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Equations with an unknown function under an integral sign
analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus
Integral_equation
In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and
Fredholm_integral_equation
Operator equation in the style of Fredholm theory
In mathematics, the Volterra integral equations are a special type of integral equations, named after Vito Volterra. They are divided into two groups
Volterra_integral_equation
Mapping involving integration between function spaces
representations. An integral transform "maps" an equation from its original "domain" into another domain, in which manipulating and solving the equation may be much
Integral_transform
Integral equation
In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted
Rendering_equation
Equation used in quantum scattering problems
the Lippmann–Schwinger equation must be written as an integral equation. For scattering problems, the Lippmann–Schwinger equation is often more convenient
Lippmann–Schwinger_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
Numerical method in computational electromagnetics
frequency-domain method, it involves the projection of an integral equation into a system of linear equations by the application of appropriate boundary conditions
Method of moments (electromagnetics)
Method_of_moments_(electromagnetics)
Term in mathematics
an integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. Integral curves
Integral_curve
Curve for which the time to roll to the end is equal for all starting points
{1}{\sqrt {y_{0}-y}}}{\frac {d\ell }{dy}}\,dy} This is called Abel's integral equation and allows us to compute the total time required for a particle to
Tautochrone_curve
Equation describing the transport of some quantity
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when
Continuity_equation
Differential equations involving stochastic processes
introduced the concept of stochastic integral and initiated the study of nonlinear stochastic differential equations. Another approach was later proposed
Stochastic differential equation
Stochastic_differential_equation
Formulation of quantum mechanics
equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows
Path-integral_formulation
One of Fredholm's theorems in mathematics
expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states
Fredholm_alternative
Type of functional equation (mathematics)
contains integrals. An integro-differential equation (IDE) is an equation that combines aspects of a differential equation and an integral equation. A stochastic
Differential_equation
Calculation of electric field generated by current distribution
The electric-field integral equation is a relationship that allows the calculation of an electric field (E) generated by an electric current distribution
Electric-field integral equation
Electric-field_integral_equation
Mathematical formula expressing equality
An integral equation is a functional equation involving the antiderivatives of the unknown functions. For functions of one variable, such an equation differs
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
Operation in calculus
portal Integral equation – Equations with an unknown function under an integral sign Integral symbol – Mathematical symbol used to denote integrals and antiderivatives
Integral
Mathematical theory of integral equations
theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader
Fredholm_theory
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
Method of solving integral equations
quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The continuous problem
Nyström_method
Generalisation of the exponential integral to non-commutative algebras
[a](0)&=1.\end{aligned}}} The ordered exponential is the solution to the integral equation: OE [ a ] ( t ) = 1 + ∫ 0 t a ( t ′ ) OE [ a ] ( t ′ ) d t ′
Ordered_exponential
Fredholm theory of integral equations. There are several closely related theorems, which may be stated in terms of integral equations, in terms of linear
Fredholm's_theorem
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
Complex-valued function
. Now, to convert this to integral equations, a matrix becomes a kernel, and a summation over indices becomes an integral over coordinates. The above
Fredholm_determinant
Equation for two-body bound states
The Bethe–Salpeter equation (BSE, named after Hans Bethe and Edwin Salpeter) is an integral equation, the solution of which describes the structure of
Bethe–Salpeter_equation
Special function defined by an integral
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied
Elliptic_integral
Equation in statistical mechanics
In statistical mechanics, the Ornstein–Zernike (OZ) equation is an integral equation introduced by Leonard Ornstein and Frits Zernike that relates different
Ornstein–Zernike_equation
Method for solving certain nonlinear partial differential equations
nonlinear partial differential equation to solving 2 linear ordinary differential equations and an ordinary integral equation, a method ultimately leading
Inverse_scattering_transform
Computer programs that solve Maxwell's equations
nearly O(n) growth in storage and solution time to integral equation methods. Sparsified integral equation techniques are typically used in the IC industry
Electromagnetic_field_solver
Integral equation
from which the potential can be read off. This equation is derived from the Gelfand–Levitan integral equation, using the Povzner–Levitan representation. Suppose
