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.
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.
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 pouch or sac developed from a tubular or saccular organ, such as the GASTROINTESTINAL TRACT.
Biphenyl compounds substituted in any position by one or more amino groups. Permitted are any substituents except fused rings.
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.
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.
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.
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.
Pathological processes of the TESTIS.
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.
Excretion of abnormally high level of CALCIUM in the URINE, greater than 4 mg/kg/day.
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.
A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.
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)
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.
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.
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.
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.
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.
Endoscopic examination, therapy or surgery of the urinary bladder.
A combination of the debris index and the dental calculus index to determine the status of oral hygiene.
A cutaneous pouch of skin containing the testicles and spermatic cords.
The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.
Formation of stones in the KIDNEY.
Inorganic compounds that contain potassium as an integral part of the molecule.
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.
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.
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.
A film that attaches to teeth, often causing DENTAL CARIES and GINGIVITIS. It is composed of MUCINS, secreted from salivary glands, and microorganisms.
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.
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.
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.
Surgical removal of the GALLBLADDER.
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.
The sesame family of the order Lamiales that are mainly herbs and shrubs growing in warm regions.
Painful URINATION. It is often associated with infections of the lower URINARY TRACT.
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)
A powder that dissolves in water, which is administered orally, and is used as a diuretic, expectorant, systemic alkalizer, and electrolyte replenisher.
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)
Elements of limited time intervals, contributing to particular results or situations.
Binary classification measures to assess test results. Sensitivity or recall rate is the proportion of true positives. Specificity is the probability of correctly determining the absence of a condition. (From Last, Dictionary of Epidemiology, 2d ed)
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.
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.
Presence of blood in the urine.
Radiography of the SALIVARY GLANDS or ducts following injection of contrast medium.
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.
Sequential operating programs and data which instruct the functioning of a digital computer.
Surgical creation of an opening (stoma) in the URINARY BLADDER for drainage.
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.
An abnormal extension of a gingival sulcus not accompanied by the apical migration of the epithelial attachment.
The period of history from the year 500 through 1450 of the common era.
A procedure for smoothing of the roughened root surface or cementum of a tooth after subgingival curettage or scaling, as part of periodontal therapy.
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.
Excision of the gallbladder through an abdominal incision using a laparoscope.
Pathological processes involving the URETHRA.
A series of steps taken in order to conduct research.
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.
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.
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)
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.
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.
The application of drug preparations to the surfaces of the body, especially the skin (ADMINISTRATION, CUTANEOUS) or mucous membranes. This method of treatment is used to avoid systemic side effects when high doses are required at a localized area or as an alternative systemic administration route, to avoid hepatic processing for example.
Pathological processes involving the PERIODONTIUM including the gum (GINGIVA), the alveolar bone (ALVEOLAR PROCESS), the DENTAL CEMENTUM, and the PERIODONTAL LIGAMENT.
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.
Injuries to the knee or the knee joint.
The formation of crystalline substances from solutions or melts. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
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.
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.
Thin strands of transparent material, usually glass, that are used for transmitting light waves over long distances.
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].
The duration of a surgical procedure in hours and minutes.
Pathological processes of the PANCREAS.
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 musculomembranous sac along the URINARY TRACT. URINE flows from the KIDNEYS into the bladder via the ureters (URETER), and is held there until URINATION.
An index which scores the degree of dental plaque accumulation.
Tomography using x-ray transmission and a computer algorithm to reconstruct the image.
Inflammatory responses of the epithelium of the URINARY TRACT to microbial invasions. They are often bacterial infections with associated BACTERIURIA and PYURIA.
A plant genus of the family APIACEAE used for flavoring food.
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.
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.
Compounds that bind to and inhibit the activation of ANDROGEN RECEPTORS.
Inflammation of the GALLBLADDER; generally caused by impairment of BILE flow, GALLSTONES in the BILIARY TRACT, infections, or other diseases.
Ducts that collect PANCREATIC JUICE from the PANCREAS and supply it to the DUODENUM.
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.
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.
The sphincter of the hepatopancreatic ampulla within the duodenal papilla. The COMMON BILE DUCT and main pancreatic duct pass through this sphincter.
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.
Body organ that filters blood for the secretion of URINE and that regulates ion concentrations.
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.
The portion of an interactive computer program that issues messages to and receives commands from a user.
The largest bile duct. It is formed by the junction of the CYSTIC DUCT and the COMMON HEPATIC DUCT.
