Calculus, the Glossary
Calculus 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.[1]
Table of Contents
219 relations: Abacus, Abraham Robinson, Acceleration, Actuarial science, Adequality, Agnes Scott College, Albert Einstein, Algebra, Allen & Unwin, American Mathematical Society, Analytic function, Analytic geometry, Ancient Egyptian mathematics, Ancient Greek, Antiderivative, Apostrophe, Arc length, Archimedes, Area, Arithmetic, Augustin-Louis Cauchy, Axiom, Émile Borel, Bernhard Riemann, Bhāskara II, Blood vessel, Bonaventura Cavalieri, Business, Calculus, Calculus (medicine), Calculus of variations, Cambridge University Press, Cancer, Cartesian coordinate system, Category theory, Cavalieri's principle, Center of mass, Chain rule, Chinese mathematics, Classical mechanics, Colin Maclaurin, Complex analysis, Complex plane, Computer science, Concave function, Constant of integration, Constructive analysis, Constructivism (philosophy of mathematics), Continuous function, Convergent series, ... Expand index (169 more) »
Abacus
An abacus (abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Arabic numeral system.
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.
See Calculus and Abraham Robinson
Acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time.
Actuarial science
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions.
See Calculus and Actuarial science
Adequality
Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam, English translation of Fermat's treatise Methodus ad disquirendam maximam et minimam.
Agnes Scott College
Agnes Scott College is a private women's liberal arts college in Decatur, Georgia.
See Calculus and Agnes Scott College
Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula, which arises from relativity theory, has been called "the world's most famous equation".
See Calculus and Albert Einstein
Algebra
Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures.
Allen & Unwin
George Allen & Unwin was a British publishing company formed in 1911 when Sir Stanley Unwin purchased a controlling interest in George Allen & Co.
See Calculus and Allen & Unwin
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
See Calculus and American Mathematical Society
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
See Calculus and Analytic function
Analytic geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
See Calculus and Analytic geometry
Ancient Egyptian mathematics
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c., from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt.
See Calculus and Ancient Egyptian mathematics
Ancient Greek
Ancient Greek (Ἑλληνῐκή) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC.
See Calculus and Ancient Greek
Antiderivative
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
See Calculus and Antiderivative
Apostrophe
The apostrophe is a punctuation mark, and sometimes a diacritical mark, in languages that use the Latin alphabet and some other alphabets.
Arc length
Arc length is the distance between two points along a section of a curve.
Archimedes
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.
Area
Area is the measure of a region's size on a surface.
Arithmetic
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.
Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy (France:, ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist.
See Calculus and Augustin-Louis Cauchy
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
Émile Borel
Félix Édouard Justin Émile Borel (7 January 1871 – 3 February 1956) was a French mathematician and politician.
Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry.
See Calculus and Bernhard Riemann
Bhāskara II
Bhāskara II (1114–1185), also known as Bhāskarāchārya, was an Indian polymath, mathematician, astronomer and engineer.
Blood vessel
Blood vessels are the structures of the circulatory system that transport blood throughout the human body.
Bonaventura Cavalieri
Bonaventura Francesco Cavalieri (Bonaventura Cavalerius; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate.
See Calculus and Bonaventura Cavalieri
Business
Business is the practice of making one's living or making money by producing or buying and selling products (such as goods and services).
Calculus
Calculus 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.
Calculus (medicine)
A calculus (calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ or duct of the body.
See Calculus and Calculus (medicine)
Calculus of variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
See Calculus and Calculus of variations
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
See Calculus and Cambridge University Press
Cancer
Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body.
Cartesian coordinate system
In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.
See Calculus and Cartesian coordinate system
Category theory
Category theory is a general theory of mathematical structures and their relations.
See Calculus and Category theory
Cavalieri's principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows.
See Calculus and Cavalieri's principle
Center of mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero.
See Calculus and Center of mass
Chain rule
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions and in terms of the derivatives of and.
Chinese mathematics
Mathematics emerged independently in China by the 11th century BCE.
See Calculus and Chinese mathematics
Classical mechanics
Classical mechanics is a physical theory describing the motion of objects such as projectiles, parts of machinery, spacecraft, planets, stars, and galaxies.
See Calculus and Classical mechanics
Colin Maclaurin
Colin Maclaurin (Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra.
