Differential and Difference Equations (eBook)

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.

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.