBN 978-0-917326-05-9. Berry, Paul; Thorstensen, John (1973). " ...
Calculus! Banking! Alchemy!", Powell's (April 23, 2004) Archived August 22, 2010, at the Wayback Machine "Yo-yos in a Tangle," ...
Calculus. II (2nd ed.). Wiley. "Scalar", Encyclopedia of Mathematics, EMS Press, 2001 [1994] "Scalar field", Encyclopedia of ...
In calculus, the racetrack principle describes the movement and growth of two functions in terms of their derivatives. This ...
Differential and Integral Calculus. 2. Wiley Classics Library. pp. 46-47. ISBN 0-471-60840-8. Rudin, W. (1976). Principles of ... F. Ayres, E. Mendelson (2009). Calculus. Schaum's outline series (5th ed.). McGraw Hill. ISBN 978-0-07-150861-2. R. Wrede, M. R ... ISBN 354-065-340-6. Multivariable Calculus L. A. Talman (2007) Differentiability for Multivariable Functions. ... Spiegel (2010). Advanced calculus. Schaum's outline series (3rd ed.). McGraw Hill. ISBN 978-0-07-162366-7. N. Bourbaki (2004). ...
The integral of secant cubed is a frequent and challenging indefinite integral of elementary calculus: ∫ sec 3 ⁡ x d x = 1 2 ( ... Spivak, Michael (2008). "Integration in Elementary Terms". Calculus. p. 382. This is a tricky and important integral that often ... CS1 maint: discouraged parameter (link) Stewart, James (2012). "Section 7.2: Trigonometric Integrals". Calculus - Early ... This is one of several integrals usually done in a first-year calculus course in which the most natural way to proceed involves ...
Calculus • California Dental Association • Canadian Academy of Endodontics • Canadian Association of Orthodontists • Canadian ...
Jacobians". Intermediate Calculus (2nd ed.). New York: Springer. pp. 390-420. ISBN 0-387-96058-9.. ... In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to ... ISBN 0-521-28952-1. Loomis, Lynn H.; Sternberg, Shlomo (1990). Advanced Calculus (Revised ed.). Boston: Jones and Bartlett. pp ... ISBN 0-387-98593-X. Edwards, Charles Henry (1994) [1973]. Advanced Calculus of Several Variables. Mineola, New York: Dover ...
Analytic geometry continues to be a mainstay of pre-calculus and calculus curriculum. Another important area of application is ... In calculus, area and volume can be defined in terms of integrals, such as the Riemann integral or the Lebesgue integral. The ... Calculus was strongly influenced by geometry. For instance, the introduction of coordinates by René Descartes and the ... Stewart, James (2012). Calculus: Early Transcendentals, 7th ed., Brooks Cole Cengage Learning. ISBN 978-0-538-49790-9 Jost, ...
deLeeuw, Karel (1966). "Calculus". Harcourt, Brace. Cite journal requires ,journal= (help) Rudin, Walter; de Leeuw, Karel (1958 ... CS1 maint: discouraged parameter (link) Dorner, George C. (1968-01-01). "Review of Calculus". The Mathematics Teacher. 61 (8): ...
Calculus BC; Calculus; AP Calculus AB; AP Calculus BC; Multivariable Calculus; Statistics Science: Concepts of Physics; ...
Calculus. Cengage Learning, 2011. Section 1.1 Anton, Howard, Irl C. Bivens, and Stephen Davis. Calculus Single Variable. John ... For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable ... Workshop calculus: guided exploration with review. Vol. 2. Springer Science & Business Media, 1998. p. 31 Carlson, Robert. A ... Calculus. Cengage Learning, 2009. Section 13.1 Dekking, Frederik Michel (2005), A modern introduction to probability and ...
Ayres, Frank; Mendelson, Elliott (2008). Calculus. Schaum's Outlines. McGraw-Hill Professional. pp. 244-248. ISBN 978-0-07- ... Application Of Integral Calculus. Discovery Publishing House. p. 168. ISBN 81-7141-967-4. Singh, Ravish R. (1993). Engineering ...
Calculus; Chemistry; Computer Science; English Language; English Literature; European History; Macroeconomics/Microeconomics ( ...