See Calculus and Colin Maclaurin
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
See Calculus and Complex analysis
Complex plane
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, called the imaginary axis, is formed by the imaginary numbers.
See Calculus and Complex plane
Computer science
Computer science is the study of computation, information, and automation.
See Calculus and Computer science
Concave function
In mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints.
See Calculus and Concave function
Constant of integration
In calculus, the constant of integration, often denoted by C (or c), is a constant term added to an antiderivative of a function f(x) to indicate that the indefinite integral of f(x) (i.e., the set of all antiderivatives of f(x)), on a connected domain, is only defined up to an additive constant.
See Calculus and Constant of integration
Constructive analysis
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics.
See Calculus and Constructive analysis
Constructivism (philosophy of mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists.
See Calculus and Constructivism (philosophy of mathematics)
Continuous function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.
See Calculus and Continuous function
Convergent series
In mathematics, a series is the sum of the terms of an infinite sequence of numbers.
See Calculus and Convergent series
Cours d'Analyse
Cours d'Analyse de l’École Royale Polytechnique; I.re Partie.
See Calculus and Cours d'Analyse
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Cycloid
In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping.
Demography
Demography is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration.
Density
Density (volumetric mass density or specific mass) is a substance's mass per unit of volume.
Derivative
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.
Difference quotient
In single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x.
See Calculus and Difference quotient
Differential calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change.
See Calculus and Differential calculus
Differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
See Calculus and Differential equation
Differentiation rules
This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus.
See Calculus and Differentiation rules
Diminutive
A diminutive is a word obtained by modifying a root word to convey a slighter degree of its root meaning, either to convey the smallness of the object or quality named, or to convey a sense of intimacy or endearment, and sometimes to derogatorily belittle something or someone.
Diophantus
Diophantus of Alexandria (born; died) was a Greek mathematician, who was the author of two main works: On Polygonal Numbers, which survives incomplete, and the Arithmetica in thirteen books, most of it extant, made up of arithmetical problems that are solved through algebraic equations.
Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
See Calculus and Discrete mathematics
Distribution (mathematics)
Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis.
See Calculus and Distribution (mathematics)
Division by zero
In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
See Calculus and Division by zero
Economics
Economics is a social science that studies the production, distribution, and consumption of goods and services.
Edwin Mellen Press
The Edwin Mellen Press, sometimes stylised as Mellen Press, is an academic publisher.
See Calculus and Edwin Mellen Press
Electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields.
See Calculus and Electromagnetism
Engineering
Engineering is the practice of using natural science, mathematics, and the engineering design process to solve technical problems, increase efficiency and productivity, and improve systems.
Ethical calculus
An ethical calculus is the application of mathematics to calculate issues in ethics.
See Calculus and Ethical calculus
Eudoxus of Cnidus
Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, doctor, and lawmaker.
See Calculus and Eudoxus of Cnidus
Euler method
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
Expected value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
See Calculus and Expected value
Felicific calculus
The felicific calculus is an algorithm formulated by utilitarian philosopher Jeremy Bentham (1748–1832) for calculating the degree or amount of pleasure that a specific action is likely to induce.
See Calculus and Felicific calculus
Finite difference
A finite difference is a mathematical expression of the form.
See Calculus and Finite difference
Fixed-point iteration
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.
See Calculus and Fixed-point iteration
Force
A force is an influence that can cause an object to change its velocity, i.e., to accelerate, meaning a change in speed or direction, unless counterbalanced by other forces.
Fourier series
A Fourier series is an expansion of a periodic function into a sum of trigonometric functions.
See Calculus and Fourier series
Fourth power
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together.
Frustum
In geometry, a morsel; (frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid.
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of.
See Calculus and Function (mathematics)
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions).
See Calculus and Fundamental theorem of calculus
General relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics.
See Calculus and General relativity
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
George Berkeley
George Berkeley (12 March 168514 January 1753) – known as Bishop Berkeley (Bishop of Cloyne of the Anglican Church of Ireland) – was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism" (later referred to as "subjective idealism" by others).
See Calculus and George Berkeley
Glossary of calculus
Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself.
See Calculus and Glossary of calculus
Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz (– 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who invented calculus in addition to many other branches of mathematics, such as binary arithmetic, and statistics.
