03861nam 2200469 450 991062430240332120230319083701.0981-19-4915-8(MiAaPQ)EBC7131190(Au-PeEL)EBL7131190(CKB)25280674100041(PPN)26635520X(EXLCZ)992528067410004120230319d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierModern methods in mathematical physics integral equations in Wolfram Mathematica /Vladimir Ryzhov [and four others]Gateway East, Singapore :Springer,[2022]©20221 online resource (201 pages) illustrationsPrint version: Ryzhov, Vladimir Modern Methods in Mathematical Physics Singapore : Springer,c2022 9789811949142 Includes bibliographical references.Introduction -- References -- Contents -- 1 Fundamentals. Classification of Integral Equations -- 1.1 Basic Types of Integral Equations: A Solution of Integral Equation -- 1.1.1 Fredholm Equation of the Second Kind -- 1.1.2 Fredholm Equation of the First Kind -- 1.1.3 Volterra Equation of the Second Kind -- 1.1.4 Volterra Equation of the First Kind -- 1.2 Equations with a Weak Singularity -- 1.3 Abel Problem: Abel Integral Equation -- 1.4 Solution of Integral Equations by the Differentiation Method -- References -- 2 Integral Equations with Difference Kernels -- 2.1 Difference Kernel Concept. Solution of Integral Equations with Difference Kernels by the Method of Differentiation -- 2.2 Solution of Integral Equations and Systems of Volterra Integral Equations with Difference Kernels Using the Laplace Transform -- 2.2.1 Solving Volterra Integral Equations with Difference Kernels Using the Laplace Transform -- 2.2.2 Solving Systems of Volterra Integral Equations with Difference Kernels Using the Laplace Transform -- 2.2.3 Solving Integro-Differential Equations with Difference Kernels Using the Laplace Transform -- 2.3 Solving Fredholm Integral Equations with Difference Kernels Using the Fourier Transform -- References -- 3 Fredholm Theory -- 3.1 Solution of Fredholm Integral Equations by the Resolvent Method: Method of Fredholm Determinants -- 3.2 Iterated Kernels Method -- 3.3 Characteristic Numbers and Eigenfunctions. Solution of Homogeneous Fredholm Integral Equations with Degenerate Kernel -- 3.4 Solution of Fredholm Inhomogeneous Integral Equations with a Degenerate Kernel. Fredholm's Theorems -- References -- 4 Symmetric Integral Equations -- 4.1 Construction of an Orthonormal System of Eigenfunctions of a Symmetric Kernel -- 4.2 Representation of the Solution as Expansion in Terms of Orthonormal Eigenfunctions of a Symmetric KernelReferences -- 5 Approximate Methods for Solving Integral Equations -- 5.1 Approximate Solution of the Fredholm Equation by Replacing the Integral by a Finite Sum -- 5.2 Successive Approximation Method -- 5.3 Bubnov-Galerkin Method -- 5.3.1 Method of Replacing a Kernel with a Degenerate One -- References -- 6 Individual Tasks. Passing the Final Test After Completing the Course -- References.Wolfram language (Computer program language)Mathematical physicsIntegral equationsWolfram language (Computer program language)Mathematical physics.Integral equations.510.285536Ryzhov Vladimir929091MiAaPQMiAaPQMiAaPQBOOK9910624302403321Modern methods in mathematical physics3058477UNINA