Differential and Difference Equations: A Comparison of Methods of Solution - Brossura

Maximon, Leonard C.

Brossura

ISBN 10: 3319806394 ISBN 13: 9783319806396

Casa editrice: Springer, 2018

Riassunto

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.

Su questo libro

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.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 3319806394
• ISBN 13: 9783319806396
• Rilegatura: Copertina flessibile
• Numero di pagine: 180
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania