List of calculus topics

From Wikipedia, the free encyclopedia

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

This is a list of calculus topics.

Note: the ordering of topics in sections is a suggestion to students.

Contents 1 Before calculus (precalculus) 2 Limits 3 Differential calculus 4 Integral calculus 5 Special functions and numbers 6 Numerical integration 7 Lists and tables 8 Multivariable 9 Series 10 History 11 Nonstandard calculus

[edit] Before calculus (precalculus)

• Graph of a function
• Linear function
• Secant
• Slope
• Tangent
• Concavity
• Finite difference
• Radian
• Factorial
• Binomial theorem
• Free variables and bound variables

[edit] Limits

• Limit of a function
  • One-sided limit
• Limit of a sequence
• Indeterminate form
• Orders of approximation
• Trigonometric rational function

[edit] Differential calculus

• Derivative
• Notations
  • Newton's notation for differentiation
  • Leibniz's notation for differentiation
• Simplest rules
  • Derivative of a constant
  • Sum rule in differentiation
  • Constant factor rule in differentiation
  • Linearity of differentiation
  • Calculus with polynomials
• Derivative (examples)
• Chain rule
• Product rule
• Quotient rule
• Inverse functions and differentiation
• Implicit differentiation
• Stationary point
  • maxima and minima
  • first derivative test
  • second derivative test
  • Extreme value theorem
• Differential equation
• Differential operator
• Newton's method
• Taylor's theorem
• L'Hôpital's rule
• Leibniz's rule
• Mean value theorem
• Logarithmic derivative
• Differential (calculus)
• Related rates

[edit] Integral calculus

• Antiderivative, Indefinite integral
• Simplest rules
  • Sum rule in integration
  • Constant factor rule in integration
  • Linearity of integration
• Arbitrary constant of integration
• Fundamental theorem of calculus
• Integration by parts
• Inverse chain rule method
• Substitution rule
• Differentiation under the integral sign
• Trigonometric substitution
• Partial fractions in integration
  • Quadratic integral
• A simple proof that 22/7 exceeds π
• Trapezium rule
• Integral of secant cubed

[edit] Special functions and numbers

• Natural logarithm
• e (mathematical constant)
• Exponential function
• Stirling's approximation
• Bernoulli numbers

[edit] Numerical integration

See also list of numerical analysis topics

• Rectangle method
• Trapezium rule
• Simpson's rule
• Newton–Cotes formulas
• Gaussian quadrature

[edit] Lists and tables

• Table of common limits
• Table of derivatives
• Table of integrals
• Table of mathematical symbols
• List of integrals
• List of integrals of rational functions
• List of integrals of irrational functions
• List of integrals of trigonometric functions
• List of integrals of inverse trigonometric functions
• List of integrals of hyperbolic functions
• List of integrals of exponential functions
• List of integrals of logarithmic functions
• List of integrals of area functions

[edit] Multivariable

• Partial derivative
• Disk integration
• Shell integration
• Gabriel's horn
• Jacobian matrix
• Hessian matrix
• Curvature
• Green's theorem
• Divergence theorem
• Stokes' theorem

[edit] Series

• Infinite series
• Maclaurin series, Taylor series
• Fourier series
• Euler–Maclaurin formula

[edit] History

• Infinitesimal
  • Archimedes' use of infinitesimals
• Gottfried Leibniz
• Isaac Newton
• Method of Fluxions
• Infinitesimal calculus
• Brook Taylor
• Colin Maclaurin
• Leonhard Euler

[edit] Nonstandard calculus

• Nonstandard calculus
• Infinitesimal
• Archimedes' use of infinitesimals

For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics.