Differential and Difference Equations

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.