List of calculus topics
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This is a list of calculus topics.
Limits
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
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
- 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
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 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.
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