This text emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green’s functions, and transform methods.
Features
1.Step-by-step approach
2.Emphasis on examples and problem solving
3.Physical and mathematical derivations
4.Clear and lively writing style
5.1,000 carefully prepared exercises
6.Learning aids
7.Pattern formation for reaction-diffusion equations and the Turing instability
8.Well done treatment of numerical methods for PDE
9.Presentation of derivation of the diffusion of a pollutant
10.Discussion on time dependent heat equations
11.Similarity solution for ht heat equation
12.Green's Functions for Wave and Heat Equations chapter
13.Shock waves chapter
14.Stability of systems of ordinary differential equation
15.Wave envelope equations
About the Author
Richard Haberman is Professor of Mathematics at Southern Methodist University, having previously taught at The Ohio State University, Rutgers University, and the University of California at San Diego. He received S.B. and Ph.D. degrees in applied mathematics from the Massachusetts Institute of Technology. He has supervised six Ph.D. students at SMU. His research has been funded by NSF and AFOSR.
Table of Contents:
1. Heat Equation
2. Method of Separation of Variables
3. Fourier Series
4. Wave Equation: Vibrating Strings and Membranes
5. Sturm-Liouville Eigenvalue Problems
6. Finite Difference Numerical Methods for Partial Differential Equations
7. Higher Dimensional Partial Differential Equations
8. Nonhomogeneous Problems
9. Green’s Functions for Time-Independent Problems
10. Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations
11. Green’s Functions for Wave and Heat Equations
12. The Method of Characteristics for Linear and Quasilinear Wave Equations
13. Laplace Transform Solution of Partial Differential Equations
14. Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods
Bibliography
Answers to Starred Exercises
Index
