Differential and Difference Equations A Comparison of Methods of Solution /
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 generat...
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| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edition: | 1st ed. 2016. |
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| Online Access: | https://doi.org/10.1007/978-3-319-29736-1 |
Table of Contents:
- Preface
- Introduction
- 1 Operators
- 2 Solution of homogeneous and inhomogeneous linear equations
- 3 First order homogeneous and inhomogeneous linear equations
- 4 Second-order homogeneous and inhomogeneous equations
- 5 Self-adjoint linear equations
- 6 Green’s function
- 7 Generating function, z-transforms, Laplace transforms and the solution of linear differential and difference equations
- 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.