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Calculus and analysis

Absolute convergence
Mode of convergence of an infinite series
Antiderivative
Indefinite integral
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
Attractor
Concept in dynamical systems
Bifurcation theory
Study of sudden qualitative behavior changes caused by small parameter changes
Binomial series
Taylor series
Bisection method
Algorithm for finding a zero of a function
Boundary value problem
Differential equation together with a set of additional constraints (boundary conditions)
Branch point
Point of interest for complex multi-valued functions
Butterfly effect
Idea that small causes can have large effects
Calculus
Branch of mathematics
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
Chain rule
For derivatives of composed functions
Change of variables (PDE)
Technique in partial differential evaluation
Chaos theory
Field of mathematics
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
Conservative vector field
Vector field that is the gradient of some function
Conserved quantity
Value remaining constant in a dynamical system
Constant of integration
Constant expressing ambiguity from indefinite integrals
Continuous function
Mathematical function with no sudden changes in value
Contour integration
A method of evaluating certain integrals along paths in the complex plane
Control theory
Branch of engineering and mathematics
Convergence tests
Mathematical criterion about whether a series converges
Convergent series
Infinite series that produces a finite sum
Convolution theorem
Theorem that under suitable conditions the Fourier transform of a convolution of two signals is the pointwise product of their Fourier transforms
Crank–Nicolson method
Finite difference method for numerically solving parabolic differential equations
Curl (mathematics)
Vector operator describing circulation density at a point in a 3D vector field
Del
Vector differential operator
Derivative
Operation in calculus
Differentiable function
Mathematical function whose derivative exists
Differential (mathematics)
Infinitesimal quantity in calculus
Differential calculus
Area of mathematics; subarea of calculus
Differential equation
Mathematical equation involving derivatives of an unknown function
Differential form
Expression that may be integrated over a region
Differential operator
Typically linear operator defined in terms of differentiation of functions
Differentiation of trigonometric functions
Mathematical process of finding the derivative of a trigonometric function
Differentiation rules
Wikimedia list article with rules for computing the derivative of a function in calculus
Directional derivative
Instantaneous rate of change of the function
Dirichlet problem
Problem of finding a function which solves a specified partial differential equation
Dirichlet series
Mathematical series
Divergence
Vector operator that measures how much a field vector is growing or fading
Divergence theorem
Theorem in calculus which relates the flux of closed surfaces to divergence over their volume
Divergent series
Infinite series that is not convergent
Dynamical system
Mathematical model which describes the time dependence of a point in a geometrical space
Dynamical system simulation
Computer modeling of time-varying behavior of a dynamical system
Dynamical systems theory
Area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations
Edge of chaos
Transition space between order and disorder
Elliptic operator
Type of differential operator
Elliptic partial differential equation
Class of partial differential equations
Euler method
An explicit, first-order method for numerically solving ordinary differential equations
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
Finite element method
Numerical method for solving physical or engineering problems
Flow (mathematics)
Mathematical formalization of the motion of particles in a fluid
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
Fundamental theorem of calculus
Links derivatives and integrals
Generalized Stokes theorem
Statement about the integration of differential forms on manifolds
Generating function
Formal power series; coefficients encode information about a sequence indexed by natural numbers
Geometric series
Sum of an (infinite) geometric progression
Gradient
Multi-variable generalization of the derivative of a function
Gradient theorem
Evaluates a line integral through a gradient field using the original scaler field
Green's theorem
Theorem in calculus relating line and double integrals
Harmonic analysis
Study of superpositions in mathematics
Harmonic conjugate
Concept in mathematics
Harmonic function
Functions in mathematics
Harmonic series (mathematics)
Infinite series of the reciprocals of the positive integers
Helmholtz decomposition
Certain vector fields are the sum of an irrotational and a solenoidal vector field
Hilbert space
Mathematical generalization of Euclidean space to infinite dimensions
Holomorphic function
Complex functions differentiable everywhere on their domains
Homogeneous differential equation
Mathematical relation with derivatives
Hyperbolic partial differential equation
Partial differential equation (PDE) of order n that has a well-posed initial value problem for the first n−1 derivatives
Improper integral
Limit of a definite integral with as one or both limits approach infinity or values at which the integrand is undefined
Indeterminate form
Term in mathematical analysis
Infinitesimal
Extremely small quantity in calculus; thing so small that there is no way to measure it
Infinity
Mathematical concept
Initial condition
Parameter in differential equations and dynamical systems
INTEGRAL