OCLC 319729593.CS1 maint: numeric names: authors list (link) Adams, Robert A.; Essex, Christopher (2009). Calculus: A Complete ... OCLC 144526840.CS1 maint: numeric names: authors list (link) 1941-, Larson, Ron (2010). Calculus. Edwards, Bruce H., 1946- (9th ... OCLC 799468131.CS1 maint: others (link) 1941-, Stewart, James (2008). Calculus : early transcendentals (6th ed.). Belmont, CA: ...
Calculus. Ed. Charles Hartford. 6th ed. Boston: Houghton Mifflin Company, 1998. Helaman Ferguson, "Two Theorems, Two Sculptures ...
Calculus. I: One-Variable Calculus, with an Introduction to Linear Algebra. pp. 58-59. ISBN 9780471000051. Moise, Edwin (1963 ... Another approach for a coordinate triangle is to use calculus to find the area. A simple polygon constructed on a grid of equal ... As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus. A ... This argument is actually a simple application of the ideas of calculus. In ancient times, the method of exhaustion was used in ...
Michael Spivak, Calculus, Cambridge University Press, 2006, pages 382-383. James Stewart, Calculus: Early Transcendentals, ... Calculus: Early Transcendentals, Brooks/Cole, Apr 1, 1991, page 436 Euler, Leonard (1768). "Institutiionum calculi integralis ... In integral calculus, the Weierstrass substitution or tangent half-angle substitution is a method for evaluating integrals, ... Stewart, James (2012). Calculus: Early Transcendentals (7th ed.). Belmont, CA, USA: Cengage Learning. pp. 493. ISBN 978-0-538- ...
... for terms of the lambda calculus (and programming languages in general by using translations to lambda calculus). It is named ... No such term exists in the lambda calculus, of course, and so Böhm trees are the objects used in this place. A Böhm-like tree ... Since a computation described using lambda calculus is the process of reducing a lambda term to its normal form, this normal ... Barendregt, Henk P. The Lambda Calculus : Its Syntax and Semantics. London: College Publications. pp. 219-221, 486-487. ISBN ...
... the calculus of structures to accommodate the calculus. The principal novelty of the calculus of structures was its pervasive ... A sequent calculus for the logic was given, but it lacked a cut-elimination theorem; instead the sense of the calculus was ... Its sequent calculus relies on the structure of order varieties (a family of cyclic orders which may be viewed as a species of ... His calculus has thus become one of the fundamental formalisms of computational linguistics. David N. Yetter proposed a weaker ...
The undecidability of typability in the lambda-pi-calculus. In M. Bezem, J.F. Groote (Eds.), Typed Lambda Calculi and ... Using typed lambda calculus to implement formal systems on a machine. Journal of Automated Reasoning, 9:309-354, 1992. Robert ... The key features of the λΠ-calculus are that it consists of entities of three levels: objects, types and kinds (or type classes ... A Note on the Proof Theory of the λ Π {\displaystyle \lambda \Pi } -calculus. Studia Logica 54: 199-230, 1995. David Pym and ...
Leonhard Euler (1755). Institutiones calculi differentialis (in Latin). Cajori, Florian (2012) [1928], A History of ...
"CS786 Spring 04, Introduction to Kleene Algebra". Peter Höfner (2009). Algebraic Calculi for Hybrid Systems. BoD - Books on ...
The nested sequent calculus is a formalisation that resembles a 2-sided calculus of structures. N. D. Belnap. "Display Logic." ... Minc, G.E. (1971) [Originally published in Russian in 1968]. "On some calculi of modal logic". The Calculi of Symbolic Logic. ... His natural deduction calculus also supports a notion of analytic proof, as was shown by Dag Prawitz; the definition is ... The notion of analytic proof was introduced into proof theory by Gerhard Gentzen for the sequent calculus; the analytic proofs ...
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Typed lambda calculus[edit]. Main article: Typed lambda calculus. A typed lambda calculus is a typed formalism that uses the ... Typed lambda calculus - Lambda calculus with typed variables (and functions). *System F - A typed lambda calculus with type- ... In the lambda calculus, Y g. is a fixed-point of g. , as it expands to: Y g. (λh.(λx.h (x x)) (λx.h (x x))) g. (λx.g (x x)) (λx ... SKI combinator calculus - A computational system based on the S, K and I combinators, equivalent to lambda calculus, but ...
