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Class of differential equations expressible in differential algebra
In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several
Algebraic differential equation
Algebraic_differential_equation
System of equations in mathematics
a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or
Differential-algebraic system of equations
Differential-algebraic_system_of_equations
Branch of numerical analysis
for the numerical integration of ordinary differential equations (ODEs) and differential algebraic equations (DAEs), to be used. A large number of integration
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Type of functional equation (mathematics)
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions
Differential_equation
Algebraic study of differential equations
equations and differential operators as algebraic objects in view of deriving properties of differential equations and operators without computing the solutions
Differential_algebra
Algebraic equation on which the solution of a differential equation depends
characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-order differential equation or
Characteristic equation (calculus)
Characteristic_equation_(calculus)
Methods used to find numerical solutions of ordinary differential equations
for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Type of differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives
Partial_differential_equation
Differential equation containing derivatives with respect to only one variable
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other
Ordinary differential equation
Ordinary_differential_equation
Study of Galois symmetry groups of differential fields
the structure is that the Galois group in differential Galois theory is an algebraic group, whereas in algebraic Galois theory, it is a profinite group equipped
Differential_Galois_theory
Differential equation that is linear with respect to the unknown function
In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written
Linear_differential_equation
Criterion for integration in terms of elementary functions
Differential algebra – Algebraic study of differential equations Differential Galois theory – Study of Galois symmetry groups of differential fields Elementary
Liouville's theorem (differential algebra)
Liouville's_theorem_(differential_algebra)
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical
List_of_equations
Mathematical notion of infinitesimal difference
mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus
Differential_(mathematics)
Mathematical formula expressing equality
integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, and
Equation
Equation involving both integrals and derivatives of a function
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function. The general first-order, linear
Integro-differential_equation
System where changes of output are not proportional to changes of input
system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear
Nonlinear_system
Differential equations involving stochastic processes
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution
Stochastic differential equation
Stochastic_differential_equation
Topic in algebra
differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set of algebraic equations
Partial differential algebraic equation
Partial_differential_algebraic_equation
Mathematics analytic function
solution of an algebraic differential equation with coefficients in Z {\displaystyle \mathbb {Z} } (the integers) and with algebraic initial conditions
Hypertranscendental_function
Technique for solving differential equations
differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
Separation_of_variables
Result on gamma function
theorem states that the gamma function does not satisfy any algebraic differential equation whose coefficients are rational functions. This result was
Hölder's_theorem
Differential equation exhibiting high rate of dissipation
nonstiff equations, or for differential-algebraic equations. For implicit Runge-Kutta methods applied to the test equation, the differential equation is replaced
Stiff_equation
Type of differential equation
In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function
Riccati_equation
Nonlinear equation which arises on linear optimal control problems
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time
Algebraic_Riccati_equation
A universal differential equation (UDE) is a non-trivial differential algebraic equation with the property that its solutions can approximate any continuous
Universal differential equation
Universal_differential_equation
Type of differential equation subject to a particular solution methodology
mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in
Exact_differential_equation
Concept in differential equation mathematics
In mathematics, in the theory of ordinary differential equations in the complex plane C {\displaystyle \mathbb {C} } , the points of C {\displaystyle \mathbb
Regular_singular_point
Technique of studying linear partial differential equations
Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis
Algebraic_analysis
Group analysis of differential equations is a branch of mathematics that studies the symmetry properties of differential equations with respect to various
Group analysis of differential equations
Group_analysis_of_differential_equations
Type of complex number
if it is not the value at an algebraic point of a function which is the solution of an algebraic differential equation with coefficients in Z [ r ] {\displaystyle
Hypertranscendental_number
Type of mathematical function
function is formalized in differential algebra. A differential field is a field with an extra operation of derivation (algebraic version of differentiation)
Elementary_function
Differential equation for the description of waves or standing wave
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves
Wave_equation
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world
List of nonlinear ordinary differential equations
List_of_nonlinear_ordinary_differential_equations
Partial differential equations with random force terms and coefficients
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary
Stochastic partial differential equation