Computer-based representation of physical systems and phenomena such as chemical processes.
Radiographic visualization of the body between the thorax and the pelvis, i.e., within the peritoneal cavity.
One of a pair of thick-walled tubes that transports urine from the KIDNEY PELVIS to the URINARY BLADDER.
Methods of creating machines and devices.
A strain of MURINE LEUKEMIA VIRUS associated with mouse tumors similar to those caused by the FRIEND MURINE LEUKEMIA VIRUS. It is a replication-competent murine leukemia virus. It can act as a helper virus when complexing with a defective transforming component, RAUSCHER SPLEEN FOCUS-FORMING VIRUS.
Infections with bacteria of the genus PROTEUS.
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.
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.
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.
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.
Hospital department which is responsible for the administration of diagnostic pulmonary function tests and of procedures to restore optimum pulmonary ventilation.
Compounds similar to hydrocarbons in which a tetravalent silicon atom replaces the carbon atom. They are very reactive, ignite in air, and form useful derivatives.
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.
Pathologic deposition of calcium salts in tissues.
Pathological processes of the KIDNEY or its component tissues.
Inability to empty the URINARY BLADDER with voiding (URINATION).
The practice of personal hygiene of the mouth. It includes the maintenance of oral cleanliness, tissue tone, and general preservation of oral health.
Body of knowledge related to the use of organisms, cells or cell-derived constituents for the purpose of developing products which are technically, scientifically and clinically useful. Alteration of biologic function at the molecular level (i.e., GENETIC ENGINEERING) is a central focus; laboratory methods used include TRANSFECTION and CLONING technologies, sequence and structure analysis algorithms, computer databases, and gene and protein structure function analysis and prediction.
The normality of a solution with respect to HYDROGEN ions; H+. It is related to acidity measurements in most cases by pH = log 1/2[1/(H+)], where (H+) is the hydrogen ion concentration in gram equivalents per liter of solution. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)
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.
The development and use of techniques to study physical phenomena and construct structures in the nanoscale size range or smaller.
Diseases of the GALLBLADDER. They generally involve the impairment of BILE flow, GALLSTONES in the BILIARY TRACT, infections, neoplasms, or other diseases.
Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.
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.
A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.
An inherited condition due to a deficiency of either LIPOPROTEIN LIPASE or APOLIPOPROTEIN C-II (a lipase-activating protein). The lack of lipase activities results in inability to remove CHYLOMICRONS and TRIGLYCERIDES from the blood which has a creamy top layer after standing.
Use of plants or herbs to treat diseases or to alleviate pain.
The duct which coveys URINE from the pelvis of the KIDNEY through the URETERS, BLADDER, and URETHRA.
Presence or formation of GALLSTONES in the COMMON BILE DUCT.
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.
The optimal state of the mouth and normal functioning of the organs of the mouth without evidence of disease.
A loose confederation of computer communication networks around the world. The networks that make up the Internet are connected through several backbone networks. The Internet grew out of the US Government ARPAnet project and was designed to facilitate information exchange.
Passage of a CATHETER into the URINARY BLADDER or kidney.
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
Localized destruction of the tooth surface initiated by decalcification of the enamel followed by enzymatic lysis of organic structures and leading to cavity formation. If left unchecked, the cavity may penetrate the enamel and dentin and reach the pulp.
Inorganic salts of phosphoric acid that contain two phosphate groups.
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.
Any of a variety of procedures which use biomolecular probes to measure the presence or concentration of biological molecules, biological structures, microorganisms, etc., by translating a biochemical interaction at the probe surface into a quantifiable physical signal.
Excision of kidney.
Liquids that dissolve other substances (solutes), generally solids, without any change in chemical composition, as, water containing sugar. (Grant & Hackh's Chemical Dictionary, 5th ed)
Substances used to allow enhanced visualization of tissues.
Nanometer-sized particles that are nanoscale in three dimensions. They include nanocrystaline materials; NANOCAPSULES; METAL NANOPARTICLES; DENDRIMERS, and QUANTUM DOTS. The uses of nanoparticles include DRUG DELIVERY SYSTEMS and cancer targeting and imaging.
An abnormal extension of a gingival sulcus accompanied by the apical migration of the epithelial attachment and bone resorption.
Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.
Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
The removal of fluids or discharges from the body, such as from a wound, sore, or cavity.
Process of applying for employment. It includes written application for employment or personal appearance.