Institutionum calculi integralis is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the ... Institutiones calculi differentialis Full text available from Archive.org. Full text (1768) available from books.google.com. [1 ... provides a complete English translation of Eulers Institutionum calculi integralis by Ian Bruce. German translation ... subject of integral calculus and contained many of Eulers discoveries about differential equations. ...
Ricci calculus, calculus of variations, lambda calculus, and process calculus. Modern calculus was developed in 17th-century ... "Calculus for Beginners and Artists". Calculus Problems and Solutions by D.A. Kouba Donald Allens notes on calculus Calculus ... Calculus Made Easy (1914) by Silvanus P. Thompson Full text in PDF Calculus on In Our Time at the BBC Calculus.org: The ... Glossary of calculus List of calculus topics List of derivatives and integrals in alternative calculi List of differentiation ...
The calculus of communicating systems (CCS) is a process calculus introduced by Robin Milner around 1980 and the title of a ... The pi-calculus, developed by Robin Milner, Joachim Parrow, and David Walker in the late 80s extends CCS with mobility of ... What characterises our calculus is not the exact choice of combinators, but rather the choice of interpretation and of ... Some other languages based on CCS: Calculus of broadcasting systems Language Of Temporal Ordering Specification (LOTOS) Process ...
Ureteric calculi are stones in the ureters, which are the narrow muscular tubes that are responsible for the drainage of urine ... Ureteric calculi are stones in the ureters, which are the narrow muscular tubes that are responsible for the drainage of urine ... They concluded that NECT can be used with a high degree of accuracy to predict the spontaneous passage of ureteric calculi, and ... The safer laparoscopic approach to managing proximal ureteric calculi. A group of researchers conducted an investigation into ...
... a fourth year of math for students who wish to further their math education or to prepare students to move on to Calculus. ...
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... According to Student PIRGS, this is "am introductory level single variable calculus book, covering standard ... You just viewed Whitman Calculus. Please take a moment to rate this material. ... topics in differential and integral calculus, and infinite series." The book also includes multivariable calculus, though there ...
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Accelerated Calculus (4cr.) N&M P: placement by examination. Designed for students with one year of calculus in high school. ...
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The two main goals of the text are to ... - Selection from Calculus for Life Sciences [Book] ... the authors present the basic canons of first-year calculus, but motivated through real biological problems. ... The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, ... In this much anticipated first edition, the authors present the basic canons of first-year calculus, but motivated through real ...
COVID calculus is about balancing risk and benefit in the whole hospital system, and its getting worse as the epidemic ... But COVID calculus may change this. The risk of aerosolizing virus during CPR is high, and a lot of people need to be in the ... One thing COVID calculus eliminates is low-value care, and were quickly learning what that is. When this is all over, will I ... More than anything else, the thing that has struck me is something Im calling "COVID calculus." Its this change in how we ...
... so that methods of differential calculus, introduced by the first example, are needed. ... Innes A.E. (1977) Calculus (i). In: Business Mathematics by Example. Palgrave, London. * DOI https://doi.org/10.1007/978-1-349- ...
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This course provides the calculus content oriented toward applications in computer and communication networks courses. The ... The course exposes students to the fundamental concepts of differential calculus and integral calculus. Coursework emphasizes ... This course provides the calculus content oriented toward applications in computer and communication networks courses. ...
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Vector calculus. [Bill Cox] -- Building on previous texts in the Modular Mathematics series, in particular Vectors in Two or ... Three Dimensions and Calculus and ODEs, this book introduces the student to the concept of vector ... ... Calculus and ODEs, this book introduces the student to the concept of vector calculus. It provides an overview of some of the ... Vector calculus.. Burlington, MA : Elsevier, 1998. (DLC) 00456322. (OCoLC)40262963. Material Type:. Document, Internet resource ...
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A calculus of broadcasting systems. In TAPSOFT91 Volume 1: CAAP, April 1991. Springer Verlag LNCS 493.Google Scholar ... Examples show the calculus describing this model to be a powerful and natural programming tool. Weak bisimulation, a candidate ... Prasad K.V.S. (1993) A calculus of value broadcasts. In: Bode A., Reeve M., Wolf G. (eds) PARLE 93 Parallel Architectures and ... Broadcast parallel computation distributed computing process calculi CCS communicating processes bisimulation observational ...
