Differential and Difference Equations

A Comparison of Methods of Solution

Authors: Maximon, Leonard C.

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  • 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
  • Provides a unique compendium of difference equations for the special functions of mathematical physics
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eBook $39.99
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  • ISBN 978-3-319-29736-1
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Hardcover $54.99
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  • ISBN 978-3-319-29735-4
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  • Usually dispatched within 3 to 5 business days.
Softcover $54.99
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  • ISBN 978-3-319-80639-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

About the authors

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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-29736-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $54.99
price for USA in USD
  • ISBN 978-3-319-29735-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-80639-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Differential and Difference Equations
Book Subtitle
A Comparison of Methods of Solution
Authors
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29736-1
DOI
10.1007/978-3-319-29736-1
Hardcover ISBN
978-3-319-29735-4
Softcover ISBN
978-3-319-80639-6
Edition Number
1
Number of Pages
XV, 162
Topics