The return of a sign, symptom, or disease after a remission.
Systems for the delivery of drugs to target sites of pharmacological actions. Technologies employed include those concerning drug preparation, route of administration, site targeting, metabolism, and toxicity.
Materials which have structured components with at least one dimension in the range of 1 to 100 nanometers. These include NANOCOMPOSITES; NANOPARTICLES; NANOTUBES; and NANOWIRES.
Concentrated pharmaceutical preparations of plants obtained by removing active constituents with a suitable solvent, which is evaporated away, and adjusting the residue to a prescribed standard.
A spectroscopic technique in which a range of wavelengths is presented simultaneously with an interferometer and the spectrum is mathematically derived from the pattern thus obtained.
INFLAMMATION of the PANCREAS. Pancreatitis is classified as acute unless there are computed tomographic or endoscopic retrograde cholangiopancreatographic findings of CHRONIC PANCREATITIS (International Symposium on Acute Pancreatitis, Atlanta, 1992). The two most common forms of acute pancreatitis are ALCOHOLIC PANCREATITIS and gallstone pancreatitis.
"Decayed, missing and filled teeth," a routinely used statistical concept in dentistry.
Automated systems applied to the patient care process including diagnosis, therapy, and systems of communicating medical data within the health care setting.
ISBN 978-1-4939-1926-0. Thomson, p. 1 Peter D. Lax; Maria Shea Terrell (2013). Calculus With Applications. Springer. p. 213. ... ISBN 978-1-4614-7946-8. Shirley O. Hockett; David Bock (2005). Barron's how to Prepare for the AP Calculus. Barron's ... As an application, the quasi-mean value theorem for f(x) = ,x, on an interval containing 0 predicts that the slope of any ... More Calculus of a Single Variable. Springer. p. 173. ...
ISBN 0-486-66169-5. Loomis, Lynn H.; Sternberg, Shlomo (1989). Advanced Calculus. Boston: Jones and Bartlett. pp. 304-473 (ch. ... ISBN 0-521-46800-0. Flanders, Harley (1989). Differential forms with applications to the physical sciences. New York: Dover ... 7-11). ISBN 0-486-66169-5. Ramanan, S. (2005). Global calculus. Providence, Rhode Island: American Mathematical Society. p. 54 ... ISBN 0-8218-3702-8. Spivak, Michael (1971). Calculus on Manifolds. Boulder, Colorado: Westview Press. ISBN 9780805390216. ...
Mathai, A.M.; Haubold, H.J. (2017). Fractional and Multivariable Calculus. Springer Optimization and Its Applications. 122. ... Saxena, R. K.; Mathai, A. M.; Haubold, H. J. (2009-09-01). "Mittag-Leffler Functions and Their Applications". arXiv:0909.0230 [ ... Lévy flight Lévy process Fractional calculus Anomalous diffusion Lihn, Stephen (2017). "A Theory of Asset Return and Volatility ... math.CA]. Barkai, E. (2001-03-29). "Fractional Fokker-Planck equation, solution, and application". Physical Review E. 63 (4): ...
Application Of Integral Calculus. Discovery Publishing House. p. 168. ISBN 81-7141-967-4. Singh, Ravish R. (1993). Engineering ... Ayres, Frank; Mendelson, Elliott (2008). Calculus. Schaum's Outlines. McGraw-Hill Professional. pp. 244-248. ISBN 978-0-07- ...
... change in the value of a variable in calculus A Functional derivative in Functional calculus An auxiliary function in calculus ... and applications. Springer. Example 2.5.6, p. 120. ISBN 978-3-540-24326-7. Irving, Ronald S. (2004). Integers, polynomials, and ... Clarence H. Richardson (1954). An Introduction to the Calculus of Finite Differences. Van Nostrand. Chapter 1, pp. ... copy Michael Comenetz (2002). Calculus: The Elements. World Scientific. pp. 73-74. ISBN 978-981-02-4904-5. Dickenstein, Alicia ...
Perloff, J. (2008). Microeconomics Theory & Applications with Calculus. Pearson. ISBN 978-0-321-27794-7. Samuelson; Nordhaus ( ...
Typed Lambda Calculi and Applications. Lecture Notes in Computer Science. 1210. Springer Berlin Heidelberg. pp. 300-318. ... 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 ...
