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List of calculus topics

This is a list of calculus topics.

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

Table of contents

1 Before calculus (pre calculus) 1.1 Limits 2 Differential calculus 3 Integral calculus 4 Special functions and numbers 5 Numerical integration 6 Lists and Tables 7 Multi variable 8 Series 9 History

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
• Limit of a sequence
• Indeterminate form
• Table of limits
• Orders of approximation
• Trigonometric rational function

Differential calculus

• Derivative
• Notations
  • Newton's notation for differentiation
  • Leibniz's notation for differentiation
  • Dot 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
• Differential equation
• Differential operator
• Newton's method
• Taylor's theorem
• L'Hopital's rule
• Mean value theorem
• Logarithmic derivative
• Differential (mathematics)

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
• Trigonometric substitution
• Partial fractions in integration
  • Quadratic integral
• A simple proof that 22/7 exceeds Pi
• Trapezium rule

Special functions and numbers

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

Numerical integration

• Simpson's rule
• Newton-Cotes formulas
• Gaussian quadrature

Lists and Tables

• 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

Multi variable

• Partial derivative
• Disk integration
• Shell integration
• Gabriel's horn
• Jacobian matrix
• Hessian
• 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

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

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