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Calculus

Analysis

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 Question
Calculus 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 Debate
Isaac 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
Pure Mathematics 1
Calculus
Filter Results5 entries
Connections

Associated With

Source Calculus (Wikipedia)

Includes

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)
Chain Rule, Theorems
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
Sources
1. Calculus (Wikipedia)
Wikimedia Foundation
  • Lead 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.
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Chain rule (Wikipedia)
Includes: Chain Rule, Lead sentence
Quote, 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
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Gradient Theorem (Wikipedia)
Includes: Gradient Theorem, Lead sentence
Quote, 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
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Squeeze Theorem (Wikipedia)
Includes: Squeeze Theorem, Lead sentence
Quote, 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
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Differentiation Rules (Wikipedia)
Includes: Differentiation Rules, Lead sentence
Quote, Includes: Differentiation Rules, Lead sentence
les for computing the derivative of a function in calculus.
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Quotient Rule (Wikipedia)
Includes: Quotient Rule, Lead sentence
Quote, 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
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Vector Field (Wikipedia)
Includes: Vector Field, Lead sentence
Quote, 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
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Limit of a Function (Wikipedia)
Includes: Limit of a function, Lead sentence
Quote, 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
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Second Derivative (Wikipedia)
Includes: Second Derivative, Lead sentence
Quote, 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.
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Cavalieri's Quadrature Formula (Wikipedia)
Includes: Cavalieri's Quadrature Formula, Lead sentence
Quote, Includes: Cavalieri's Quadrature Formula, Lead sentence
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral ∫
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Divergence (Wikipedia)
Includes: Divergence, Lead sentence
Quote, 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
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Integral of the Secant Function (Wikipedia)
Includes: Integral of the Secant Function, Lead sentence
Quote, 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
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Wikipedia: John Wallis
Includes: John Wallis, Lead
Quote, Includes: John Wallis, Lead
who is given partial credit for the development of infinitesimal calculus
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Wikipedia: Pietro Mengoli
Includes: Pietro Mengoli, Lead
Quote, Includes: Pietro Mengoli, Lead
was a pivotal figure in the development of calculus
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Wikipedia: George Gabriel Stokes
WikipediaIncludes: George Gabriel Stokes, Lead paragraph
Quote, Includes: George Gabriel Stokes, Lead paragraph
As a mathematician, he popularised Stokes' theorem in vector calculus and contributed to the theory of asymptotic expansions.
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Infinitesimal (Wikipedia)
Includes: Infinitesimal, Lead paragraph
Quote, 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.
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Wolfram MathWorld: Dirichlet Function
Wolfram MathWorldIncludes: Dirichlet Function, Subject classifications
Quote, Includes: Dirichlet Function, Subject classifications
Calculus and Analysis Calculus
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Wolfram MathWorld: Weierstrass Function
Wolfram MathWorldIncludes: Weierstrass Function, Subject classifications
Quote, Includes: Weierstrass Function, Subject classifications
Calculus and Analysis Calculus
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Riemann-Stieltjes Integral (Wikipedia)
Includes: Riemann-Stieltjes Integral, Lead section
Quote, Includes: Riemann-Stieltjes Integral, Lead section
In mathematics, the Riemann-Stieltjes integral is a generalization of the Riemann integral
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Borwein Integral (Wikipedia)
Includes: Borwein integral, Lead section
Quote, Includes: Borwein integral, Lead section
In mathematics, a Borwein integral is an integral whose unusual properties were
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Symmetric Derivative (Wikipedia)
Includes: Symmetric Derivative, Lead section
Quote, Includes: Symmetric Derivative, Lead section
In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative.
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Euler-Maclaurin Formula (Wikipedia)
Includes: Euler-Maclaurin Formula, Lead section
Quote, 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
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Bonaventura Cavalieri, Biography (MacTutor History of Mathematics)
Includes: Bonaventura Cavalieri, Summary
Quote, 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.
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Brook Taylor, Biography (MacTutor History of Mathematics)
Includes: Brook Taylor, Summary
Quote, 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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