Advanced Calculus, Prentice-Hall, 2002. Real Analysis: Modern Techniques and their Applications (2nd ed.), John Wiley, 1999, ... Fourier Analysis and Its Applications, Pacific Grove, Calif. : Wadsworth & Brooks/Cole Advanced Books & Software, 1992. ...
In M. Bezem, J.F. Groote (Eds.), Typed Lambda Calculi and Applications. Volume 664 of Lecture Notes in Computer Science, 139- ... 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 ...
Springer Optimization and Its Applications, vol 138. Springer. Duran, U. (2016). Post Quantum Calculus, M.Sc. Thesis in ... 196, 320-337 (2006). Auch, T. (2013): Development and Application of Difference and Fractional Calculus on Discrete Time Scales ... Post quantum calculus is a generalization of the theory of quantum calculus, and it uses the following operator: D p , q f ( x ... Gupta V., Rassias T.M., Agrawal P.N., Acu A.M. (2018) Basics of Post-Quantum Calculus. In: Recent Advances in Constructive ...
Efe Ok (2007). Real analysis with economics applications. Princeton University Press. ISBN 0-691-11768-3. Henri Cartan (1971). ... Differential Calculus. Kershaw Publishing Company LTD. ISBN 0-395-12033-0.. ...
Churchill, R. V. (1954). "The Operational Calculus of Legendre Transforms". Journal of Mathematics and Physics. 33 (1-4): 165- ... Integral transforms and their applications (2nd ed.). Boca Raton: Chapman & Hall/CRC. ISBN 9781482223576. ...
"Infinitary Lambda Calculi and Böhm Models". In Hsiang, Jieh (ed.). 6th Int. Conf. on Rewriting Techniques and Applications (RTA ... Lambda Calculus, and the Mind - Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday]. University Nijmegen ... Rewriting Techniques and Applications, 4th Int. Conf., RTA-91 (PDF). LNCS. 488. Springer. pp. 1-12.CS1 maint: multiple names: ... Rewriting Techniques and Applications, 4th Int. Conf., RTA-91 (PDF). LNCS. 488. Springer. pp. 445-456.CS1 maint: multiple names ...
volume= has extra text (help) Weinstock, R. (1952). Calculus of Variations with Applications to Physics and Engineering. New ... "Calculus of Variations". PlanetMath. Gelfand, Izrail Moiseevich (1963). Calculus of Variations. Dover. ISBN 0-486-41448-5. ... In the calculus of variations and classical mechanics, the Euler-Lagrange equations is a system of second-order ordinary ... This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local ...
They also occur in many applications, such as in the Faà di Bruno's formula. The partial or incomplete exponential Bell ... Roman, S. (2013). The Umbral Calculus. Dover Publications. p. 208. ISBN 9780486153421. Voinov, V. G.; Nikulin, M. S. (1994). " ... "On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications". Kybernetika. 30 (3): ... Journal of Computational Analysis and Applications. 5 (3): 333-340. doi:10.1023/A:1023227705558. S2CID 118361207. ...
Communications in Fractional Calculus (ISSN 2218-3892) Specialized journal: Journal of Fractional Calculus and Applications ( ... Tarasov, V.E. (2010). Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. ... ISBN 0-471-58884-9. Oldham, Keith B.; Spanier, Jerome (1974). The Fractional Calculus; Theory and Applications of ... ISBN 0-387-95554-2. MathWorld - Fractional calculus MathWorld - Fractional derivative Specialized journal: Fractional Calculus ...
Bell, Denis R. (2006). The Malliavin calculus. Mineola, NY: Dover Publications Inc. pp. x+113. ISBN 0-486-44994-7. MR2250060 ( ... Global analysis and its applications (Lectures, Internat. Sem. Course, Internat. Centre Theoret. Phys., Trieste, 1972), Vol. II ... integration by parts operators occur in infinite-dimensional settings and find uses in stochastic analysis and its applications ...
Sheffer sequence Umbral calculus Generalized Appell polynomials Wick product Appell, Paul (1880). "Sur une classe de polynômes ... Journal of Mathematical Analysis and Applications. 42 (3): 685-760. doi:10.1016/0022-247X(73)90172-8. Reprinted in the book ... The Umbral Calculus. Dover Publications. Theodore Seio Chihara (1978). An Introduction to Orthogonal Polynomials. Gordon and ... Roman, Steven; Rota, Gian-Carlo (1978). "The Umbral Calculus". Advances in Mathematics. 27 (2): 95-188. doi:10.1016/0001-8708( ...