In this case study we define a model-checker for the Mu-Calculus in ACL2 and show how to translate CTL into the Mu-Calculus. In ... Many temporal logics, e.g., CTL, LTL, and CTL* can be translated into the Mu-Calculus. In addition, the algorithm that decides ... Mu-Calculus Model-Checking. Panagiotis Manolios.. Computer-Aided Reasoning: ACL2 Case Studies, pages 93-111. Kluwer Academic ... the Mu-Calculus is used for symbolic (BDD-based) model-checking, a technique that has greatly extended the applicability of ...
Search for functional calculus at other dictionaries: OneLook, Oxford, American Heritage, Merriam-Webster, Wikipedia. Help ... Definitions of functional calculus: *noun: a system of symbolic logic that represents individuals and predicates and ...
2020 SAS summer courses will take place remotely. For undergraduates, please check Penn InTouch for updated summer course information. For graduate and professional students, please consult your schools and programs. Summer study abroad remains cancelled.. The College of Liberal and Professional Studies staff is working remotely to comply with University protocols as we navigate the COVID-19 virus. Penn is committed to maintaining a safe campus and workplace for faculty, students, staff, and visitors. While we are not onsite, we are still available Monday through Friday from 9 a.m. - 5 p.m. by phone and online in case you need support: (215) 898-7326 or [email protected] Visit coronavirus.upenn.edu, the Universitys dedicated coronavirus COVID-19 web page, for the latest updates.. ...
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  • These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. (wikipedia.org)
  • They understand the foundation of the Fundamental Theorem of Calculus. (ti.com)
  • vector fields, line integrals, flux integrals and integration theorems generalizing the Fundamental Theorem of Calculus. (princeton.edu)
  • It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations. (wikipedia.org)
  • the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves. (wikipedia.org)
  • The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. (wikipedia.org)
  • From the age of Greek mathematics, Eudoxus (c. 408-355 BC) used the method of exhaustion, which foreshadows the concept of the limit, to calculate areas and volumes, while Archimedes (c. 287-212 BC) developed this idea further, inventing heuristics which resemble the methods of integral calculus. (wikipedia.org)
  • According to Student PIRGS, this is "am introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. (merlot.org)
  • The course exposes students to the fundamental concepts of differential calculus and integral calculus. (centennialcollege.ca)
  • 6. Integral Calculus. (doverpublications.com)
  • The remainder of the Sullivan book, 320 pages, provides an overview of differential and integral calculus up through partial differentiation. (maa.org)
  • The Himonas book is also an overview of differential and integral calculus, with very little in the way of theory. (maa.org)
  • One could use these "indivisibles," he said, to calculate length, area and volume-an important step on the way to modern integral calculus. (scientificamerican.com)
  • Editors' note: Countless students learn integral calculus-the branch of mathematics concerned with finding the length, area or volume of an object by slicing it into small pieces and adding them up. (scientificamerican.com)
  • His "method of indivisibles" became a forerunner of integral calculus-but not before surviving attacks from Swiss mathematician Paul Guldin, ostensibly for empirical reasons. (scientificamerican.com)
  • The book also includes multivariable calculus, though there is a single variable version. (merlot.org)
  • In addition to a strong background of single-variable calculus and precalclulus, students should have a serious interest in thinking rigorously about problems involving space and time. (princeton.edu)
  • Lambda calculus (also written as λ-calculus ) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution . (wikipedia.org)
  • Lambda calculus consists of constructing lambda terms and performing reduction operations on them. (wikipedia.org)
  • Lambda calculus is Turing complete , that is, it is a universal model of computation that can be used to simulate any Turing machine . (wikipedia.org)
  • Lambda calculus may be untyped or typed . (wikipedia.org)
  • In typed lambda calculus, functions can be applied only if they are capable of accepting the given input's "type" of data. (wikipedia.org)
  • in the simply typed lambda calculus it is, for example, a theorem that every evaluation strategy terminates for every simply typed lambda-term, whereas evaluation of untyped lambda-terms need not terminate. (wikipedia.org)