Stochastic_partial_differential_equation
solutions. Pre-algebra Elementary algebra Boolean algebra Abstract algebra Linear algebra Universal algebra An algebraic equation is an equation involving
Outline_of_algebra
Class of numerical techniques
solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE)
Finite_difference_method
Field-equations in general relativity
tensor allows the EFE to be written as a set of nonlinear partial differential equations when used in this way. The solutions of the EFE are the components
Einstein_field_equations
Type of ordinary differential equation
A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written
Homogeneous differential equation
Homogeneous_differential_equation
In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other
Differential_ideal
Branch of functional analysis
operator algebras are often phrased in algebraic terms, while the techniques used are often highly analytic. Although the study of operator algebras is usually
Operator_algebra
Type of differential operator
partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric pseudo-differential equations in a non-Archimedean
Pseudo-differential_operator
Topics referred to by the same term
program Advection-diffusion equation, a partial differential equation Algebraic differential equation, a kind of differential equation Amsterdam Dance Event
Ade
Manifold or algebraic variety of dimension n in a space of dimension n+1
Jordan–Brouwer separation theorem. An algebraic hypersurface is an algebraic variety that may be defined by a single implicit equation of the form p ( x 1 , … , x
Hypersurface
Type of ordinary differential equation
In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form y ( x ) = x d y d x + f ( d y d x ) {\displaystyle
Clairaut's_equation
Differential algebraic geometry is an area of differential algebra that adapts concepts and methods from algebraic geometry and applies them to systems
Differential algebraic geometry
Differential_algebraic_geometry
Curve defined as zeros of polynomials
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in
Algebraic_curve
Elementary functions and their finitely iterated integrals
solutions of algebraic differential equations, but not conversely. Examples of functions which are solutions of algebraic differential equations but not Liouvillian
Liouvillian_function
Branch of mathematics
of algebraic structures. Within certain algebraic structures, it examines the use of variables in equations and how to manipulate these equations. Algebra
Algebra
Equations with an unknown function under an integral sign
integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals
Integral_equation
Set of equations to be solved together
of linear equations System of nonlinear equations System of bilinear equations System of polynomial equations System of differential equations System of
System_of_equations
Relativistic wave equation in quantum mechanics
where the equation describes the dynamics of spin-0 fields. Mathematically, it is a linear second-order hyperbolic partial differential equation that is
Klein–Gordon_equation
Module over a sheaf of differential operators
relation [∂i, f] = ∂f / ∂xi, thereby relating the Weyl algebra to differential equations. An (algebraic) D-module is, by definition, a left module over the
D-module
Study of differential field extensions induced by linear differential equations
differential equation, using the differential Galois group of the field extension. A major goal is to describe when the differential equation can be solved
Picard–Vessiot_theory
Identity relating to differential equations
Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous
Abel's_identity
Topics referred to by the same term
interpreted as infinitesimals Differential equation, an equation relating derivatives of a function Differential topology Differential (pushforward) The total
Differential
Necessary condition for optimality associated with dynamic programming
The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can
Bellman_equation
Equations describing classical electromagnetism
Maxwell's equations are a set of coupled partial differential equations that describe how electric and magnetic fields are generated by electric charges
Maxwell's_equations
Mathematical descriptions of transmission line voltage and current
The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and current along
Telegrapher's_equations
Basic concepts of algebra
relationships in science and mathematics are expressed as algebraic equations. In mathematics, a basic algebraic operation is a mathematical operation similar to
Elementary_algebra
Method for solving differential equations
series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown
Power series solution of differential equations
Power_series_solution_of_differential_equations
Branch of mathematics
Beside the algebraic properties this enjoys also differential geometric properties. The most obvious construction is that of a Lie algebra which is the
Differential_geometry
Calculus of vector-valued functions
in geometric algebra, as described below. The algebraic (non-differential) operations in vector calculus are referred to as vector algebra, being defined
Vector_calculus
Otherwise, Euler's equation may refer to a non-differential equation, as in these three cases: Euler–Lotka equation, a characteristic equation employed in mathematical
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Finding values for variables that make an equation true
generally algebraic varieties or manifolds. In particular, algebraic geometry may be viewed as the study of solution sets of algebraic equations. The methods
Equation_solving
Mathematical expression using basic operations
{\sqrt {\frac {1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If the
Algebraic_expression
Typically linear operator defined in terms of differentiation of functions
partial differential equations. In differential topology, the exterior derivative and Lie derivative operators have intrinsic meaning. In abstract algebra, the
Differential_operator
equation Hypergeometric differential equation Jimbo–Miwa–Ueno isomonodromy equations Painlevé equations Picard–Fuchs equation to describe the periods
List of named differential equations
List_of_named_differential_equations
Study of rates of change