Marchenko_equation
Description of a quantum-mechanical system
the path integral formulation, developed chiefly by Richard Feynman. When these approaches are compared, the use of the Schrödinger equation is sometimes
Schrödinger_equation
Physical quantity of dimension energy × time
states that the differential equations of motion for any physical system can be re-formulated as an equivalent integral equation. Thus, there are two distinct
Action_(physics)
Second-order partial differential equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its
Laplace's_equation
Split of materials or structures under stress
used computational numerical methods are finite element and boundary integral equation methods. Other methods include stress and displacement matching, element
Fracture
Optical filter
it additionally employs the method of moments to produce a surface integral equation, it is significantly more efficient both in terms of the number of
Frequency_selective_surface
Concept in the theory of integral equations
that results from applying the resolvent formalism to solve Fredholm integral equations in Fredholm theory. The Liouville–Neumann series is defined as ϕ (
Liouville–Neumann_series
Hungarian mathematician
He made significant contributions to analysis, algebra, geometry, integral equations and many other fields that pertain to his interests. István Fenyő
István_Fenyő
Method of solving linear partial differential equations
This is accomplished by re-formulating the PDEs as integral equations (i.e. in boundary integral form). This reduces the calculation of the larger volume
Boundary_element_method
Partial differential equation
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas
Burgers'_equation
Methods used to find numerical solutions of ordinary differential equations
although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
History of radiation-based medical imaging
it was necessary to formulate an integral equation that accounted for the setup's geometry. Given the line integrals of a function f ( x , y ) {\displaystyle
History of computed tomography
History_of_computed_tomography
Integral equation in quantum simulations
Nakajima–Zwanzig equation (named after the physicists who developed it, Sadao Nakajima and Robert Zwanzig) is an integral equation describing the time
Nakajima–Zwanzig_equation
Equation composed of a function being summed
In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories
Summation_equation
Integral used in physics
used to formulate stochastic differential equations (SDEs), which are really equations about stochastic integrals. It is compatible with the notation from
Stratonovich_integral
Integral transform useful in probability theory, physics, and engineering
differential equations and dynamical systems by replacing ordinary differential equations and integral equations with algebraic polynomial equations, and by
Laplace_transform
Equation used in demography
number of births in this cohort, which suggest the following Volterra integral equation for B: B ( t ) = ∫ 0 t B ( t − a ) ℓ ( a ) b ( a ) d a . {\displaystyle
Euler–Lotka_equation
Mathematical concept
potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on
Poisson_kernel
Concept in classical electromagnetism
constitutive equation: B = μ0H in non-magnetic materials where μ0 is the magnetic constant. The integral form of the original circuital law is a line integral of
Ampère's_circuital_law
Double integral Vitali set, non-measurable set Henstock–Kurzweil integral Amenable group Banach–Tarski paradox Hausdorff paradox Fredholm equation Fredholm
List of integration and measure theory topics
List_of_integration_and_measure_theory_topics
Branch of mathematical analysis
Riemann–Liouville fractional derivative and integral has multiple applications, such as in case of solutions to the equation in the case of multiple systems such
Fractional_calculus
Branch of mathematics
information such as the evolution of a system, a differential or integral equation, or a quantum state or observable. The spectral theory of operators
Mathematical_analysis
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
Eigenvalue problem for the Laplace operator
integral transforms, such as the Laplace or Fourier transform, are often used to transform a hyperbolic PDE into a form of the Helmholtz equation. Because
Helmholtz_equation
Mathematical equation describing the motion of a rocket
The classical rocket equation, Tsiolkovsky rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that
Tsiolkovsky_rocket_equation
Mathematical nomenclature
In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous
Sides_of_an_equation
Branch of probability theory
The renewal function satisfies a recursive integral equation, the renewal equation. The key renewal equation gives the limiting value of the convolution
Renewal_theory
Scientific journal
Integral Equations and Operator Theory is a peer-reviewed scientific journal published quarterly by Springer Science+Business Media. Established in 1978
Integral Equations and Operator Theory
Integral_Equations_and_Operator_Theory
Foundational law of electromagnetism relating electric field and charge distributions
Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the distribution
Gauss's_law
Partial differential equation
mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability
Fokker–Planck_equation
Dimensionless astrophysics equation
In astrophysics, the Lane–Emden equation is a dimensionless form of Poisson's equation for the gravitational potential of a Newtonian self-gravitating