European gamma-ray space observatory for general astronomy; medium-class mission in the ESA Science Programme
Integrating factor
Function that is commonly used to solve ordinary differential equations
Integration by parts
Mathematical method in calculus
Integration by substitution
Technique in integral evaluation
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
Iterated integral
Type of integral of functions of multiple variables
Jacobian matrix and determinant
Matrix of all first-order partial derivatives of a vector-valued function
Lagrange multiplier
A method to solve constrained optimization problems
Laplace operator
Differential operator
Laplace transform
Integral transform useful in probability theory, physics, and engineering
Laplace's equation
Second order partial differential equation
Laurent series
Power series generalized to allow negative powers
Lebesgue integral
Method of integration
L'Hôpital's rule
Mathematical rule for evaluating certain limits
Limit (mathematics)
Value that a function or sequence "approaches" as the input or index approaches some value
Limit cycle
Behavior in a nonlinear system
Limit of a sequence
Value that the terms of a sequence "tend to"
Limits of integration
Upper and lower limits applied in definite integration
Line integral
Definite integral of a scalar or vector field along a path
Linear approximation
Approximation of a function by its tangent line at a point
Linear differential equation
Differential equations that are linear with respect to the unknown function and its derivatives
Linear dynamical system
Type of mathematical system
Linearization
Finding linear approximation of function at given point
Liouville's theorem (complex analysis)
Theorem in complex analysis
Lyapunov exponent
The rate of separation of infinitesimally close trajectories
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
Method of lines
Numerical method for solving partial differential equations
Multibody system
A tool to study dynamic behavior of interconnected rigid or flexible bodies;
Multiple integral
Generalization of definite integrals to functions of multiple variables
Multipole expansion
Mathematical series approximating an angle-dependent function
Multivariable calculus
Calculus of functions of several independent variables
Newton's method
Algorithm for finding a zero of a function
Nonlinear system
System where changes of output are not proportional to changes of input
Number line
Line that represents the real numbers
Numerical analysis
Field of mathematics
Numerical integration
Family of algorithms for finding the definite integral of a function
Numerical methods for ordinary differential equations
Methods used to find numerical solutions of ordinary differential equations
Numerical Methods for Partial Differential Equations
Academic journal
Ordinary differential equation
Differential equation containing derivatives with respect to only one variable
Parabolic partial differential equation
Class of second-order linear partial differential equations
Partial derivative
Derivative of a function of several variables with respect to one variable, with the others held constant
Partial differential equation
Multivariable functions and their partial derivatives
Phase space (disambiguation)
Topics referred to by the same term
Picard theorem
Theorem
Poisson's equation
elliptic partial differential equation
Potential theory
Branch of mathematic studying harmonic functions
Power rule
Method of differentiating single term polynomials
Power series
Infinite sum of monomials
Power series solution of differential equations
Method for solving differential equations
Product rule
Formula for the derivative of a product
Radius of convergence
Mathematical concept
Real analysis
Mathematics of real numbers and real functions
Regula falsi
Numerical method used to approximate solutions of univariate equations
Related rates
Problems that make use of the relations to rates of change
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
Ricci calculus
Extension of vector calculus to tensors
Riemann integral
Basic Integral in Elementary Calculus
Riemann sphere
Model of the extended complex plane plus a point at infinity
Riemann sum
Approximation technique in integral calculus
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
Runge–Kutta methods
Family of implicit and explicit iterative methods
Secant method
Root-finding method
Second derivative
Mathematical operation
Separation of variables
Technique for solving differential equations
Sequence
Finite or infinite ordered list of elements
Series (mathematics)
Infinite sum
Series expansion
Concept in mathematics
Shooting method
Method for solving boundary value problems
Singularity (mathematics)
Point where a function, a curve or another mathematical object does not behave regularly
Solenoidal vector field
Vector field with zero divergence
Squeeze theorem
On calculating limits by bounding a function between two other functions
Stability theory
Part of mathematics that addresses the stability of solutions
Summation
Addition of a finite sequence of numbers
Surface integral
Integration over a non-flat region in 3D space
System of differential equations
Group of differential equations
Taylor series
Expression of a function as an infinite sum
Taylor's theorem
Approximation of a function by a truncated power series
Three-body problem
Physics problem related to laws of motion and gravity
Total derivative
Derivative of a function of several variables with respect to one variable, without the others held constant
Vector calculus
Calculus of vector-valued functions
Vector field
Assignment of a vector to each point in a subset of Euclidean space
Volume integral
Integral over a 3-D domain
Zeros and poles
Concept in complex analysis