LEADER 03861nam 2200469 450 001 9910624302403321 005 20230319083701.0 010 $a981-19-4915-8 035 $a(MiAaPQ)EBC7131190 035 $a(Au-PeEL)EBL7131190 035 $a(CKB)25280674100041 035 $a(PPN)26635520X 035 $a(EXLCZ)9925280674100041 100 $a20230319d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModern methods in mathematical physics $eintegral equations in Wolfram Mathematica /$fVladimir Ryzhov [and four others] 210 1$aGateway East, Singapore :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (201 pages) $cillustrations 311 08$aPrint version: Ryzhov, Vladimir Modern Methods in Mathematical Physics Singapore : Springer,c2022 9789811949142 320 $aIncludes bibliographical references. 327 $aIntroduction -- 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 Kernel 327 $aReferences -- 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. 606 $aWolfram language (Computer program language) 606 $aMathematical physics 606 $aIntegral equations 615 0$aWolfram language (Computer program language) 615 0$aMathematical physics. 615 0$aIntegral equations. 676 $a510.285536 700 $aRyzhov$b Vladimir$0929091 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910624302403321 996 $aModern methods in mathematical physics$93058477 997 $aUNINA