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Revision as of 15:43, 15 March 2018
This is a list of calculus topics.
Before calculus (precalculus)
- Graph of a function
- Linear function
- Secant line
- Slope
- Tangent
- Concave function
- Finite difference
- Radian
- Factorial
- Binomial theorem
- Free variables and bound variables
- Complex numbers
Limits
- Limit (mathematics)
- Limit of a function
- Limit of a sequence
- Indeterminate form
- Orders of approximation
- (ε, δ)-definition of limit
Differential calculus
- Derivative
- Notation
- Simplest rules
- Derivative (examples)
- Chain rule
- local linearization
- Product rule
- Quotient rule
- Inverse functions and differentiation
- Implicit differentiation
- Stationary point
- 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
- Arbitrary constant of integration
- Fundamental theorem of calculus
- Integration by parts
- Inverse chain rule method
- Integration by 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
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
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
- Shell integration
- Gabriel's horn
- Jacobian matrix
- Hessian matrix
- Curvature
- Green's theorem
- Divergence theorem
- Stokes' theorem
Series
History
- Adequality
- Infinitesimal
- Gottfried Leibniz
- Isaac Newton
- Method of Fluxions
- Infinitesimal calculus
- Brook Taylor
- Colin Maclaurin
- Leonhard Euler
- 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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