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
[Absolute numerical]
See also list of numerical analysis topicsLists 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
- Vector Calculus
Series
History
- Adequality
- Infinitesimal
- * Archimedes' use of infinitesimals
- Gottfried Leibniz
- Isaac NewtonMethod 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 ApproachFor further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics.