Differential and Difference Equations: A Comparison of Methods of Solution - Couverture rigide

Maximon, Leonard C.

Couverture rigide

ISBN 10 : 331929735X ISBN 13 : 9783319297354

Editeur : Springer International Publishing AG, 2016

Synopsis

Preface.

Introduction.

1 Operators.

2 Solution of homogeneous and inhomogeneous linear equations.
2.1 Variation of constants. 2.2 Reduction of order when one solution to the homogeneous equation is known.

3 First order homogeneous and inhomogeneous linear equations.

4 Second-order homogeneous and inhomogeneous equations.

5 Self-adjoint linear equations.

6 Green's function.
6.1 Differential equations. 6.2 Difference equations.

7 Generating function, z-transforms, Laplace transforms and the solution of linear differential and difference equations.
7.1 Laplace transforms and the solution of linear differential equations with constant coefficients. 7.2 Generating functions and the solution of linear difference equations with constant coefficient. 7.3 Laplace transforms and the solution of linear differential equations with polynomial coefficients. 7.4 Alternative method for the solution of homogeneous linear differential equations with linear coefficients. 7.5 Generating functions and the solution of linear difference equations with polynomial coefficients. 7.6 Solution of homogeneous linear difference equations with linear coefficients.

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.

A propos du livre

À propos de l?auteur

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.

Détails de l'édition

• Éditeur: Springer International Publishing AG
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 331929735X
• ISBN 13: 9783319297354
• Reliure: Relié
• Numéro d'édition: 1
• Nombre de pages: 177
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible