List Of Calculus Topics

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

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
• first derivative test
• second derivative test
• Extreme value theorem
• Differential equation
• Differential operator
• Newton's method
• Taylor's theorem
• L'Hopital's rule
• Leibniz'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
• Differentiation under the integral sign
• 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

• Rectangle method
• Trapezium rule
• 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
• Infinity tricks

Multivariable

• Partial derivative
• Disk integration
• Shell 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

• Infinitesimal
• How Archimedes used infinitesimals
• Gottfried Leibniz
• Isaac Newton
• Method of Fluxions
• Infinitesimal calculus
• Brook Taylor
• Colin Maclaurin
• Leonhard Euler

Nonstandard calculus

• Nonstandard calculus
• Infinitesimal
• How Archimedes used infinitesimals

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