Calculus and analysis
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A
- Abel's identityIdentity relating to differential equations
- Abel's testTest for series convergence
- Absolute convergenceMode of convergence of an infinite series
- Alexander HrennikoffRussian-Canadian structural engineer
- Algebraic analysisAlgebraic analysis is an area of mathematics that deals with systems of linear partial dif
- Alternating seriesInfinite series whose terms alternate in sign
- Alternating series testTest for convergence of alternating series
- AntiderivativeIndefinite integral
- Approximation theoryTheory of getting acceptably close inexact mathematical calculations
- Arithmetico-geometric sequenceMathematical sequence satisfying a specific pattern
- AsymptoteLimit of the tangent line at a point that tends to infinity
- Asymptotic analysisDescription of limiting behavior of a function
- AttractorLimiting set in dynamical systems
B
- Bell seriesIn mathematics, the Bell series is a formal power series used to study properties of arith
- Bernt Michael HolmboeBernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. He wa
- Bifurcation theoryStudy of sudden qualitative behavior changes caused by small parameter changes
- Binomial seriesMathematical series
- Bisection methodAlgorithm for finding a zero of a function
- Boundary value problemType of problem involving ODEs or PDEs
- Branch pointPoint of interest for complex multi-valued functions
- Butterfly effectIdea that small causes can have large effects
C
- Calculus of variationsDifferential calculus on function spaces
- Carathéodory's existence theoremStatement on solutions to ordinary differential equations
- Cauchy condensation testConvergence test for infinite series
- Cauchy principal valueMethod for assigning values to integrals
- Cauchy problemA Cauchy problem in mathematics asks for the solution of a partial differential equation t
- Cauchy sequenceSequence of points that get progressively closer to each other
- Cauchy–Riemann equationsCharacteristic property of holomorphic functions
- Cauchy's integral formulaProvides integral formulas for all derivatives of a holomorphic function
- Cauchy's integral theoremTheorem in complex analysis
- Chain ruleFormula in calculus
- Compact convergenceIn mathematics compact convergence (or uniform convergence on compact sets) is a type of c
- Completeness of the real numbersNonexistence of gaps in the number line
- Complex analysisBranch of mathematics studying functions of a complex variable
- Complex dynamicsBranch of mathematics
- Complex planeGeometric representation of the complex numbers
- Conformal mapMathematical function that preserves angles
- Conservative vector fieldVector field that is the gradient of some function
- Conserved quantityValue remaining constant in a dynamical system
- Constant of integrationConstant expressing ambiguity from indefinite integrals
- Continuous functionMathematical function with no sudden changes
- Contour integrationMethod of evaluating certain integrals along paths in the complex plane
- Convergence testsMathematical criterion about whether a series converges
- Convergent seriesMathematical series with a finite sum
- Convergent Series (short story collection)Convergent Series is a collection of science fiction and fantasy short stories by American
- ConvolutionIntegral expressing the amount of overlap of one function as it is shifted over another
- Convolution theoremTheorem in mathematics
- Crank–Nicolson methodFinite difference method for numerically solving parabolic differential equations
- Critical point (mathematics)Point where the derivative of a function is zero or undefined (in certain cases)
- Curl (mathematics)Circulation density in a vector field
D
- Daniel W. StroockDaniel Wyler Stroock (born March 20, 1940) is an American mathematician, a probabilist. He
- De Moivre's formulaTheorem: (cos x + i sin x)^n = cos nx + i sin nx
- DelVector differential operator
- Delay differential equationType of differential equation
- DerangementType of permutation of a set of elements
- DerivativeInstantaneous rate of change (mathematics)
- Derivative (multivariable calculus)Type of derivative in mathematics
- Differentiable functionMathematical function whose derivative exists
- Differential (mathematics)Mathematical notion of infinitesimal difference
- Differential calculusStudy of rates of change
- Differential equationType of functional equation (mathematics)
- Differential formExpression that may be integrated over a region
- Differential operatorTypically linear operator defined in terms of differentiation of functions
