Examples of using Partial differential in English and their translations into Turkish
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Generalized Functions and Partial Differential Equations.
This equation, along with the continuity equation for J and the Poisson's equation for E, form a set of partial differential equations.
Maxwell's equations(in partial differential form) are modified to central-difference equations, discretized, and implemented in software.
Introduction==The wave equation is a hyperbolic partial differential equation.
Solutions==Maxwell's equations are partial differential equations that relate the electric and magnetic fields to each other and to the electric charges and currents.
The equations for an individual slice are elliptic partial differential equations.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum.
Therefore, the above procedure is not much different from those ingeneral numerical simulation based on the discretization of partial differential equations.
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
Solutions to the Helmholtz equation may readily be found inrectangular coordinates via the principle of separation of variables for partial differential equations.
When modeling the weather, ocean circulation, or the climate, partial differential equations are used to describe the evolution of these systems over time.
Other than partial differential equations, other parts of(classical) real analysis and complex analysis were either inspired by or have techniques applied(or both) in field theory.
The finite volume method(FVM)is a method for representing and evaluating partial differential equations in the form of algebraic equations.
In mathematics, a partial differential equation(PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
One of the most frequent problems in physical sciences is to obtain the solution of a(linear ornonlinear) partial differential equation which satisfies a set of functional values on a rectangular boundary.
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits.
Relaxation methods are important especially in the solution oflinear systems used to model elliptic partial differential equations, such as Laplace's equation and its generalization, Poisson's equation.
John Forbes Nash Jr.(June 13, 1928- May 23, 2015) was an American mathematician who made fundamental contributions to gametheory, differential geometry, and the study of partial differential equations.
The finite elementmethod is a good choice for solving partial differential equations over complex domains or when the desired precision varies over the entire domain.
The French mathematical physicist Joseph Fourier- 1830 introduced the notion of Fourier series to solve the heat equationgiving rise to a new approach to handle partial differential equations by means of integral transforms.
The aim of this method is towards a unified theory for the solution of partial differential equations(PDE); an aim which has been superseded by the more general theory of the homotopy analysis method.
Partial Differential Equations===== Application to a rectangular system with nonlinearity===One of the most frequent problems in physical sciences is to obtain the solution of a(linear or nonlinear) partial differential equation which satisfies a set of functional values on a rectangular boundary.
Intuitively, a Sobolev space is a space of functions with sufficiently many derivatives for some application domain,such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function.
In the mathematical study of partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables.
Unsolved problems remain in multiple domains, including physics, computer science, algebra, additive and algebraic number theories, analysis, combinatorics, algebraic, discrete and Euclidean geometries, graph, group, model, number, set and Ramsey theories,dynamical systems, partial differential equations.
Their importance comes from the fact that solutions of partial differential equations are naturally found in Sobolev spaces, rather than in spaces of continuous functions and with the derivatives understood in the classical sense.
Ilya Vekua Georgian: ილია ვეკუა, Russian: Илья́ Не́сторович Ве́куа; 23 April 1907 in the village of Sheshelety, Kutais Governorate, Russian Empire(modern day Ochamchira District, Abkhazia, Republic of Georgia- 2 December 1977 in Tbilisi, USSR) was a distinguished Georgian mathematician,specializing in partial differential equations, singular integral equations, generalized analytic functions and the mathematical theory of elastic shells.
When a 3-dimensional spherically symmetric partial differential equation is solved by the method of separation of variables in spherical coordinates, the part that remains after removal of the radial part is typicallyof the form: formula_108and hence the solutions are spherical harmonics.
Another example is(slow) fluid in a straight circular pipe: inCartesian coordinates, one has to solve a(difficult) two dimensional boundary value problem involving a partial differential equation, but in cylindrical coordinates the problem becomes one-dimensional with an ordinary differential equation instead of a partial differential equation.
When a 3-dimensional spherically symmetric partial differential equation is solved by the method of separation of variables in spherical coordinates, the part that remains after removal of the radial part is typically of the form∇ 2 ψ( θ, ϕ)+ λ ψ( θ, ϕ) 0,{\displaystyle\nabla^{2}\psi(\theta,\phi)+\lambda\psi(\theta,\phi)=0,} and hence the solutions are spherical harmonics.