ISBN 0-471-58884-9. Oldham, Keith B.; Spanier, Jerome (1974). The Fractional Calculus; Theory and Applications of ... "Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics". Abstract and ... by Richard Herrmann Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to ... ISBN 2-88124-864-0 Theory and Applications of Fractional Differential Equations, by Kilbas, A. A.; Srivastava, H. M.; and ...
Calculus. Vector calculus. Differential equations. Dynamical systems. Chaos theory. Complex analysis Applied mathematics. Main ... One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a ... Main article: Calculus. Understanding and describing change is a common theme in the natural sciences, and calculus was ... The mathematical study of change, motion, growth or decay is calculus.. *^ Ziegler, Günter M. (2011). "What Is Mathematics?". ...
As a simple application of the above, consider the plane, parametrised by polar coordinates (R, θ). We can go to a new ... 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 ...
London: George Allen & Unwin, Ltd., S. 155 Zadeh, L. A. (1975). Calculus of fuzzy restrictions. In L. A. Zadeh, K.-S. Fu, K. ... Zimmermann, H.-J. (2000). Practical Applications of Fuzzy Technologies. Springer. Meier, A., Schindler, G., & Werro, N. (2008 ... Tanaka, & M. Shimura (Hrsg.), Fuzzy sets and Their Applications to Cognitive and Decision Processes. New York: Academic Press. ...
ISBN 0-387-90974-5. Shockley, James E. (1976). The Brief Calculus : with Applications in the Social Sciences (2nd ed.). New ... ISBN 978-0-495-01166-8. Willard, Stephen (1976). Calculus and its Applications. Boston: Prindle, Weber & Schmidt. pp. 103-145. ... One can examine a function's monotonicity without calculus. However, calculus is usually helpful because there are sufficient ... In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine ...
Hildebrand, F. B. (1976). Advanced Calculus for Applications. Prentice Hall. ISBN 0-13-011189-9. K.F. Riley; M.P. Hobson; S.J. ... Thomas, George B. Jr.; and Finney, Ross L. (1979) Calculus and Analytic Geometry, Addison-Wesley Publ. Co., fifth edition, p. ... Edwards, Ron Larson, Robert, Bruce H. (2010). Calculus of a single variable (9th ed.). Belmont: Brooks/Cole. ISBN 9780547209982 ... Hughes-Hallet, Deborah; McCallum, William G.; Gleason, Andrew M. (2012-01-01). Calculus : Single and multivariable. John wiley ...
ISBN 978-0-387-90346-0. Wilson, R. L. (1979). Much Ado About Calculus: A Modern Treatment with Applications Prepared for Use ... Calculus with Applications (2nd ed.). doi:10.1007/978-1-4614-7946-8. ISBN 978-1-4614-7945-1. Axler, Sheldon (2015). Linear ... Multivariable Calculus with Applications. doi:10.1007/978-3-319-74073-7. ISBN 978-3-319-74072-0. Shores, Thomas S. (2018). ... Calculus II. ISBN 978-0-387-90975-2. Marsden, Jerrold; Weinstein, Alan (1985). Calculus III. ISBN 978-0-387-90985-1. Lang, ...
81-102, MR 0656721 Peter Freyd and David Yetter (1989). "Braided Compact Closed Categories with Applications to Low-Dimensional ... "The Geometry of Tensor calculus II". Synthese Library. 259: 29-68. v t e. ...
Differential and integral calculus: with applications by George Greenhill (1891) p326 ff. (Internet Archive) J. Dennis Lawrence ... Benjamin Williamson (1899). An elementary treatise on the differential calculus. Logmans, Green, and Co. pp. 227 ff. ... Differential Calculus. London: MacMillan and Co. pp. 161 ff. ...
International Conference on Typed Lambda Calculi and Applications. TLCA 2009. 5608. Springer. pp. 356-370. doi:10.1007/978-3- ... The underlying motivation was to study semantic properties (such as normalization) of the λ-calculus by means of type theory. ... The Coppo-Dezani type assignment system ( ⊢ CD ) {\displaystyle (\vdash _{\text{CD}})} extends the simply typed λ-calculus by ... van Bakel, Steffen (2011). "Strict intersection types for the Lambda calculus". ACM Computing Surveys. 43 (3): 20:1-20:49. doi: ...