  • One reason there are many different typed lambda calculi has been the desire to do more (of what the untyped calculus can do) without giving up on being able to prove strong theorems about the calculus. (wikipedia.org)
  • [5] Lambda calculus has played an important role in the development of the theory of programming languages . (wikipedia.org)
  • Functional programming languages implement the lambda calculus. (wikipedia.org)
  • Lambda calculus is also a current research topic in Category theory . (wikipedia.org)
  • The lambda calculus was introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics . (wikipedia.org)
  • Subsequently, in 1936 Church isolated and published just the portion relevant to computation, what is now called the untyped lambda calculus. (wikipedia.org)
  • [11] In 1940, he also introduced a computationally weaker, but logically consistent system, known as the simply typed lambda calculus . (wikipedia.org)
  • Until the 1960s when its relation to programming languages was clarified, the lambda calculus was only a formalism. (wikipedia.org)
  • Thanks to Richard Montague and other linguists' applications in the semantics of natural language, the lambda calculus has begun to enjoy a respectable place in both linguistics [13] and computer science. (wikipedia.org)
  • There is a bit of controversy over the reason for Church's use of the Greek letter lambda (λ) as the notation for function-abstraction in the lambda calculus, perhaps in part due to conflicting explanations by Church himself. (wikipedia.org)
  • It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus. (wikipedia.org)
  • In pure lambda calculus , there are no constants . (planetmath.org)
  • This question is a bit off topic, but I hope it is of sufficient interest [because of lambda calculus] to this group anyway. (upenn.edu)
  • My favorites would be lambda calculus, RAM's, and imperative language models (e.g., the LOOP language). (upenn.edu)
  • Occasionally, a book will cover the RAM model as a side-light, but I have been unable to find a book, for example, that covers lambda calculus. (upenn.edu)
  • Though of course the lambda calculus was contemporaneous - or even earlier than - Turing machines. (upenn.edu)
  • It covers the basic theory of pi-calculus, typed pi-calculi, higher-order processes, the relationship between pi-calculus and lambda-calculus, and applications of pi-calculus to object-oriented design and programming. (upenn.edu)
  • We present the notion of recognizability in the simply typed lambda-calculus by showing the equivalence between intersection types and finite standard models. (labri.fr)
  • We then show this notion of recognizability does not coincide with locally finite congruences of the lambda-calculus. (labri.fr)
  • The Simple Yuser-friendly Lambda Visualization Interaction Application (SYLVIA) is a unique way to manipulate untyped lambda calculus expressions, by representing them as boxes connected by wires. (haskell.org)
  • There's finally a lambda calculus lecture series on YouTube. (msdn.com)
  • I looked through their lectures, and they have some very interesting ones, but I don't see anything on lambda calculus. (msdn.com)
  • but I don't see anything in particular on lambda calculus. (msdn.com)
  • Bart De Smet's posts on lambda calculus are also very good http://community.bartdesmet.net/blogs/bart/archive/2009/08/17/mis-using-c-4-0-dynamic-type-free-lambda-calculus-church-numerals-and-more.aspx . (msdn.com)
  • Well, I am since lambda calculus is the essence of all functional programming. (msdn.com)
  • It's just that in this case I'm particularly interested in the nitty gritty details of the simplest possible programming language, which is lambda calculus. (msdn.com)
  • The following outlines a standard propositional calculus. (planetmath.org)
  • Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. (wikipedia.org)
  • Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz (independently of each other, first publishing around the same time) but elements of it appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. (wikipedia.org)
  • The coverage is up through vector calculus, partial derivatives and multiple integrals. (maa.org)
  • Calculus II continues to develop the basic ideas introduced in Calculus I: limits, derivatives, and integrals. (hsc.edu)
  • Calculus I is the study of limits, rates of change of a function, derivative of algebraic and trigonometric functions, applications of derivatives, integration and applications of the definite integral. (bucks.edu)
  • Nobody actually explained that we were learning calculus at the time, but by the time I was being taught derivatives, I already had a really intuitive notion of how and why this stuff all worked. (metafilter.com)
  • There are higher derivatives in vector calculus as well. (everything2.com)
