List of calculus topics

This is a list of calculus topics.

Limits

• Limit (mathematics)
• Limit of a function
  • One-sided limit
• Limit of a sequence
• Indeterminate form
• Orders of approximation
• (ε, δ)-definition of limit
• Continuous function

Differential calculus

• Derivative
• Notation
  • 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
  • Power rule
• Chain rule
• Local linearization
• 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
• General Leibniz rule
• Mean value theorem
• Logarithmic derivative
• Differential (calculus)
• Related rates
• Regiomontanus' angle maximization problem

• Rolle's theorem

Integral calculus

• Antiderivative/Indefinite integral
• Simplest rules
  • Sum rule in integration
  • Constant factor rule in integration
  • Linearity of integration
• Arbitrary constant of integration
• Cavalieri's quadrature formula
• Fundamental theorem of calculus
• Integration by parts
• Inverse chain rule method
• Integration by substitution
  • Tangent half-angle substitution

• Differentiation under the integral sign
• Trigonometric substitution
• Partial fractions in integration
  • Quadratic integral
• Proof that 22/7 exceeds π
• Trapezium rule
• Integral of the secant function
• Integral of secant cubed
• Arclength
• Solid of revolution
• Shell integration

Special functions and numbers

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

Numerical integration

See also list of numerical analysis topics

• Rectangle method
• Trapezoidal 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 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

Multivariable

• Partial derivative
• Disk 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

• Adequality
• Infinitesimal
  • Archimedes' use of infinitesimals
• Gottfried Leibniz
• Isaac Newton
• Method of Fluxions
• Infinitesimal calculus
• Brook Taylor
• Colin Maclaurin
• Leonhard Euler
• Gauss
• Joseph Fourier
• Law of continuity
• History of calculus
• Generality of algebra

Nonstandard calculus

• Elementary Calculus: An Infinitesimal Approach
• 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.