The most famous application of revision theory is to the theory of truth, as developed in Gupta and Belnap (1993), for example ... Bruni, R. (2013). Analytic calculi for circular concepts by finite revision. Studia Logica, 101(5):915-932. Chapuis, A. (2003 ... Repeated application of a rule of revision generates sequences of hypotheses, which can be used to define logics of circular ... An application of circular definitions: Rational decision. In Löwe, B., R ̈asch, T., and Malzkorn, W., editors, Foundations of ...
In Geometria Motus, he anticipated the infinitesimal calculus. Finally, Ceva wrote De Re Nummeraria in 1711, which was one of ... Giovanni Ceva also studied applications of mechanics and statics to geometric systems. At one point, however, he incorrectly ...
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Theory and Applications with Calculus, Global Edition, 4/E ... Theory and Applications with Calculus, Global Edition, 4/E. ... MyEconLab with Pearson eText - Instant Access - for Microeconomics: Theory and Applications with Calculus, Global Edition, 4/E ... Open Companion Website for Microeconomics: Theory and Applications with Calculus, Global Edition, 4/E. Perloff ... Theory and Applications with Calculus remains the premiere microeconomics text to marry formal theory with robust, thoroughly ...
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  • In mathematics education , calculus denotes courses of elementary mathematical analysis , which are mainly devoted to the study of functions and limits. (
  • 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. (
  • Madhava of Sangamagrama and the Kerala School of Astronomy and Mathematics thereby stated components of calculus. (
  • The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. (
  • The lambda calculus was introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics . (
  • These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Calculus Volume I. They were created through a Round Eight Textbook Transformation Grant. (
  • Calculus is a part of modern mathematics education . (
  • A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis . (
  • Calculus is one kind of mathematics and deals with finding different properties of integrals of functions and other derivatives. (
  • Mathematics builds upon itself very strongly -- you need to have mastered all of algebra and trigonometry before even attempting calculus, because you will need those skills at every step. (
  • Even if the ideas and concepts of calculus -- limits and derivatives and integrals and so on -- are clear as a bell to you (and they can be made clear through self-study with an appropriate book), the mechanics of actually solving problems will require you to thoroughly understand the underlying mathematics: advanced algebra and trig. (
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  • Prerequisite: Pre-Calculus 11 or Foundations of Mathematics 11 (or equivalent) with a grade of at least B or Pre-Calculus 12 (or equivalent), with a grade of at least C and SFU FAN credit, or SFU FAN X99 course with a grade of at least B-, or achieving a satisfactory grade on the Simon Fraser University Quantitative Placement Test. (
  • MATH 150 or MATH 151 or MATH 154 with a grade of at least B or IB Mathematics HL with a score of 6 or better or AP Calculus AB or BC with a grade of at least 4, or BC Calculus 12 and a pass on the Calculus Challenge Exam. (
  • Prerequisite: Pre-Calculus 12 or Foundations of Mathematics 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C. Quantitative. (
  • Academic skills: the application of rigorous mathematical techniques and ideas to the development of mathematics;the power of abstraction as a way of solving many similar problems at the same time;the development and consolidation of essential skills which a mathematician needs in their toolkit and needs to be able to use without pausing for thought. (
  • As an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students. (
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  • In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. (
  • In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid discrete-continuous dynamical systems. (
  • The remainder of the Sullivan book, 320 pages, provides an overview of differential and integral calculus up through partial differentiation. (
  • The Himonas book is also an overview of differential and integral calculus, with very little in the way of theory. (
  • Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. (
  • As in the first edition, an interesting historical introduction precedes each important new concept.Tom M. Apostol is the author of 'Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2)', published 1969 under ISBN 9780471000075 and ISBN 0471000078. (
  • It has two major branches, differential calculus (concerning instantaneous rates of change and slopes of curves), [2] and integral calculus (concerning accumulation of quantities and the areas under and between curves). (
  • There are two primary types of calculus, which are integral calculus and differential calculus. (
  • Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. (
  • This course covers functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. (
  • Stochastic Integrals discusses one area of diffusion processes: the differential and integral calculus based upon the Brownian motion. (
  • 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. (
  • In addition to the above broad aims of the first year, this module focusses on ensuring that students have competence in a wide range of essential concepts, techniques and applications of differential and integral calculus, and differential equations. (
  • Extends the concepts developed in Calculus to functions of several variables and differential equations. (
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  • In this third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals. (
  • An introduction to differential and integral calculus. (
  • Techniques of integration, L’Hôpital’s Rule, infinite sequences and series, Taylor series and applications, first-order differential equations, and introduction to the calculus of multivariable functions, including partial derivatives and multiple integrals. (