- Differential-algebraic system of equationsSystem of equations in mathematics
- Differentiation of trigonometric functionsMathematical process of finding the derivative of a trigonometric function
- Differentiation rulesRules for computing derivatives of functions
- DifferintegralIn fractional calculus, an area of mathematical analysis, the differintegral is a combined
- Directional derivativeInstantaneous rate of change of the function
- Dirichlet boundary conditionIn mathematics, the Dirichlet boundary condition is imposed on an ordinary or partial diff
- Dirichlet problemProblem of solving a partial differential equation subject to prescribed boundary values
- Dirichlet seriesMathematical series
- Dirichlet's testTest for series convergence
- Disc integrationIntegration method to calculate volume
- Discrete-time Fourier transformFourier analysis technique applied to sequences
- DivergenceVector operator in vector calculus
- Divergence theoremTheorem in calculus
- Divergent seriesInfinite series that is not convergent
- Dynamical system simulationComputer modeling of time-varying behavior of a dynamical system
E
- Edge of chaosTransition space between order and disorder
- Edwin HewittEdwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) was an American mathe
- Elliptic operatorType of differential operator
- Elliptic partial differential equationClass of partial differential equations
- Euler methodApproach to finding numerical solutions of ordinary differential equations
- Euler substitutionMethod of integration for rational functions
- Euler's factorization methodEuler's factorization method is a technique for factoring a number by writing it as a sum
- Euler's formulaComplex exponential in terms of sine and cosine
- Euler's identityMathematical equation linking e, i and π
- Exponential stabilityContinuous-time linear system with only negative real parts
- Extended real number lineReal numbers with + and - infinity added
- Extreme value theoremContinuous real function on a closed interval has a maximum and a minimum
F
- Faà di Bruno's formulaGeneralized chain rule in calculus
- Fast Fourier transformDiscrete Fourier transform algorithm
- Fibonacci sequenceNumbers obtained by adding the two previous ones
- Finite element methodNumerical method for solving physical or engineering problems
- Finite impulse responseType of filter in signal processing
- Finite volume methodMethod for representing and evaluating partial differential equations
- FK-spaceIn functional analysis and related areas of mathematics a FK-space or Fréchet coordinate s
- Floquet theoryBranch of ordinary differential equations
- Flow (mathematics)Motion of particles in a fluid
- Fourier analysisBranch of mathematics
- Fourier seriesDecomposition of periodic functions
- Fourier transformMathematical transform that expresses a function of time as a function of frequency
- Fractional calculusBranch of mathematical analysis
- Fubini's theoremConditions for switching order of integration in calculus
- Function approximationApproximating an arbitrary function with a well-behaved one
- Functional analysisArea of mathematics
- Functional differential equationA functional differential equation is a differential equation with deviating argument. Tha
- Fundamental theorem of calculusRelationship between derivatives and integrals
G
- Galerkin methodMethod for solving continuous operator problems (such as differential equations)
- Gateaux derivativeIn mathematics, the Gateaux differential or Gateaux derivative is a generalization of the
- General Dirichlet seriesIn the field of mathematical analysis, a general Dirichlet series is an infinite series th
- General Leibniz ruleGeneralization of the product rule in calculus
- Generalizations of the derivativeFundamental construction of differential calculus
- Generalized functionObjects extending the notion of functions
- Generating functionFormal power series
- Geometric calculusInfinitesimal calculus on functions defined on a geometric algebra
- Geometric seriesSum of an (infinite) geometric progression
- GradientMultivariate derivative (mathematics)
- Gradient theoremEvaluates a line integral through a gradient field using the original scalar field
- Green's functionMethod of solution to differential equations
- Green's theoremTheorem in calculus relating line and double integrals
H
- Harmonic analysisArea of mathematical analysis
- Harmonic functionFunctions in mathematics
- Harmonic series (mathematics)Divergent sum of positive unit fractions
- Heaviside cover-up methodMethod for partial-fraction expansion