Lane–Emden_equation
Mathematical method extending convergence
Integral equations containing Hadamard finite part integrals (with f (t) unknown) are termed hypersingular integral equations. Hypersingular integral
Hadamard_regularization
Indian mathematician
and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001, 341pp. R.P. Agarwal, M. Meehan and D. O’Regan, Nonlinear Integral Equations and Inclusions
Ravi_Agarwal
Markovian quantum master equation for density matrices (mixed states)
master equation, master equation in Lindblad form, quantum Liouvillian, or Lindbladian is one of the general forms of Markovian master equations describing
Lindbladian
This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Scottish mathematician
'Expansion Theorems for Solution of a Fredholm's Linear Homogeneous Integral Equation of the Second Kind with Kernel of Special Non-Symmetric Type' and
Eleanor_Pairman
Equations of motion for viscous fluids
Navier–Stokes equations (/nævˈjeɪ ˈstoʊks/ nav-YAY STOHKS) describe the motion of viscous fluids. This system of partial differential equations was named
Navier–Stokes_equations
Branch of physics
targets of arbitrary geometry. The formulation is based on integral form of Maxwell equations. The DDA is an approximation of the continuum target by a
Computational electromagnetics
Computational_electromagnetics
English physicist and mathematician
algorithm. He also derived the first equation for the current in a wire antenna, Pocklington's integral equation. "Pocklington's test". Archived from
Henry_Cabourn_Pocklington
Mathematical method for approximating solutions to differential and integral equations
numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-dimensional
Collocation_method
Generalization of a positive-definite matrix
Mercer in the early 20th century, in the context of solving integral operator equations. Since then, positive-definite functions and their various analogues
Positive-definite_kernel
Equation whose unknown is a function
functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations
Functional_equation
Principle of least length in physics
Using the calculus of variations, it results in an integral equation formulation of the equations of motion for the system. Maupertuis's principle states
Maupertuis's_principle
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
Mathematical theorem
(1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for
Mercer's_theorem
Pattern defining an infinite sequence of numbers
equations as integral equations relate to differential equations. See time scale calculus for a unification of the theory of difference equations with that
Recurrence_relation
partial differential equations with as many arbitrary constants as the number of independent variables is called the complete integral. The following n-parameter
First-order partial differential equation
First-order_partial_differential_equation
function f {\displaystyle \mathbf {f} } . An equation of this form can be transformed into an integral equation d d t ∫ V ξ d V = − ∮ ∂ V f ( ξ ) ⋅ n ^
Conservation_form
Heat transfer calculation
integral equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation
Kernel function for solving integral equation of surface radiation exchanges
Kernel_function_for_solving_integral_equation_of_surface_radiation_exchanges
Soviet mathematician
singular integral equation in the euclidean space is zero. In 1961 Mikhlin developed a theory of multidimensional singular integral equations on Lipschitz
Solomon_Mikhlin
Existence and uniqueness of solutions to initial value problems
A standard proof relies on transforming the differential equation into an integral equation, then applying the Banach fixed-point theorem to prove the
Picard–Lindelöf_theorem
German mathematician (1862–1943)
of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly
David_Hilbert
Equations describing behavior of a model
function for solving integral equation of surface radiation exchanges Nonlinear acoustics Large eddy simulation Föppl–von Kármán equations Timoshenko beam
Governing_equation
Type of calculus problem
theorem proceeds by reformulating the problem as an equivalent integral equation. The integral can be considered an operator which maps one function into
Initial_value_problem
Theorem In probability theory and statistics
either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean
Campbell's theorem (probability)
Campbell's_theorem_(probability)
Topics referred to by the same term
The Volterra equation may refer to the Volterra integral equation, an integral in the style of Fredholm theory. Product integral, an integral over an operator-valued
Volterra_equation
length process can also be written in the form of a Lindley equation. Lindley's integral equation is a relationship satisfied by the stationary waiting time
Lindley_equation
Equation in statistical mechanics
1103/PhysRev.110.1 Wertheim, M. S. Exact Solution of the Percus–Yevick Integral Equation for Hard Spheres. Phys. Rev. Lett. 1963, 10, 321-323, doi:10.1103/PhysRevLett
Percus–Yevick_approximation
Italian mathematician and physicist (1860–1940)
physicist, known for his contributions to mathematical biology and integral equations, being one of the founders of functional analysis. Born in Ancona
Vito_Volterra
Bessarabian-born Soviet and Israeli mathematician
theory and functional analysis, in particular linear operators and integral equations. Gohberg was born in Tarutino to parents Tsudik and Haya Gohberg.