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  • Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration. (
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  • The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. (
  • The three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus. (
  • The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. (
  • It explains, clearly and concisely, partial differentiation, multiple integration, vectors and vector calculus, and provides end-of-chapter exercises along with their solutions to aid the readers′ understanding. (
  • Written in an approachable style and filled with numerous illustrative examples throughout, Two and Three Dimensional Calculus: with Applications in Science and Engineering assumes no prior knowledge of partial differentiation or vectors and explains difficult concepts with easy to follow examples. (
  • Basic concepts of differentiation and integration with applications. (
  • Partial differentiation and applications. (
  • Introduction to vector calculus, including differentiation, decompositions via potentials. (
  • The coverage is up through vector calculus, partial derivatives and multiple integrals. (
  • integral Calculus, what it says is that we can compute the anti-derivative of x. (
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  • is the derivative used in standard calculus. (
  • This series of videos focusing on calculus covers using definite integrals with the shell and disc methods to find volumes of solids of revolution. (
  • The area under curve in calculus can be determined through the use of a specific formula that uses both definite and indefinite integrals. (
  • The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals. (
  • Limits and continuity, derivatives and integrals of polynomial, trigonometric, exponential, and logarithmic functions, applications of derivatives to optimization and approximation, the Mean Value Theorem, and the Fundamental Theorem of Calculus. (
  • Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. (
  • Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz . (
  • 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. (
  • Both kinds of calculus use notions such as infinite sequences, convergence, and infinite series as it applies to limits that are well defined. (
  • Calculus is now part of the modern curriculum taught in most schools, and it can serve as a gateway to more complicated mathematical learning, and other studies regarding limits, functions, and additional mathematical analysis. (
  • Calculus dates back to ancient and even medieval times where it was used to develop different ideas surrounding calculations such as area, volume, and early ideas about limits. (
  • 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 . (
  • The term calculus (plural calculi ) is also used for naming specific methods of calculation or notation as well as some theories, such as propositional calculus , Ricci calculus , calculus of variations , lambda calculus , and process calculus . (
  • Calculus has also been employed as a name for different kinds of mathematical notation such as Ricci calculus, lambda calculus, propositional calculus, process calculus, and calculus of variations. (
  • Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and. (
  • Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. (
  • eta], v) was intensively studied when F itself is symplectic (i.e., of the form (D) below), or when we are in the calculus of variations setting. (
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  • Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. (
  • Functions of Several Variables and Applications. (
  • It includes an elementary introduction to complex numbers and complex-valued functions, key applications of calculus, and an introduction to probability and information theory. (
  • In typed lambda calculus, functions can be applied only if they are capable of accepting the given input's "type" of data. (
  • This series of videos focusing on calculus covers line integral of scalar and vector-valued functions, Green's Theorem and 2-D Divergence Teorem. (
  • This lucid and balanced introduction for first year engineers and applied mathematicians conveys the clear understanding of the fundamentals and applications of calculus, as a prelude to studying more advanced functions. (
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  • 12. Standard Calculus and Sequences of Functions. (
  • Calculus introduces two fundamental concepts which enable us to describe and investigate functions. (
  • Learn applications of integral - understand the average value of function, understand how to find - volume of revolution, surface of revolution and arc length of functions. (
  • This book clearly explains the important theorems of single variable calculus. (
  • This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. (
  • The Anton book is a traditional calculus book with formal theorems and explanations of the theoretical background of how calculus works. (
  • Covers multivariable calculus, starting from the basics and leading up to the three theorems of Green, Gauss, and Stokes, but always with an eye on practical applications. (
  • Written for a wide spectrum of undergraduate students by an experienced author, this book provides a very practical approach to advanced calculus starting from the basics and leading up to the theorems of Green, Gauss, and Stokes. (
  • This Second Edition introduces the mean-value theorems & their applications earlier in the text, incorporates a treatment of linear algebra, & contains many new & easier exercises. (
  • 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. (
  • Fundamental Theorems of Calculus. (
  • of Tokyo) introduces researchers and graduate students to the stochastic calculus of variation , also called Malliavin calculus, for processes with jumps--that is both pure jump processes and jump-diffusions. (
  • The following outlines a standard propositional calculus. (
  • 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 . (
