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. Basic topics in calculus include:

Contents 1 Nature of calculus 2 Branches of calculus 3 History of calculus 4 Basic calculus concepts 5 Calculus scholars 6 Calculus lists 7 See also 8 External links

[edit] Nature of calculus

Topics in calculus

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

Differentiation

Product rule Quotient rule Chain rule Implicit differentiation Taylor's theorem Related rates Table of derivatives

Integration

Lists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution

Main article: Calculus

[edit] Branches of calculus

[edit] History of calculus

Main article: History of calculus

[edit] Basic calculus concepts

• Differentiation rules
• Calculus with polynomials
• Differential calculus
• Integral calculus
• List of calculus topics
• Important publications in calculus
• Mathematics
• Multivariable calculus
• Nonstandard analysis

[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

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