Israel_Gohberg
Stochastsic differential equations with terminal condition
{F}}_{t})_{t\in [0,T]}} . A backward stochastic differential equation is an integral equation of the type where f : [ 0 , T ] × R × R → R {\displaystyle
Backward stochastic differential equation
Backward_stochastic_differential_equation
Integral using products instead of sums
Volterra in 1887 to solve systems of linear differential equations. The classical Riemann integral of a function f : [ a , b ] → R {\displaystyle f:[a,b]\to
Product_integral
British-American mathematician
to apply Laplace transform to the integral equation in 1906. He submitted a detailed report on integral equations in 1911 to the British association
Harry_Bateman
substitutions for integrals involving a square root. Euler's summation formula, a theorem about integrals. Cauchy–Euler equation (or Euler equation), a second-order
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Statistical mechanics framework
theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation. The technique justifies the otherwise
Chapman–Enskog_theory
German mathematician
specializing in numerical analysis of partial differential equations and boundary integral equations. He studied mathematics from 1982 to 1985 at the Technische
Christoph_Schwab
applications. The name is an acronym for Higher Order Basis Based Integral Equation Solver. The software is based on the Method of Moments (MoM), and
HOBBIES (electromagnetic solver)
HOBBIES_(electromagnetic_solver)
Approximation method
discretizing integral equations, preconditioning the resulting systems of linear equations, or solving elliptic partial differential equations, a rank proportional
Hierarchical_matrix
View of quantum mechanics
interpretation of this equation. This approach is called the 'differential' and 'field' approach by Schwinger, as opposed to the 'integral' and 'particle' approach
Interaction_picture
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INTEGRAL EQUATION
INTEGRAL EQUATION
Boy/Male
Indian
Internal Cleanliness
Surname or Lastname
English and French
English and French : nickname for a handsome man (perhaps also ironically for an ugly one), from Old French beu, bel ‘fair’, ‘lovely’ (Late Latin bellus).Hungarian (Bél) : from the old secular Hungarian name Bél, or alternatively from bél ‘internal part’, probably an occupational name for a servant who worked in the household.Czech (BÄ›l) from Czech bÃlý ‘white’.
Surname or Lastname
Irish
Irish : reduced Anglicized form of either of two Gaelic names, Ó DuibhÃn ‘descendant of DuibhÃn’, a byname meaning ‘little black one’, or Ó DaimhÃn ‘descendant of DaimhÃn’, a byname meaning ‘fawn’, ‘little stag’. These are attenuated versions of Ó Dubháin and Ó Damháin, and are the phonetic origin of Anglicizations with an internal v (as opposed to w, as in Dewan, or monosyllabic forms with an o or u) (see Doane).English and French : nickname, of literal or ironic application, from Middle English, Old French devin, divin ‘excellent’, ‘perfect’ (Latin divinus ‘divine’).
Girl/Female
American, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Plucked Flower; Voice of Heart; Woman; Intellect; Behold of Any Beautiful Scene; Internal Beauty
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Punjabi, Sikh, Sindhi, Telugu
Heart; Inner Beauty; Fame; Internal Nature; Wisdom
INTEGRAL EQUATION
INTEGRAL EQUATION
INTEGRAL EQUATION
INTEGRAL EQUATION
INTEGRAL EQUATION
INTEGRAL EQUATION
INTEGRAL EQUATION
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