Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linearwave equations and a brief introduction to Laplace transform solution ofpartial differential equations.For scientists and engineers.
|Publisher:||Prentice Hall Professional Technical Reference|
Table of Contents1. Heat Equation.
2. Method of Separation of Variables.
3. Fourier Series.
4. Vibrating Strings and Membranes.
5. Sturm-Liouville Eigenvalue Problems.
6. Finite Difference Numerical Methods for Partial DifferentialEquations.
7. Partial Differential Equations with at Least ThreeIndependent Variables.
8. Nonhomogeneous Problems.
9. Green's Functions for Time-Independent Problems.
10. Infinite Domain Problems—Fourier Transform Solutionsof Partial Differential Equations.
11. Green's Functions for Wave and Heat Equations.
12. The Method of Characteristics for Linear and Quasi-LinearWave Equations.
13. A Brief Introduction to Laplace Transform Solution ofPartial Differential Equations.
14. Topics: Dispersive Waves, Stability, Nonlinearity, andPerturbation Methods.
Selected Answers to Starred Exercises.