Differential and Difference Equations: A Comparison of Methods of Solution

Preface.

Introduction.

1 Operators.

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

3 First order homogeneous and inhomogeneous linearequations.

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 andthe solution of linear differential and difference equations.
7.1 Laplace transforms and the solution of linear differential equations  with constant coefficients. 7.2 Generatingfunctions and the solution of linear difference equations with constantcoefficient. 7.3 Laplace transforms and the solution of linear differentialequations with polynomial coefficients. 7.4 Alternative method for the solutionof homogeneous linear differential equations with linear coefficients.  7.5 Generating functions and the solution oflinear difference equations with polynomial coefficients. 7.6 Solution ofhomogeneous linear difference equations with linear coefficients.

8 Dictionary of difference equations with polynomialcoefficients.

Appendix A: Difference operator.

Appendix B: Notation.

Appendix C: Wronskian Determinant.

Appendix D: Casoratian Determinant.

Appendix E: Cramer's Rule.

Appendix G: Inverse Laplace transforms and InverseGenerating functions.

Appendix H: Hypergeometric function.

Appendix I:  ConfluentHypergeometric function.

Appendix J. Solutions of the second kind.

Bibliography.