Differential and Difference Equations : A Comparison of Methods of Solution

Leonard C. Maximon

ISBN 10: 331929735X / ISBN 13: 9783319297354

Editore: Springer International Publishing, Springer International Publishing, 2016

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - This book, intended for researchers andgraduate students in physics, applied mathematics and engineering, presents adetailed comparison of the important methods of solution for lineardifferential and difference equations - variation of constants, reduction oforder, Laplace transforms and generating functions - bringing out thesimilarities as well as the significant differences in the respective analyses.Equations of arbitrary order are studied, followed by a detailed analysis forequations of first and second order. Equations with polynomial coefficients areconsidered and explicit solutions for equations with linear coefficients aregiven, showing significant differences in the functional form of solutions ofdifferential equations from those of difference equations. An alternativemethod of solution involving transformation of both the dependent andindependent variables is given for both differential and difference equations.A comprehensive, detailed treatment of Green's functions and the associatedinitial and boundary conditions is presented for differential and differenceequations of both arbitrary and second order. A dictionary of differenceequations with polynomial coefficients provides a unique compilation of secondorder difference equations obeyed by the special functions of mathematicalphysics. Appendices augmenting the text include, in particular, a proof ofCramer's rule, a detailed consideration of the role of the superpositionprincipal in the Green's function, and a derivation of the inverse of Laplacetransforms and generating functions of particular use in the solution of secondorder linear differential and difference equations with linear coefficients.

Codice articolo 9783319297354

Dati bibliografici

• Titolo: Differential and Difference Equations : A Comparison of Methods of Solution
• Editore: Springer International Publishing, Springer International Publishing
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 331929735X
• ISBN 13: 9783319297354
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 16 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 16 millimetri di profondità
• Peso: 442 grammi

Descrizione articolo

Riassunto

This book, intended for researchers andgraduate students in physics, applied mathematics and engineering, presents adetailed comparison of the important methods of solution for lineardifferential and difference equations - variation of constants, reduction oforder, Laplace transforms and generating functions - bringing out thesimilarities as well as the significant differences in the respective analyses.Equations of arbitrary order are studied, followed by a detailed analysis forequations of first and second order. Equations with polynomial coefficients areconsidered and explicit solutions for equations with linear coefficients aregiven, showing significant differences in the functional form of solutions ofdifferential equations from those of difference equations. An alternativemethod of solution involving transformation of both the dependent andindependent variables is given for both differential and difference equations.A comprehensive, detailed treatment of Green’s functions and the associatedinitial and boundary conditions is presented for differential and differenceequations of both arbitrary and second order. A dictionary of differenceequations with polynomial coefficients provides a unique compilation of secondorder difference equations obeyed by the special functions of mathematicalphysics. Appendices augmenting the text include, in particular, a proof ofCramer’s rule, a detailed consideration of the role of the superpositionprincipal in the Green’s function, and a derivation of the inverse of Laplacetransforms and generating functions of particular use in the solution of secondorder linear differential and difference equations with linear coefficients.

Informazioni sull?autore

LeonardMaximon is Research Professor of Physics in the Department of Physics at TheGeorge Washington University and Adjunct Professor in the Department of Physicsat Arizona State University. He has been an Assistant Professor in the GraduateDivision of Applied Mathematics at Brown University, a Visiting Professor atthe Norwegian Technical University in Trondheim, Norway, and a Physicist at theCenter for Radiation Research at the National Bureau of Standards. He is alsoan Associate Editor for Physics for the DLMF project and a Fellow of theAmerican Physical Society.

Maximonhas published numerous papers on the fundamental processes of quantumelectrodynamics and on the special functions of mathematical physics.