- Helmholtz decompositionCertain vector fields are the sum of an irrotational and a solenoidal vector field
- Hessian matrixMatrix of second derivatives
- Hilbert spaceType of vector space in math
- Hölder's inequalityInequality between integrals in Lp spaces
- Holomorphic functionComplex-differentiable (mathematical) function
- Homogeneous differential equationType of ordinary differential equation
- Hörmander's conditionIn mathematics, Hörmander's condition is a property of vector fields that, if satisfied, h
- Hyperbolic partial differential equationType of partial differential equations
I
- Ideal pointIn hyperbolic geometry, an ideal point, omega point or point at infinity is a well-defined
- Implicit differentiationMathematical operation in calculus
- Improper integralConcept in mathematical analysis
- Indeterminate formExpression in mathematical analysis
- Infinite element methodThe infinite element method is a numerical method for solving problems of engineering and
- InfinitesimalExtremely small quantity in calculus; thing so small that there is no way to measure it
- Infinity symbolMathematical symbol representing infinity
- Inflection pointPoint where the curvature of a curve changes sign
- Initial conditionParameter in differential equations and dynamical systems
- Initial value problemType of calculus problem
- Integer sequenceOrdered list of whole numbers
- IntegralOperation in calculus
- Integral of inverse functionsMathematical theorem, used in calculus
- Integral test for convergenceTest for infinite series of monotonous terms for convergence
- Integral transformMapping involving integration between function spaces
- Integrating factorTechnique for solving differential equations
- Integration BeeAnnual integral calculus competition
- Integration by partsMathematical method in calculus
- Integration by reduction formulaeIntegration technique using recurrence relations
- Integration by substitutionTechnique in integral evaluation
- Integration using Euler's formulaUse of complex numbers to evaluate integrals
- Integro-differential equationEquation involving both integrals and derivatives of a function
- Interior productIn mathematics, the interior product (also known as interior derivative, interior multipli
- Intermediate value theoremContinuous function on an interval takes on every value between its values at the ends
- InterpolationMethod for estimating new data within known data points
- Interval (mathematics)All numbers between two given numbers
- Inverse function ruleFormula for the derivative of an inverse function
- Isolated singularityHas no other singularities close to it
- Iterated functionIn mathematics, an iterated function is a function that is obtained by composing another f
- Iterated integralType of integral of functions of multiple variables
J
L
- L'Hôpital's ruleMathematical rule for evaluating limits
- Lagrange multiplierMethod to solve constrained optimization problems
- Laplace operatorDifferential operator in mathematics
- Laplace transformIntegral transform useful in probability theory, physics, and engineering
- Laplace's equationSecond-order partial differential equation
- Laurent seriesPower series with negative powers
- Lebesgue integralMethod of mathematical integration
- Leibniz's notationMathematical notation used for calculus
- Lev SchnirelmannLev Genrikhovich Schnirelmann (also Shnirelman, Shnirel'man; Лев Ге́нрихович Шнирельма́н;
- Limit comparison testMethod of testing for the convergence of an infinite series
- Limit cycleBehavior in a nonlinear system
- Limit of a functionPoint to which functions converge in analysis
- Limit of a sequenceValue to which an infinite sequence tends
- Limit of distributionsIn mathematics, specifically in the theory of generalized functions, the limit of a sequen
- Limits of integrationUpper and lower limits applied in definite integration
- Lindemann–Weierstrass theoremTheorem in transcendental number theory
- Line integralDefinite integral of a scalar or vector field along a path
- Linear approximationApproximation of a function by its tangent line at a point
- Linear differential equationDifferential equation that is linear with respect to the unknown function
- Linear dynamical systemType of mathematical system
- LinearizationFinding linear approximation of function at given point
- Liouville's formulaIn mathematics, Liouville's formula, also known as the Abel–Jacobi–Liouville identity, is
- Liouville's theorem (complex analysis)Theorem in complex analysis
- Logarithmic differentiationMethod of mathematical differentiation
- Lp spaceFunction spaces generalizing finite-dimensional p norm spaces