See Calculus and Gottfried Wilhelm Leibniz
Graph of a function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x).
See Calculus and Graph of a function
Greek mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century BC to the 6th century AD, around the shores of the Mediterranean.
See Calculus and Greek mathematics
Green's theorem
In vector calculus, Green's theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by.
See Calculus and Green's theorem
Hellenistic period
In classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra in 30 BC, which was followed by the ascendancy of the Roman Empire, as signified by the Battle of Actium in 31 BC and the Roman conquest of Ptolemaic Egypt the following year, which eliminated the last major Hellenistic kingdom.
See Calculus and Hellenistic period
Henri Lebesgue
Henri Léon Lebesgue (June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of a function defined for that axis.
See Calculus and Henri Lebesgue
Historia Mathematica
Historia Mathematica: International Journal of History of Mathematics is an academic journal on the history of mathematics published by Elsevier.
See Calculus and Historia Mathematica
Hyperreal number
In mathematics, hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers.
See Calculus and Hyperreal number
Ibn al-Haytham
Ḥasan Ibn al-Haytham (Latinized as Alhazen;; full name أبو علي، الحسن بن الحسن بن الهيثم) was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.
See Calculus and Ibn al-Haytham
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century.
See Calculus and Indian mathematics
Infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is.
See Calculus and Infinitesimal
Infinity
Infinity is something which is boundless, endless, or larger than any natural number.
Inflection point
In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign.
See Calculus and Inflection point
Integral
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.
Isaac Barrow
Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus.
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher.
Isis (journal)
Isis is a quarterly peer-reviewed academic journal published by the University of Chicago Press.
See Calculus and Isis (journal)
James Gregory (mathematician)
James Gregory (November 1638 – October 1675) was a Scottish mathematician and astronomer.
See Calculus and James Gregory (mathematician)
Japanese mathematics
denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867).
See Calculus and Japanese mathematics
Jeremy Bentham
Jeremy Bentham (4 February 1747/8 O.S. – 6 June 1832) was an English philosopher, jurist, and social reformer regarded as the founder of modern utilitarianism.
See Calculus and Jeremy Bentham
Johannes Kepler
Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music.
See Calculus and Johannes Kepler
John von Neumann
John von Neumann (Neumann János Lajos; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist, engineer and polymath.
See Calculus and John von Neumann
John Wallis
John Wallis (Wallisius) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
See Calculus and Karl Weierstrass
Kerala school of astronomy and mathematics
The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.
See Calculus and Kerala school of astronomy and mathematics
Lambda calculus
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.
See Calculus and Lambda calculus
Latin
Latin (lingua Latina,, or Latinum) is a classical language belonging to the Italic branch of the Indo-European languages.
Laurent Schwartz
Laurent-Moïse Schwartz (5 March 1915 – 4 July 2002) was a French mathematician.
See Calculus and Laurent Schwartz
Law of excluded middle
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true.
See Calculus and Law of excluded middle
Least-upper-bound property
In mathematics, the least-upper-bound property (sometimes called completeness, supremum property or l.u.b. property) is a fundamental property of the real numbers.
See Calculus and Least-upper-bound property
Leibniz–Newton calculus controversy
In the history of calculus, the calculus controversy (lit) was an argument between the mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first invented calculus.
See Calculus and Leibniz–Newton calculus controversy
Lewiston, New York
Lewiston is a town in Niagara County, New York, United States.
See Calculus and Lewiston, New York
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
See Calculus and Limit (mathematics)
Limit of a function
Although the function is not defined at zero, as becomes closer and closer to zero, becomes arbitrarily close to 1.
See Calculus and Limit of a function
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.
See Calculus and Linear algebra
Linear approximation
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
See Calculus and Linear approximation
Linear function
In mathematics, the term linear function refers to two distinct but related notions.
See Calculus and Linear function
Linear map
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication.
List of calculus topics
This is a list of calculus topics.
See Calculus and List of calculus topics
List of derivatives and integrals in alternative calculi
There are many alternatives to the classical calculus of Newton and Leibniz; for example, each of the infinitely many non-Newtonian calculi.
See Calculus and List of derivatives and integrals in alternative calculi
Lists of integrals
Integration is the basic operation in integral calculus.