  • It's possible that you may have also heard calculus referred to by other names such as infinitesimal calculus, or "the calculus of infinitesimals. (
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  • An introduction to the calculus, with an excellent balance between theory & technique. (
  • [5] Lambda calculus has played an important role in the development of the theory of programming languages . (
  • Lambda calculus is also a current research topic in Category theory . (
  • This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. (
  • These two kinds of calculus are connected to each other by a theory called the fundamental theorem of calculus. (
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  • APEX Calculus is a calculus textbook written for traditional college/university calculus courses. (
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  • Calculus (from Latin calculus , literally 'small pebble', used for counting and calculations, as on an abacus ) [1] 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 . (
  • surprise: Since I just past Geometry do you think its possible for me to be in calculus next year? (
  • Im attempting to go from Geometry to Calculus AB. (
  • Geometry, however, will not help you much in calculus class. (
  • Brief Calculus:An Applied Approach , 8th Edition, by Michael Sullivan. (
  • Until the discovery that matter is discontinuous, applying Calculus in Physics was reasonable. (
  • So I believe that application of Calculus is inappropriate in areas like Gravitation, Electromagnetism and Nuclear Physics. (
  • Physics is one subject that uses calculus quite frequently, and it is often used to find values such as the distance and velocity as well as the rate of change within specific environments. (
  • For the calculus-based General Physics course primarily taken by engineers and science majors (including physics majors). (
  • Physics for Scientists and Engineers combines outstanding pedagogy with a clear and direct narrative and applications that draw the student into the physics. (
  • The wide range of Applications have been carefully chosen and integrated into the text so as not to interfere with the development of the physics, but rather to illuminate it.Some serve only as examples of physical principles, some are treated in greater depth. (
  • To make it easy to spot the Applications, a Physics Applied marginal note is placed in the margin. (
  • In my opinion, students are there to learn calculus and should already know what a function is. (
  • Calculus for Biology and Medicine motivates life and health science majors to learn calculus through relevant and strategically placed applications to their chosen fields. (
  • Process calculus and parallel object-oriented programming languages. (
  • 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 . (
  • Lambda calculus is Turing complete , that is, it is a universal model of computation that can be used to simulate any Turing machine . (
  • Subsequently, in 1936 Church isolated and published just the portion relevant to computation, what is now called the untyped lambda calculus. (
  • CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator. (
  • Calculus: Early Transcendentals , 8th Edition, by Howard Anton, Irl Bivens and Stephen Davis. (
  • James Stewart's CALCULUS, 7e, International Metric Edition texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. (
  • With CALCULUS, 7e, International Metric Edition Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. (
  • In the 4th Edition, new co-author Marcus Roper (UCLA) partners with author Claudia Neuhauser to preserve these strengths while adding an unprecedented number of real applications and an infusion of modeling and technology. (
  • 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. (
  • Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. (
  • 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. (
  • Self-contained and suitable for undergraduate students, this text offers a working knowledge of calculus and statistics. (
  • Deadline to submit all required credentials for PhD applications from international and domestic students to all departments/divisions. (
  • Students should complete and upload the Statement of Purpose before submitting the online application. (
  • Designed to prepare students for first year Calculus courses. (
  • Recommended for students with no previous knowledge of Calculus. (
  • For the first time, instructors teaching with Calculus for Biology and Medicine can assign text-specific online homework and other resources to students outside of the classroom. (
  • 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 . (
  • [3] These two branches are related to each other by the fundamental theorem of calculus . (
  • This is accomplished by means of the Fundamental Theorem of Calculus. (
  • If repeated application of the reduction steps eventually terminates, then by the Church-Rosser theorem it will produce a β-normal form . (
  • 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. (
  • Lambda calculus consists of constructing lambda terms and performing reduction operations on them. (
  • Lambda calculus may be untyped or typed . (
  • Functional programming languages implement the lambda calculus. (
  • [11] In 1940, he also introduced a computationally weaker, but logically consistent system, known as the simply typed lambda calculus . (
  • Until the 1960s when its relation to programming languages was clarified, the lambda calculus was only a formalism. (
  • 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. (
  • 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. (
  • We present the notion of recognizability in the simply typed lambda-calculus by showing the equivalence between intersection types and finite standard models. (
  • We then show this notion of recognizability does not coincide with locally finite congruences of the lambda-calculus. (
  • 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. (
  • In Proceedings of the REX Workshop on Semantics: Foundations and Applications , volume 506 of Lecture Notes in Computer Science . (
  • Use of symbolic manipulation and graphics software in calculus. (