- Lyapunov exponentRate of separation of infinitesimally close trajectories
- Lyapunov functionIn the theory of ordinary differential equations (ODEs), Lyapunov functions, named after A
M
- Malliavin calculusMathematical techniques used in probability theory and related fields
- Matrix calculusSpecialized notation for multivariable calculus
- Maximal functionMaximal functions appear in many forms in harmonic analysis (an area of mathematics). One
- Maximum and minimumLargest and smallest value taken by a function at a given point
- Maximum modulus principleMathematical theorem in complex analysis
- Maximum principleIn the mathematical fields of differential equations and geometric analysis, the maximum p
- Mean value theoremTheorem in mathematics
- Measure (mathematics)Generalization of mass, length, area and volume
- Measure spaceA measure space is a basic object of measure theory, a branch of mathematics that studies
- Meromorphic functionClass of mathematical function
- Method of characteristicsTechnique for solving hyperbolic partial differential equations
- Method of linesNumerical method
- Method of undetermined coefficientsMethod of solution for inhomogeneous ODEs
- Midpoint methodIn numerical analysis, a branch of applied mathematics, the midpoint method is a one-step
- Multibody systemTool to study dynamic behavior of interconnected rigid or flexible bodies
- Multiple integralGeneralization of definite integrals to functions of multiple variables
- Multipole expansionMathematical series
- Multivariable calculusCalculus of functions of several variables
N
- Nabla symbolSymbol used to indicate the del operator
- Nevanlinna theoryArea of mathematics
- Newton's methodAlgorithm for finding zeros of functions
- Nikolai LuzinRussian mathematician
- Nonelementary integralIntegrals not expressible in closed-form from elementary functions
- Nonlinear systemSystem where changes of output are not proportional to changes of input
- Nonstandard analysisCalculus using a logically rigorous notion of infinitesimal numbers
- Notation for differentiationNotation of differential calculus
- Number lineLine formed by the real numbers
- Numerical analysisMethods for numerical approximations
- Numerical methods for ordinary differential equationsMethods used to find numerical solutions of ordinary differential equations
- Numerical methods for partial differential equationsBranch of numerical analysis
- Numerical Methods for Partial Differential EquationsNumerical Methods for Partial Differential Equations is a bimonthly peer-reviewed scientif
O
- Open mapping theorem (complex analysis)Theorem on holomorphic functions
- Operator (mathematics)Function acting on function spaces
- Operator theoryMathematical study of linear operators
- Order of integration (calculus)Order in which multiple or iterated integrals are computed
- Ordinary differential equationDifferential equation containing derivatives with respect to only one variable
P
- Parabolic partial differential equationClass of second-order linear partial differential equations
- Parallelogram lawSides and diagonals have equal sums of squares
- Partial derivativeDerivative of a function with multiple variables
- Partial differential equationType of differential equation
- Paul MalliavinPaul Malliavin (French: ; September 10, 1925 – June 3, 2010) was a French mathematician wh
- Peano existence theoremTheorem regarding the existence of a solution to a differential equation
- Periodic boundary conditionsConcept in molecular modelling
- Petrov–Galerkin methodMathematical method
- Phase portraitPlot of a dynamical system's trajectories in phase space
- Phase spaceSpace of all possible states that a system can take
- Picard theoremTheorem about the range of an analytic function
- Point at infinityConcept in geometry
- Pointwise productIn mathematics, the pointwise product of two functions is another function, obtained by mu
- Poisson's equationElliptic partial differential equation
- Potential theoryHarmonic functions as solutions to Laplace's equation
- Power ruleMethod of differentiating single-term polynomials
- Power seriesInfinite sum of monomials
- Power series solution of differential equationsMethod for solving differential equations
- PrecalculusCourse designed to prepare students for calculus
- Product ruleFormula for the derivative of a product
- Proof that e is irrationalThe number e was introduced by Jacob Bernoulli in 1683. More than half a century later, Eu
Q
R
- Radius of convergenceDomain of convergence of power series
- Ratio testCriterion for the convergence of a series