  • Starting in Fall, 2018, we will restructure our calculus sequence from the current sequence of four three-credit courses to the new sequence of three four-credit courses to better align with other schools in Virginia, including the Virginia Community College System. (radford.edu)
  • Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. (wikipedia.org)
  • Am I ready for Calculus and Analytic Geometry? (physicsforums.com)
  • The topics of Schubert varieties and the intersection theory of Schubert calculus are at the crossroads of algebraic geometry, representation theory, symplectic geometry and combinatorics. (utoronto.ca)
  • The Anton book is a traditional calculus book with formal theorems and explanations of the theoretical background of how calculus works. (maa.org)
  • Calculus, including integration, differentiation, and differential equations are insufficient to model stochastic phenomena like noise disturbances of signals in engineering, uncertainty about future stock prices in finance, and microscopic particle movement in natural sciences. (gu.se)
  • Calculus: Early Transcendentals , originally by D. Guichard, has been redesigned by the Lyryx editorial team. (merlot.org)
  • You just viewed Calculus: Early Transcendentals . (merlot.org)
  • Calculus: Early Transcendentals , 8th Edition, by Howard Anton, Irl Bivens and Stephen Davis. (maa.org)
  • Calculus uses methods originally based on the summation of infinitesimal differences. (wikiversity.org)
  • This is entirely analogous to ordinary function calculus, where the infinitesimal change in the value of a function is df/dx * dx, and the total change over an interval is ∫ df/dx * dx = ΔF. (everything2.com)
  • Tubeless percutaneous nephrolithotomy (PCNL) is a well-accepted procedure for uncomplicated renal calculi. (urotoday.com)
  • Total tubeless PCNL was planned in 40 easily accessible patients with uncomplicated renal calculi, with single infracostal punctures, normal intraoperative events, and acceptable postoperative parameters (visual analogue pain score, parenteral analgesic requirement, bleeding, urinary soakage, hemodynamic stability), allowing an early discharge within 24 hours. (urotoday.com)
  • Renal sonogram demonstrates an echogenic shadowing calculus in the renal collecting system with hydronephrosis. (medscape.com)
  • Contrast-enhanced CT scan demonstrates an opaque staghorn calculus filling the left renal collecting system. (medscape.com)
  • Calculi too large to pass spontaneously range in size from 1 cm to the staghorn stones that occupy the renal pelvis and calyces. (labome.org)
  • The calculus of communicating systems (CCS) is a process calculus introduced by Robin Milner around 1980 and the title of a book describing the calculus. (wikipedia.org)
  • The pi-calculus, developed by Robin Milner, Joachim Parrow, and David Walker in the late 80's extends CCS with mobility of communication links, by allowing processes to communicate the names of communication channels themselves. (wikipedia.org)
  • Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. (google.com)
  • I'll take this opportunity to mention Orc , a language in the process calculi tradition that I really like. (lambda-the-ultimate.org)
  • Unlike some other process calculi, Orc does not make unreasonable assumptions (like mobility) about what properties are implementable in a distributed system. (lambda-the-ultimate.org)
  • I couldn't really figure out how to get transactions into a process calculi with multiple named input channels. (lambda-the-ultimate.org)
  • It's probably worth noting that Montanari and Zavatarro (both authors on one or more of the references mentioned in the original post) have also done work on developing formalizations of the actor model based on process calculi. (lambda-the-ultimate.org)
  • As time permits, the latter part of the course will explore type systems for process calculi and the current research on designing programming languages that make it easier to reason about process behavior, for instance to rule out dead lock. (upenn.edu)
  • So now let's consider the moral calculus surrounding Medicaid expansion from the perspective of taxpayers and society in general. (forbes.com)
  • Ureteric calculi are stones in the ureters, which are the narrow muscular tubes that are responsible for the drainage of urine from the kidneys to the bladder. (news-medical.net)
  • Stone size can predict the spontaneous passage of ureteric calculi. (news-medical.net)
  • Also implicated in the etiopathogenesis of ureteric calculi are heredity, diet, anatomical abnormalities of the urinary tract and chronic urinary tract infections (UTIs). (news-medical.net)
  • Hormonal imbalances and metabolic derangements, as well as hot/ dry climates, are also linked to ureteric calculi. (news-medical.net)
  • They concluded that NECT can be used with a high degree of accuracy to predict the spontaneous passage of ureteric calculi, and that size combined with location of the stone are the most important parameters in this prediction. (news-medical.net)
