Calculus is the branch of mathematics that studies continuous change and is the principal precursor of modern mathematical analysis. It rests on two complementary divisions: differential calculus, which examines instantaneous rates of change and the slopes of curves, and integral calculus, which studies the accumulation of quantities and areas under curves. The two divisions are connected by the fundamental theorem of calculus, and both rest on the concept of a limit applied to infinite sequences and series.
Facts
Central QuestionCalculus studies continuous change: how the instantaneous rate at which a quantity changes (the derivative) and the total accumulation of a changing quantity (the integral) can each be defined rigorously and are related to one another through the fundamental theorem of calculus. 1 Key DebateIsaac Newton and Gottfried Wilhelm Leibniz each independently formulated infinitesimal calculus in the late 17th century, and when both published, a bitter priority dispute broke out over which mathematician, and therefore which country, deserved credit; it divided English-speaking mathematicians from continental European mathematicians for many years. 1 Classification
Pure or Applied Calculus
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Source Calculus (Wikipedia)
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Source Bonaventura Cavalieri, Biography (MacTutor History of Mathematics)
Source Borwein Integral (Wikipedia)
Source Brook Taylor, Biography (MacTutor History of Mathematics)
Source Cavalieri's Quadrature Formula (Wikipedia)
Source Chain rule (Wikipedia)
Source Differentiation Rules (Wikipedia)
Source Wolfram MathWorld: Dirichlet Function
Source Divergence (Wikipedia)
Source Euler-Maclaurin Formula (Wikipedia)
Source Wikipedia: George Gabriel Stokes
Source Gradient Theorem (Wikipedia)
Source Infinitesimal (Wikipedia)
Source Integral of the Secant Function (Wikipedia)
Source Wikipedia: John Wallis
Source Limit of a Function (Wikipedia)
Source Wikipedia: Pietro Mengoli
Source Quotient Rule (Wikipedia)
Source Riemann-Stieltjes Integral (Wikipedia)
Source Second Derivative (Wikipedia)
Source Squeeze Theorem (Wikipedia)
Source Symmetric Derivative (Wikipedia)
Source Vector Field (Wikipedia)
Source Wolfram MathWorld: Weierstrass Function
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1. Calculus (Wikipedia)
Wikimedia FoundationLead section
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus.
History section, Newton and Leibniz passage
When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit.
Associated With: Analysis, Wikipedia lead paragraph, Calculus
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis.
View the Source Chain rule (Wikipedia)
Includes: Chain Rule, Lead sentenceQuote, Includes: Chain Rule, Lead sentence
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y
View the Source Gradient Theorem (Wikipedia)
Includes: Gradient Theorem, Lead sentenceQuote, Includes: Gradient Theorem, Lead sentence
theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field
View the Source Squeeze Theorem (Wikipedia)
Includes: Squeeze Theorem, Lead sentenceQuote, Includes: Squeeze Theorem, Lead sentence
In calculus, the squeeze theorem (also known as the sandwich theorem, the two policeman and a drunk theorem among other names) is
View the Source Differentiation Rules (Wikipedia)
Includes: Differentiation Rules, Lead sentenceQuote, Includes: Differentiation Rules, Lead sentence
les for computing the derivative of a function in calculus.
View the Source Quotient Rule (Wikipedia)
Includes: Quotient Rule, Lead sentenceQuote, Includes: Quotient Rule, Lead sentence
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functio
View the Source Vector Field (Wikipedia)
Includes: Vector Field, Lead sentenceQuote, Includes: Vector Field, Lead sentence
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean spac
View the Source Limit of a Function (Wikipedia)
Includes: Limit of a function, Lead sentenceQuote, Includes: Limit of a function, Lead sentence
e limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular
View the Source Second Derivative (Wikipedia)
Includes: Second Derivative, Lead sentenceQuote, Includes: Second Derivative, Lead sentence
In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f.
View the Source Cavalieri's Quadrature Formula (Wikipedia)
Includes: Cavalieri's Quadrature Formula, Lead sentenceQuote, Includes: Cavalieri's Quadrature Formula, Lead sentence
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral ∫
View the Source Divergence (Wikipedia)
Includes: Divergence, Lead sentenceQuote, Includes: Divergence, Lead sentence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that
View the Source Integral of the Secant Function (Wikipedia)
Includes: Integral of the Secant Function, Lead sentenceQuote, Includes: Integral of the Secant Function, Lead sentence
In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expres
View the Source Wikipedia: John Wallis
Includes: John Wallis, LeadQuote, Includes: John Wallis, Lead
who is given partial credit for the development of infinitesimal calculus
View the Source Wikipedia: Pietro Mengoli
Includes: Pietro Mengoli, LeadQuote, Includes: Pietro Mengoli, Lead
was a pivotal figure in the development of calculus
View the Source Wikipedia: George Gabriel Stokes
WikipediaIncludes: George Gabriel Stokes, Lead paragraphQuote, Includes: George Gabriel Stokes, Lead paragraph
As a mathematician, he popularised Stokes' theorem in vector calculus and contributed to the theory of asymptotic expansions.
View the Source Infinitesimal (Wikipedia)
Includes: Infinitesimal, Lead paragraphQuote, Includes: Infinitesimal, Lead paragraph
Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities.
View the Source Wolfram MathWorld: Dirichlet Function
Wolfram MathWorldIncludes: Dirichlet Function, Subject classificationsQuote, Includes: Dirichlet Function, Subject classifications
Calculus and Analysis Calculus
View the Source Wolfram MathWorld: Weierstrass Function
Wolfram MathWorldIncludes: Weierstrass Function, Subject classificationsQuote, Includes: Weierstrass Function, Subject classifications
Calculus and Analysis Calculus
View the Source Riemann-Stieltjes Integral (Wikipedia)
Includes: Riemann-Stieltjes Integral, Lead sectionQuote, Includes: Riemann-Stieltjes Integral, Lead section
In mathematics, the Riemann-Stieltjes integral is a generalization of the Riemann integral
View the Source Borwein Integral (Wikipedia)
Includes: Borwein integral, Lead sectionQuote, Includes: Borwein integral, Lead section
In mathematics, a Borwein integral is an integral whose unusual properties were
View the Source Symmetric Derivative (Wikipedia)
Includes: Symmetric Derivative, Lead sectionQuote, Includes: Symmetric Derivative, Lead section
In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative.
View the Source Euler-Maclaurin Formula (Wikipedia)
Includes: Euler-Maclaurin Formula, Lead sectionQuote, Includes: Euler-Maclaurin Formula, Lead section
formula is a formula for the difference between an integral and a closely related sum. It can be used to
View the Source Bonaventura Cavalieri, Biography (MacTutor History of Mathematics)
Includes: Bonaventura Cavalieri, SummaryQuote, Includes: Bonaventura Cavalieri, Summary
Bonaventura Cavalieri was an Italian mathematician who developed a method of indivisibles which became a factor in the development of the integral calculus.
View the Source Brook Taylor, Biography (MacTutor History of Mathematics)
Includes: Brook Taylor, SummaryQuote, Includes: Brook Taylor, Summary
Brook Taylor was an English mathematician who added to mathematics a new branch now called the 'calculus of finite differences', invented integration by parts, and discovered the celebrated formula known as Taylor's expansion.
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