- Real analysisMathematics of real numbers and real functions
- Reduction of orderTechnique for solving linear ordinary differential equations
- Regula falsiNumerical method used to approximate solutions of univariate equations
- Related ratesProblems that make use of the relations to rates of change
- Residue (complex analysis)Attribute of a mathematical function
- Residue number systemA residue numeral system (RNS) is a numeral system representing integers by their values m
- Residue theoremConcept of complex analysis
- Ricci calculusTensor index notation for tensor-based calculations
- Riemann integralBasic integral in elementary calculus
- Riemann mapping theoremMathematical theorem
- Riemann sphereModel of the extended complex plane plus a point at infinity
- Riemann sumApproximation technique in integral calculus
- Riemann surfaceOne-dimensional complex manifold
- Risch algorithmMethod for evaluating indefinite integrals
- Robin boundary conditionType of boundary condition in mathematics
- Rolle's theoremTheorem in real analysis
- Root of unityNumber with an integer power equal to 1
- Root testCriterion for the convergence of an infinite series
- Root-finding algorithmAlgorithms for zeros of functions
- Rotor (mathematics)A rotor is an object in the geometric algebra (also called Clifford algebra) of a vector s
- Runge–Kutta methodsFamily of implicit and explicit iterative methods
S
- Saddle pointCritical point on a surface graph which is not a local extremum
- Scalar fieldAssignment of numbers to points in space
- Schanuel's conjectureMajor unsolved problem in transcendental number theory
- Schwarz lemmaStatement in complex analysis
- Secant lineLine that intersects a curve at least twice
- Secant methodRoot-finding method
- Second derivativeMathematical operation
- Separation of variablesTechnique for solving differential equations
- SequenceFinite or infinite ordered list of elements
- Sequence spaceVector space of infinite sequences
- Series expansionExpression of a function as an infinite sum of simpler functions
- Shell integrationMethod for calculating the volume of a solid of revolution
- Shooting methodMethod for solving boundary value problems
- Signed areaArea interpreted positively or negatively
- Singularity (mathematics)Point where a mathematical object behaves irregularly
- Solenoidal vector fieldVector field with zero divergence
- Sparse matrixMatrix in which most of the elements are zero
- Special functionsMathematical functions having established names and notations
- Squeeze theoremMethod for finding limits in calculus
- Stability theoryPart of mathematics that addresses the stability of solutions
- Stationary pointZero of the derivative of a function
- Stochastic calculusCalculus on stochastic processes
- Stochastic partial differential equationPartial differential equations with random force terms and coefficients
- Stokes' theoremTheorem in vector calculus
- Sturm–Liouville theoryClass of ordinary differential equations
- Sturm's theoremIn mathematics, the Sturm sequence of a univariate polynomial p is a sequence of polynomia
- SummationAddition of several numbers or other values
- Summation by partsIn mathematics, summation by parts transforms the summation of products of sequences into
- Surface integralIntegration over a non-flat region in 3D space
- Symmetry of second derivativesMathematical theorem
- System of differential equationsGroup of differential equations
T
- Tangent half-angle substitutionChange of variable for integrals involving trigonometric functions
- Tatsujiro ShimizuTatsujiro Shimizu (清水 辰次郎, Shimizu Tatsujirō, 7 April 1897 – 8 November 1992) was a Japane
- Taylor seriesMathematical approximation of a function
- Taylor's theoremApproximation of a function by a polynomial
- Tensor calculusIn mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vec
- Three-body problemPhysics problem related to laws of motion and gravity
- Time derivativeDerivative of a function with respect to time
- Time evolutionTime evolution is the change of state brought about by the passage of time, applicable to
- Trigonometric substitutionTechnique of integral evaluation
- Types of meshA mesh is a representation of a larger geometric domain by smaller discrete cells. Meshes
U
V
W
- Walther RitzWalther Heinrich Wilhelm Ritz (22 February 1878 – 7 July 1909) was a Swiss theoretical phy
- WaveletFunction for integral Fourier-like transform
- Weierstrass factorization theoremTheorem in complex analysis
- Well-posed problemProperty of differential equations describing physical phenomena
- WronskianDeterminant of the matrix of first derivatives of a set of functions