List of calculus topics

This is a list of calculus topics.

1 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

2 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

3 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

4 Special functions and numbers

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

5 Absolute numerical

See also list of numerical analysis topics

Rectangle method
Trapezoidal rule
Simpson’s rule
Newton–Cotes formulas
Gaussian quadrature

6 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

7 Multivariable

Partial derivative
Disk integration
Gabriel’s horn
Jacobian matrix
Hessian matrix
Curvature
Green’s theorem
Divergence theorem
Stokes’ theorem

8 Series

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

9 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

10 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.