2016, ISBN: 331929735X
Differential and Difference Equations: A Comparison of Methods of SolutionEinbandHardbackAutor(en)Maximon, Leonard C.VerlagSpringer, BerlinAuflage1st ed. 2016Ausgabe2016Formatangaben162 p… More...
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2016, ISBN: 331929735X
[EAN: 9783319297354], Neubuch, [SC: 14.12], [PU: Springer International Publishing], MATHEMATIK / PHYSIK, CHEMIE; TECHNIK, INGENIEURWISSENSCHAFTEN, HANDWERK; SOLUTIONOFLINEARDIFFERENTIALE… More...
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[ED: Buch], [PU: Springer International Publishing], Neuware - This book, intended for researchers andgraduate students in physics, applied mathematics and engineering, presents adetailed… More...
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2016, ISBN: 331929735X
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2016, ISBN: 331929735X
Differential and Difference Equations: A Comparison of Methods of SolutionEinbandHardbackAutor(en)Maximon, Leonard C.VerlagSpringer, BerlinAuflage1st ed. 2016Ausgabe2016Formatangaben162 p… More...
Leonard C. Maximon:
Differential and Difference Equations : A Comparison of Methods of Solution - hardcover2016, ISBN: 331929735X
[EAN: 9783319297354], Neubuch, [SC: 14.12], [PU: Springer International Publishing], MATHEMATIK / PHYSIK, CHEMIE; TECHNIK, INGENIEURWISSENSCHAFTEN, HANDWERK; SOLUTIONOFLINEARDIFFERENTIALE… More...
2016
ISBN: 331929735X
[EAN: 9783319297354], Neubuch, [PU: Springer International Publishing Apr 2016], MATHEMATIK / PHYSIK, CHEMIE; TECHNIK, INGENIEURWISSENSCHAFTEN, HANDWERK; SOLUTIONOFLINEARDIFFERENTIALEQUAT… More...
2026, ISBN: 9783319297354
[ED: Buch], [PU: Springer International Publishing], Neuware - This book, intended for researchers andgraduate students in physics, applied mathematics and engineering, presents adetailed… More...
2016, ISBN: 331929735X
1st ed. 2016 Gebundene Ausgabe Mathematik / Physik, Chemie, Mathematik / Technik, Ingenieurwissenschaften, Handwerk, Mathematische Physik, Mathematik für Ingenieure, Solution of linear … More...
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Details of the book - Differential and Difference Equations
EAN (ISBN-13): 9783319297354
ISBN (ISBN-10): 331929735X
Hardcover
Paperback
Publishing year: 2016
Publisher: Springer International Publishing
Book in our database since 2016-01-16T19:38:22-05:00 (New York)
Detail page last modified on 2024-04-02T23:59:02-04:00 (New York)
ISBN/EAN: 9783319297354
ISBN - alternate spelling:
3-319-29735-X, 978-3-319-29735-4
Alternate spelling and related search-keywords:
Book author: leonard, maxim leo
Book title: solution equations, differential difference equations, methods
Information from Publisher
Author: Leonard C. Maximon
Title: Differential and Difference Equations - A Comparison of Methods of Solution
Publisher: Springer; Springer International Publishing
162 Pages
Publishing year: 2016-04-26
Cham; CH
Printed / Made in
Language: English
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
XV, 162 p.
BB; Hardcover, Softcover / Physik, Astronomie/Theoretische Physik; Mathematische Physik; Verstehen; Solution of linear differential equations; Solution of linear difference equations; Wronskian determinant; Green’s function and the superposition principle; Proof of Cramer's rule; Method of variation of constants; Casoratian determinant; Difference equations; Ordinary differential equations; Classical hypergeometric functions; Confluent hypergeometric functions; Special functions of mathematical physics; Mathematical Methods in Physics; Mathematical and Computational Engineering Applications; Difference and Functional Equations; Mathematical Physics; Differential Equations; Mathematik für Ingenieure; Differentialrechnung und -gleichungen; EA; BC
This 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.
Preface.- 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.
is Research Professor of Physics in the Department of Physics at The George Washington University and Adjunct Professor in the Department of Physics at Arizona State University. He has been an Assistant Professor in the Graduate Division of Applied Mathematics at Brown University, a Visiting Professor at the Norwegian Technical University in Trondheim, Norway, and a Physicist at the Center for Radiation Research at the National Bureau of Standards. He is also an Associate Editor for Physics for the DLMF project and a Fellow of the American Physical Society.
Maximon has published numerous papers on the fundamental processes of quantum electrodynamics and on the special functions of mathematical physics.
Leonard MaximonThis 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.
Provides a unique and detailed comparison of methods of solution of differential and difference equations in application to problems in physical sciences and engineering Places emphasis on application of these methods to specific problems a unique compendium of difference equations for the special functions of mathematical physics Includes supplementary material: sn.pub/extras
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