find the maxima and minima of functions. Equations involving derivatives are called differential equations and are fundamental in describing natural
Differential_calculus
Mathematical model of waves on a shallow water surface
In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow
Korteweg–De_Vries_equation
Formulation of classical mechanics using momenta
without resorting to differential equations, see Lie algebra; a Poisson bracket is the name for the Lie bracket in a Poisson algebra. These Poisson brackets
Hamiltonian_mechanics
Field of mathematics
linear algebraic problems like solving linear systems of equations, locating eigenvalues, or least squares optimisation. Numerical linear algebra's central
Numerical_linear_algebra
In mathematics, a non-algebraic number
number that is not the value at an algebraic point of a function which is the solution of an algebraic differential equation with coefficients in Z [ r ] {\displaystyle
Transcendental_number
Branch of mathematics
theory, harmonic analysis, and the theory of ordinary and partial differential equations. Mathematical analysis formally developed in the 17th century during
Mathematical_analysis
S-shaped curve
exponentially decaying gap. The differential equation derived above is a special case of a general differential equation that only models the sigmoid function
Logistic_function
Partial differential equations whose solutions are instantons
mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on
Yang–Mills_equations
Modern discipline
employing algebraic methods. Secondary calculus acts on the space of solutions of a system of partial differential equations (usually nonlinear equations). When
Secondary calculus and cohomological physics
Secondary_calculus_and_cohomological_physics
Type of ordinary differential equation
In mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form y ′ + P ( x ) y = Q ( x ) y n , {\displaystyle
Bernoulli differential equation
Bernoulli_differential_equation
Characteristic property of holomorphic functions
Cauchy–Riemann equations are two partial differential equations that characterize differentiability of complex functions. The equations are and where u(x
Cauchy–Riemann_equations
Quasilinear first-order ordinary differential equation
classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid
Euler's equations (rigid body dynamics)
Euler's_equations_(rigid_body_dynamics)
Equation that is satisfied for all values of the variables
ISBN (link) The Encyclopedia of Equation Online encyclopedia of mathematical identities (archived) A Collection of Algebraic Identities Archived 2011-10-01
Identity_(mathematics)
Nonlinear partial differential equation
The sine-Gordon equation is a second-order nonlinear partial differential equation for a function φ {\displaystyle \varphi } dependent on two variables
Sine-Gordon_equation
Concept in mathematics
correspondence between abstract algebra (specifically group theory) and mathematical analysis (specifically differential equations). Classically, David Hilbert
Riemann–Hilbert correspondence
Riemann–Hilbert_correspondence
Concepts from linear algebra
context of linear algebra or matrix theory. Historically, however, they arose in the study of quadratic forms and differential equations. In the 18th century
Eigenvalues_and_eigenvectors
Set of partial differential equations on fluid flow
The shallow-water equations (SWE) are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the
Shallow_water_equations
Class of partial differential equations
In mathematical physics and differential geometry, the Euler–Arnold equations are a class of partial differential equations (PDEs) that describe the geodesic
Euler–Arnold_equation
theorem (algebraic topology) Homotopy excision theorem (algebraic topology) Hopf theorem (differential topology) Hurewicz theorem (algebraic topology)
List_of_theorems
French mathematician (1906–1998)
1998) was a French mathematician, who worked on both partial differential equations and algebraic topology. He was born in Chantenay-sur-Loire (today part
Jean_Leray
elements of algebraic structures. Algebraic analysis motivated by systems of linear partial differential equations, it is a branch of algebraic geometry
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Equations that describe the behavior of a physical system
relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics. There are
Equations_of_motion
Relativistic quantum mechanical wave equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including
Dirac_equation
Technique for solving hyperbolic partial differential equations
partial differential equations. The method is to reduce a partial differential equation (PDE) to a family of ordinary differential equations (ODEs) along
Method_of_characteristics
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
Awarded every year by the American Mathematical Society
ISBN 978-0-69114794-9. Evans, Lawrence C. (2010) [1998]. Partial Differential Equations. Graduate Studies in Mathematics. Vol. 19 (2nd ed.). Providence:
Leroy_P._Steele_Prize
Algebra associated to any vector space
Exterior differential systems, Springer-Verlag This book contains applications of exterior algebras to problems in partial differential equations. Rank and
Exterior_algebra
systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms
Integrability conditions for differential systems
Integrability_conditions_for_differential_systems
Mathematical manifold theory
studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given a Riemannian metric on M, every
Hodge_theory
Polynomial equation of degree 3
In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is
Cubic_equation
variety Picard group Modular form Moduli space Modular equation J-invariant Algebraic function Algebraic form Addition theorem Invariant theory Symbolic method
List of algebraic geometry topics
List_of_algebraic_geometry_topics
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ALGEBRAIC DIFFERENTIAL-EQUATION
ALGEBRAIC DIFFERENTIAL-EQUATION
ALGEBRAIC DIFFERENTIAL-EQUATION
ALGEBRAIC DIFFERENTIAL-EQUATION
ALGEBRAIC DIFFERENTIAL-EQUATION
ALGEBRAIC DIFFERENTIAL-EQUATION
ALGEBRAIC DIFFERENTIAL-EQUATION
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ALGEBRAIC DIFFERENTIAL-EQUATION
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