  • In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. (wikipedia.org)
  • The formal study of calculus brought together Cavalieri's infinitesimals with the calculus of finite differences developed in Europe at around the same time. (wikipedia.org)
  • As a general consideration, a calculus is a formal system that consists of a set of syntactic expressions, a distinguished subset of these expressions, plus a set of transformation rules that define a binary relation on the space of expressions. (planetmath.org)
  • Although it is possible to construct an abstract formal calculus that has no immediate practical use and next to nothing in the way of obvious applications, the very name calculus indicates that this species of formal system owes its origin to the utility of its prototypical members in practical calculation. (planetmath.org)
  • Generally speaking, any mathematical calculus is designed with the intention of representing a given domain of formal objects, and typically with the aim of facilitating the computations and inferences that need to be carried out in this representation . (planetmath.org)
  • Thus some idea of the intended denotation , the formal objects that the formulas of the calculus are intended to denote, is given in advance of developing the calculus itself. (planetmath.org)
  • Anybody who has taken Algebra 1 and has ever ridden in a car or pushed a toy train down a track can understand the basic concepts behind calculus. (metafilter.com)
  • Obviously, a deep understanding of vector calculus requires a knowledge of the basics of vector algebra . (everything2.com)
  • The spi-calculus is basically a pure process algebra spiced up with security primitives, and the applied pi-calculus can be seen as a generalisation of the spi-calculus where you allow arbitrary data signatures. (uu.se)
  • Chemistry vs Ap Calculus Ab? (yahoo.com)
  • I now have Ap Calculus Ab and i was just wondering if it is as hard or harder than Chemistry. (yahoo.com)
  • Many students find physical chemistry difficult not because the concepts are hard, but because they have to apply the calculus and physics they learned previously to problems in chemistry. (washington.edu)
  • When freshmen and sophomores merely memorize calculus and physics for their exams rather than truly learning the material, they have difficulty later in senior-level physical chemistry courses. (washington.edu)
  • The main operational difference between function calculus and vector calculus is that the standard derivative d/dx is replaced with the differential operator ∇, pronounced ' del ' or in the olden days' nabla . (everything2.com)
  • What few realize is that their calculus homework originated, in part, in a debate between two 17th-century scholars. (scientificamerican.com)
  • Use of symbolic manipulation and graphics software in calculus. (upenn.edu)
  • In addition, the algorithm that decides the Mu-Calculus is used for symbolic (BDD-based) model-checking, a technique that has greatly extended the applicability of model-checking. (neu.edu)
  • The Psi-calculi are in themselves unsuitable for some kinds of automated reasoning, and because of this we have developed a symbolic semantics for Psi-calculi. (uu.se)
  • Rigorous undergraduate treatment introduces calculus at the basic level, using infinitesimals and concentrating on theory rather than applications. (doverpublications.com)
  • The two-part treatment offers a rigorous presentation of tensor calculus as a development of vector analysis as well as discussions of the most important applications of tensor calculus. (doverpublications.com)
  • The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, analytical techniques, and numerical methods and to have students understand how, when, and why calculus can be used to model biological phenomena. (oreilly.com)
  • Calculus: Ideas & Applications , by Alex Himonas and Alan Howard. (maa.org)
  • With an informal, engaging tone and sound applications, The Calculus of Happiness facilitates financial literacy. (princeton.edu)
  • Welcome to the SageMath Calculus Tutorial! (sagemath.org)
  • No previous experience with SageMath or calculus is necessary, though you will need to either download SageMath or work online at CoCalc in order to participate actively in the following lessons. (sagemath.org)
  • SageMath Calculus Tutorial - Last Visited , then select "Bookmark This Link" or your browser's equivalent. (sagemath.org)
  • Nonenhanced CT image shows an obstructing left proximal ureteral calculus with a slight soft-tissue rim around the stone (ie, rim sign). (medscape.com)
  • We investigated the characteristics and diagnosis of primary asymptomatic ureteral calculi. (nih.gov)
  • De novo asymptomatic ureteral calculi do exist. (nih.gov)
