LEADER 05532nam 22007455 450 001 9910254642903321 005 20220413173557.0 010 $a3-319-29736-8 024 7 $a10.1007/978-3-319-29736-1 035 $a(CKB)3710000000649180 035 $a(EBL)4508874 035 $a(SSID)ssj0001665944 035 $a(PQKBManifestationID)16454866 035 $a(PQKBTitleCode)TC0001665944 035 $a(PQKBWorkID)14999715 035 $a(PQKB)10136427 035 $a(DE-He213)978-3-319-29736-1 035 $a(MiAaPQ)EBC4508874 035 $a(PPN)193446510 035 $a(EXLCZ)993710000000649180 100 $a20160418d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential and difference equations $ea comparison of methods of solution /$fby Leonard C. Maximon 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (166 p.) 300 $aDescription based upon print version of record. 311 $a3-319-29735-X 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- 1 Operators -- 2 Solution of homogeneous and inhomogeneous linear equations -- 3 First order homogeneous and inhomogeneous linear equations -- 4 Second-order homogeneous and inhomogeneous equations -- 5 Self-adjoint linear equations -- 6 Green?s function -- 7 Generating function, z-transforms, Laplace transforms and the solution of linear differential and difference equations -- 8 Dictionary of difference equations with polynomial coefficients -- Appendix A: Difference operator -- Appendix B: Notation -- Appendix C: Wronskian Determinant -- Appendix D: Casoratian Determinant -- Appendix E: Cramer?s Rule -- Appendix F: Green?s function and the Superposition principle -- Appendix G: Inverse Laplace transforms and Inverse Generating functions -- Appendix H: Hypergeometric function -- Appendix I: Confluent Hypergeometric function -- Appendix J. Solutions of the second kind -- Bibliography. 330 $aThis book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green?s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer?s rule, a detailed consideration of the role of the superposition principal in the Green?s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients. 606 $aPhysics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aDifference equations 606 $aFunctional equations 606 $aMathematical physics 606 $aDifferential equations 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aPhysics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aMathematical physics. 615 0$aDifferential equations. 615 14$aMathematical Methods in Physics. 615 24$aMathematical and Computational Engineering. 615 24$aDifference and Functional Equations. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aOrdinary Differential Equations. 676 $a530 700 $aMaximon$b Leonard C$4aut$4http://id.loc.gov/vocabulary/relators/aut$0803798 906 $aBOOK 912 $a9910254642903321 996 $aDifferential and Difference Equations$92509830 997 $aUNINA