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Mathematical analysis

Approximation theory
Theory of getting acceptably close inexact mathematical calculations
Asymptote
In geometry, limit of the tangent at a point that tends to infinity
Asymptotic analysis
Description of limiting behavior of a function
Bisection method
Algorithm for finding a zero of a function
Branch point
Point of interest for complex multi-valued functions
Calculus of variations
Differential calculus on function spaces (e.g. spaces of curves, etc.)
Cauchy principal value
Method for assigning values to certain improper integrals which would otherwise be undefined
Cauchy–Riemann equations
Conditions required of holomorphic (complex differentiable) functions
Cauchy's integral formula
Provides integral formulas for all derivatives of a holomorphic function
Complex analysis
Branch of mathematics studying functions of a complex variable
Complex plane
Geometric representation of the complex numbers
Conformal map
Mathematical function that preserves angles
Contour integration
A method of evaluating certain integrals along paths in the complex plane
Convolution theorem
Theorem that under suitable conditions the Fourier transform of a convolution of two signals is the pointwise product of their Fourier transforms
Euler's formula
Complex exponential in terms of sine and cosine
Euler's identity
E^(iπ) + 1 equals 0
Extended real number line
Real numbers with +∞ and −∞ added
Extreme value theorem
A continuous real function on a closed interval has a maximum and a minimum
Fast Fourier transform
Discrete Fourier transform algorithm
Fourier analysis
Branch of mathematics
Fourier series
Decomposition of periodic functions into sums of simpler sinusoidal forms
Fourier transform
Mathematical transform that expresses a function of time as a function of frequency
Functional analysis
Branch of mathematical analysis
Harmonic analysis
Study of superpositions in mathematics
Harmonic conjugate
Concept in mathematics
Harmonic function
Functions in mathematics
Hilbert space
Mathematical generalization of Euclidean space to infinite dimensions
Holomorphic function
Complex functions differentiable everywhere on their domains
Intermediate value theorem
A continuous function on an interval takes on every value between its values at the ends
Interpolation
Method for estimating new data within known data points
Laplace transform
Integral transform useful in probability theory, physics, and engineering
Liouville's theorem (complex analysis)
Theorem in complex analysis
Mathematical analysis
Branch of mathematics
Mean value theorem
On the existence of a tangent to an arc parallel to the line through its endpoints
Measure (mathematics)
Generalization of length, area, volume and integral
Newton's method
Algorithm for finding a zero of a function
Number line
Line that represents the real numbers
Numerical analysis
Field of mathematics
Picard theorem
Theorem
Potential theory
Branch of mathematic studying harmonic functions
Real analysis
Mathematics of real numbers and real functions
Regula falsi
Numerical method used to approximate solutions of univariate equations
Residue (complex analysis)
Coefficient of the term of order −1 in the Laurent expansion of a function holomorphic outside a point, whose value can be extracted by a contour integral
Residue theorem
Concept of complex analysis
Riemann sphere
Model of the extended complex plane plus a point at infinity
Riemann surface
One-dimensional complex manifold
Root of unity
Number that has an integer power equal to 1
Root-finding algorithm
Algorithms for finding roots of continuous functions
Secant method
Root-finding method
Singularity (mathematics)
Point where a function, a curve or another mathematical object does not behave regularly
Squeeze theorem
On calculating limits by bounding a function between two other functions
Zeros and poles
Concept in complex analysis