  • calculus) was invented in the 1930s by Alonzo Church, as a form of mathematical logic dealing primarly with functions and the application of functions to their arguments . (planetmath.org)
  • 12. Standard Calculus and Sequences of Functions. (doverpublications.com)
  • We have developed Hennessy-Milner style modal logics for general nominal transition systems (of which the Psi-calculi form an example), and showed adequacy for both strong and weak bisimulation. (uu.se)
  • If you would first like to brush up on some pre-calculus and trigonometry concepts, this review may be of help. (sagemath.org)
  • The goals of imaging of urinary calculi are to determine the presence of stones witin the urinary tract, evaluate for complications, estimate the likelihood of stone passage, confirm stone passage, assess the stone burden, and evaluate disease activity. (medscape.com)
  • Ultrasonography (US) use for initial evaluation of suspected urinary calculi is common outside the United States. (medscape.com)
  • In order to take college-level Calculus in high school, students must begin Pre-Calculus no later than their junior year. (google.com)
  • Designed for students with one year of calculus in high school. (indiana.edu)
  • There are likely to be more, better prepared students here than in your high school, but remember that you are trying to learn Calculus and not competing with other students. (unl.edu)
  • In my opinion, students are there to learn calculus and should already know what a function is. (maa.org)
  • Presenting Newton's problem to students and then proposing Calculus as the solution seems so much better than the reverse. (metafilter.com)
  • For many students, calculus is more like an afterbirth. (metafilter.com)
  • MATH 171 will be for all students starting the calculus sequence for the first time. (radford.edu)
  • This classic introductory text, geared toward undergraduate students of mathematics, is the work of an internationally renowned authority on tensor calculus. (doverpublications.com)
  • He himself built a tool - using Markov chains - that set students new calculus problems in function of their past performance He argues that at present MOOCs may not be very good at teaching people. (scoop.it)
  • Info concerning El Paso Community College calculus courses, registering for required degree courses, and taking free tests online. (calculuscourse.org)
  • Taking calculus courses, for example, can give you an advantage in job recruiting in fields that require advanced math skills. (calculuscourse.org)
  • Get info about Shasta College calculus courses, registering for elective courses, and taking tests for free online. (calculuscourse.org)
  • This sequence of courses is the Calculus Path and is shown in the right column of the chart below. (google.com)
  • Calculus courses are sequential, so the stuff you see in 191, for example, will enable you to make sense of a lot of the stuff you will see in 192. (unl.edu)
  • Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple "all-weather" investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. (princeton.edu)
  • We are pleased to announce the book: ------------------------------------------------------- The Pi-Calculus: A Theory of Mobile Processes Davide Sangiorgi and David Walker Cambridge University Press, 592 pp, ISBN 0521781779 ------------------------------------------------------- Below is the blurb and the table of contents. (upenn.edu)
  • im not gonna complain, i got 95-99 averages throughout all 4 hs semesters on those 2 classes, but AP calculus has alot of annoying word problems and analyzing graphs. (yahoo.com)
  • The pi-calculus provides a conceptual framework for understanding mobility, and mathematical tools for expressing systems and reasoning about their behaviours. (upenn.edu)
  • I'm of the opinion that basic Physics, at least the force/acceleration/velocity/displacement relationship, needs to be taught before calculus. (metafilter.com)
  • Scout intravenous urogram shows a smooth, dense, round calculus in the left kidney. (medscape.com)
  • Calculi occurring in the KIDNEY. (labome.org)
  • Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. (worldcat.org)
  • Brief Calculus:An Applied Approach , 8th Edition, by Michael Sullivan. (maa.org)
  • Wikibooks has a book on the topic of Calculus . (wikiversity.org)
  • The explanations are adequate for the purpose, but the book is suitable only for the most basic overview of calculus. (maa.org)
  • Since there are so many calculus books and the coverage in them is so similar, I cannot say that this book is outstanding. (maa.org)
  • This book presents the pi-calculus, a theory of mobile systems. (upenn.edu)
  • The book serves both as a reference for the theory and as an extended demonstration of how to use pi-calculus to describe systems and analyse their properties. (upenn.edu)