See Calculus and Lists of integrals
Liu Hui
Liu Hui was a Chinese mathematician who published a commentary in 263 CE on Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art). He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state of Cao Wei during the Three Kingdoms period (220–280 CE) of China.
Long s
The long s,, also known as the medial s or initial s, is an archaic form of the lowercase letter, found mostly in works from the late 8th to early 19th centuries.
Madhava of Sangamagrama
Mādhava of Sangamagrāma (Mādhavan) Available was an Indian mathematician and astronomer who is considered to be the founder of the Kerala school of astronomy and mathematics in the Late Middle Ages.
See Calculus and Madhava of Sangamagrama
Marginal cost
In economics, the marginal cost is the change in the total cost that arises when the quantity produced is increased, i.e. the cost of producing additional quantity.
See Calculus and Marginal cost
Marginal revenue
Marginal revenue (or marginal benefit) is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit.
See Calculus and Marginal revenue
Maria Gaetana Agnesi
Maria Gaetana Agnesi (16 May 1718 – 9 January 1799) was an Italian mathematician, philosopher, theologian, and humanitarian.
See Calculus and Maria Gaetana Agnesi
Mass
Mass is an intrinsic property of a body.
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts.
See Calculus and Massachusetts Institute of Technology
Mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
See Calculus and Mathematical analysis
Mathematical Association of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.
See Calculus and Mathematical Association of America
Mathematical logic
Mathematical logic is the study of formal logic within mathematics.
See Calculus and Mathematical logic
Mathematical model
A mathematical model is an abstract description of a concrete system using mathematical concepts and language.
See Calculus and Mathematical model
Mathematical optimization
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.
See Calculus and Mathematical optimization
Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
See Calculus and Mathematical physics
Mathematical proof
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.
See Calculus and Mathematical proof
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Mathematics education
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
See Calculus and Mathematics education
Mathematics in the medieval Islamic world
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built upon syntheses of Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).
See Calculus and Mathematics in the medieval Islamic world
Mathematics Magazine
Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.
See Calculus and Mathematics Magazine
Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.
See Calculus and Measure (mathematics)
Medicine
Medicine is the science and practice of caring for patients, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health.
Method of exhaustion
The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
See Calculus and Method of exhaustion
Method of Fluxions
Method of Fluxions (De Methodis Serierum et Fluxionum) is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus.
See Calculus and Method of Fluxions
Metric space
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.
Michel Rolle
Michel Rolle (21 April 1652 – 8 November 1719) was a French mathematician.
Michiel Hazewinkel
Michiel Hazewinkel (born 22 June 1943) is a Dutch mathematician, and Emeritus Professor of Mathematics at the Centre for Mathematics and Computer Science and the University of Amsterdam, particularly known for his 1978 book Formal groups and applications and as editor of the Encyclopedia of Mathematics.
See Calculus and Michiel Hazewinkel
Moment of inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.
See Calculus and Moment of inertia
Momentum
In Newtonian mechanics, momentum (momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object.
Moscow Mathematical Papyrus
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra.
See Calculus and Moscow Mathematical Papyrus
Motion
In physics, motion is when an object changes its position with respect to a reference point in a given time.
Multiple discovery
The concept of multiple discovery (also known as simultaneous invention) is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors.
See Calculus and Multiple discovery
Newton's law of universal gravitation
Newton's law of universal gravitation says that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
See Calculus and Newton's law of universal gravitation
Newton's laws of motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it.
See Calculus and Newton's laws of motion
Newton's method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.
See Calculus and Newton's method
Nilpotent
In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n.
Nonstandard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
See Calculus and Nonstandard analysis
Notation for differentiation
In differential calculus, there is no single uniform notation for differentiation.
See Calculus and Notation for differentiation
Notes and Records
Notes and Records: the Royal Society Journal of the History of Science is an international, quarterly peer-reviewed academic journal which publishes original research in the history of science, technology, and medicine.
See Calculus and Notes and Records
Nova Methodus pro Maximis et Minimis
"Nova Methodus pro Maximis et Minimis" is the first published work on the subject of calculus.
See Calculus and Nova Methodus pro Maximis et Minimis
Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
Paraboloid
In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry.
Pathological (mathematics)
In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological.
See Calculus and Pathological (mathematics)
Philosophiæ Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy) often referred to as simply the Principia, is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation.
