Overview
- 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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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
- 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
About this book
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.
Authors and Affiliations
About the author
Leonard Maximon 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.
Bibliographic Information
Book Title: Differential and Difference Equations
Book Subtitle: A Comparison of Methods of Solution
Authors: Leonard C. Maximon
DOI: https://doi.org/10.1007/978-3-319-29736-1
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-29735-4Published: 26 April 2016
Softcover ISBN: 978-3-319-80639-6Published: 22 April 2018
eBook ISBN: 978-3-319-29736-1Published: 18 April 2016
Edition Number: 1
Number of Pages: XV, 162
Topics: Mathematical Methods in Physics, Mathematical and Computational Engineering, Difference and Functional Equations, Mathematical Applications in the Physical Sciences, Ordinary Differential Equations