Mathematical Methods in Physics and Engineering with Mathematica

INTRODUCTION What is a Boundary Problem? Classification of Partial Differential Equations Types of Boundary Conditions and the Collocation Method Differential Equations as Models for Nature BOUNDARY PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS Linear Differential Equations Solving Linear Differential Equations Differential Equations of Physics and Engineering Boundary Value Problems and Eigenvalues Boundary Value Problems as Initial Value Problems Nonlinear Ordinary Differential Equations Solutions of Nonlinear Differential Equations PARTIAL DIFFERENTIAL EQUATIONS Coordinate Systems and Separability Methods to Reduce Partial to Ordinary Differential Equations The Method of Characteristics Nonlinear Partial Differential Equations BOUNDARY PROBLEMS WITH ONE CLOSED BOUNDARY Laplace and Poisson Equations Conformal Mapping in Two and Three Dimensions d'Alembert Wave Equation and String Vibrations Helmholtz Equation and Membrane Vibrations Rods and the Plate Equation Approximation Methods Variational Calculus Collocation Methods BOUNDARY PROBLEMS WITH TWO CLOSED BOUNDARIES Inseparable Problems Holes in the Domain. Two Boundaries Belonging to Different Coordinate Systems Corners in the Boundary NONLINEAR BOUNDARY PROBLEMS Some Definitions and Examples Moving and Free Boundaries Waves of Large Amplitudes. Solitons The Rupture of an Embankment-Type Water Dam Gas Flow with Combustion REFERENCES APPENDIX INDEX