See Calculus and Philosophiæ Naturalis Principia Mathematica
Physics
Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.
Pierre de Fermat
Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
See Calculus and Pierre de Fermat
Plagiarism
Plagiarism is the representation of another person's language, thoughts, ideas, or expressions as one's own original work.
Planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape.
Potential energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
See Calculus and Potential energy
Power series
In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n.
Pressure
Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Prime (symbol)
The prime symbol, double prime symbol, triple prime symbol, and quadruple prime symbol are used to designate units and for other purposes in mathematics, science, linguistics and music.
See Calculus and Prime (symbol)
Probability density function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.
See Calculus and Probability density function
Probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability.
See Calculus and Probability theory
Process calculus
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems.
See Calculus and Process calculus
Product rule
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.
Propositional calculus
The propositional calculus is a branch of logic.
See Calculus and Propositional calculus
Rate (mathematics)
In mathematics, a rate is the quotient of two quantities in different units of measurement, often represented as a fraction.
See Calculus and Rate (mathematics)
Real analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions.
See Calculus and Real analysis
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection.
See Calculus and Ricci calculus
Riemann sum
In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum.
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences.
See Calculus and Royal Society
Science
Science is a strict systematic discipline that builds and organizes knowledge in the form of testable hypotheses and predictions about the world.
Secant line
In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Sequent calculus
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology.
See Calculus and Sequent calculus
Series (mathematics)
In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
See Calculus and Series (mathematics)
Sine and cosine
In mathematics, sine and cosine are trigonometric functions of an angle.
See Calculus and Sine and cosine
Slope
In mathematics, the slope or gradient of a line is a number that describes the direction and steepness of the line.
Smooth infinitesimal analysis
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.
See Calculus and Smooth infinitesimal analysis
Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies.
See Calculus and Social science
Society for Industrial and Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community.
See Calculus and Society for Industrial and Applied Mathematics
Sphere
A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.
Stanford Encyclopedia of Philosophy
The Stanford Encyclopedia of Philosophy (SEP) is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication.
See Calculus and Stanford Encyclopedia of Philosophy
Statistics
Statistics (from German: Statistik, "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Synthetic differential geometry
In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory.
See Calculus and Synthetic differential geometry
Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point.
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.
See Calculus and Taylor series
The American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
See Calculus and The American Mathematical Monthly
The Analyst
The Analyst (subtitled A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, and Inferences of the Modern Analysis Are More Distinctly Conceived, or More Evidently Deduced, Than Religious Mysteries and Points of Faith) is a book by George Berkeley.
The Method of Mechanical Theorems
The Method of Mechanical Theorems (Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as The Method, is one of the major surviving works of the ancient Greek polymath Archimedes.
See Calculus and The Method of Mechanical Theorems
Total derivative
In mathematics, the total derivative of a function at a point is the best linear approximation near this point of the function with respect to its arguments.
See Calculus and Total derivative
Velocity
Velocity is the speed in combination with the direction of motion of an object.
Victor J. Katz
Victor Joseph Katz (born 31 December 1942, Philadelphia) is an American mathematician, historian of mathematics, and teacher known for using the history of mathematics in teaching mathematics.
See Calculus and Victor J. Katz
Volume
Volume is a measure of regions in three-dimensional space.
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.
See Calculus and Wiley (publisher)
William Lawvere
Francis William Lawvere (February 9, 1937 – January 23, 2023) was an American mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
See Calculus and William Lawvere
Work (physics)
In science, work is the energy transferred to or from an object via the application of force along a displacement.
See Calculus and Work (physics)
Zeno of Elea
Zeno of Elea (Ζήνων ὁ Ἐλεᾱ́της) was a pre-Socratic Greek philosopher.
Zeno's paradoxes
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.
See Calculus and Zeno's paradoxes
Zu Chongzhi
Zu Chongzhi (429 – 500), courtesy name Wenyuan, was a Chinese astronomer, inventor, mathematician, politician, and writer during the Liu Song and Southern Qi dynasties.
Zu Gengzhi
Zu Geng or Zu Gengzhi (ca. 480 – ca. 525) was a Chinese mathematician, politician, and writer.
References
[1] https://en.wikipedia.org/wiki/Calculus
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