List of basic calculus topics

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For a more comprehensive list, see the List of calculus topics.

Calculus is a central branch of mathematics, developed from algebra and geometry. It is built around two major complementary ideas, both of which rely critically on the concept of limits:

1. Differential calculus – concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. This can be illustrated by the slope of a function's graph.
2. Integral calculus  – studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced.

These two processes act inversely to each other, as shown by the fundamental theorem of calculus. The following list of topics is provided as an overview of and introduction to calculus:

Contents 1 Essence of calculus 2 History of calculus 3 Basic calculus concepts 4 Calculus scholars 5 Calculus lists 6 See also 7 External links

[edit] Essence of calculus

Topics in calculus

Fundamental theorem Limits of functions Continuity Vector calculus Matrix calculus Mean value theorem

Differentiation

Product rule Quotient rule Chain rule Implicit differentiation Taylor's theorem Related rates List of differentiation identities

Integration

Lists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order

Main article: Calculus

[edit] History of calculus

Main article: History of calculus

[edit] Basic calculus concepts

Derivative - Differentiation rules - Calculus with polynomials - Fundamental theorem of calculus - Differential calculus - Integral calculus - Limits of integration - List of calculus topics - Important publications in calculus - Mathematics - Multivariable calculus - Nonstandard analysis - Partial derivative

[edit] Calculus scholars

Gottfried Leibniz - Sir Isaac Newton

[edit] Calculus lists

Main article: List of calculus topics

• Table of mathematical symbols

[edit] See also

• Table of mathematical symbols

[edit] External links

Find more about Calculus on Wikipedia's sister projects:
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	Learning resources

• Eric W. Weisstein, Calculus at MathWorld.
• Topics on Calculus at PlanetMath.
• Calculus Made Easy (1914) by Silvanus P. ThompsonFull text in PDF
• Calculus.org: The Calculus page at University of California, Davis — contains resources and links to other sites
• COW: Calculus on the Web at Temple University - contains resources ranging from pre-calculus and associated algebra
• Online Integrator (WebMathematica) from Wolfram Research
• The Role of Calculus in College Mathematics from ERICDigests.org
• OpenCourseWare Calculus from the Massachusetts Institute of Technology
• Infinitesimal Calculus — an article on its historical development, in Encyclopaedia of Mathematics, Michiel Hazewinkel ed. .

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