Portal:Analysis

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Analysis

Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development. As a formal concept, the method has variously been ascribed to Ibn al-Haytham, Descartes (Discourse on the Method), Galileo, and Newton, as a practical method of physical discovery.

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In calculus, a branch of mathematics, the derivative is a measurement of how a function changes when the values of its inputs change. Loosely speaking, a derivative can be thought of as how much a quantity is changing at some given point. For example, the derivative of the position or distance of a car at some point in time is the instantaneous velocity, or instantaneous speed (respectively), at which that car is traveling (conversely the integral of the velocity is the car's position).

A closely related notion is the differential of a function.

The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization..

The process of finding a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration.

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Analytic number theory • Asymptotic analysis • Calculus • Calculus of variations • Complex analysis • Continuous mappings • Differential operators • Dynamical systems • Ergodic theory • Finite differences • Fixed points • Fourier analysis • Fractals • Functional analysis • Generalized functions • Harmonic analysis • Inequalities • Interpolation • Inverse functions • Mathematical analysts • Means • Norms (mathematics) • Numerical analysis • Optimization • Perturbation theory • Real analysis • Sequences and series
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Topics in Analysis

General Calculus Differentiation Integration
  • Differentiation
  • Differential calculus
  • Differential equation
    • Ordinary differential equation
    • Partial differential equation
  • Numerical differentiation
    • Numerical ordinary differential equations
  • Table of derivatives
  • Differential equations topics
    • Partial differential equation topics
  • Integration
    • Improper integral
  • Riemann integral
  • Lebesgue integral
  • Other integral types
  • Numerical integration
    • Trapezium rule
    • Simpson's rule
  • Multiple integral
  • Integral equation
  • List of integrals
Functions Harmonic/Fourier analysis Measure theory Miscellaneous
  • Function
  • Special functions
  • Function composition
  • Implicit function
  • Parametric equation
  • List of types of functions
  • List of mathematical functions
  • Harmonic analysis
  • Fourier analysis
  • Fourier transforms
    • Continuous Fourier transform
    • Fourier series
    • Discrete Fourier transform
    • Discrete-time Fourier transform
  • List of Fourier-related transforms
  • Trigonometric approximation
  • Trigonometric interpolation
  • Orthogonal function
  • List of topics
  • Measure
  • Measurable function
  • Outer measure
  • Inner measure
  • Hausdorff measure
  • Product measure
  • Pushforward measure
  • Lebesgue measure
  • Vector measure
  • Geometric measure theory
  • Functional decomposition
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