List of calculus topics

From Free net encyclopedia

Topics in calculus

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

Differentiation

Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem | Related rates

Integration

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

This is a list of calculus topics.

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

Contents 1 Before calculus (pre calculus) 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

Before calculus (pre calculus)

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

Limits

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

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'Hopital's rule
• Leibniz's rule
• Mean value theorem
• Logarithmic derivative
• Differential (mathematics)
• Related rates

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

Special functions and numbers

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

Numerical integration

See also list of numerical analysis topics

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

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 hyperbolic functions
• List of integrals of exponential functions
• List of integrals of logarithmic functions
• List of integrals of arc functions
• List of integrals of area functions

Multivariable

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

Series

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

History

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

Nonstandard calculus

• Nonstandard calculus
• Infinitesimal
• How Archimedes used infinitesimals

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