Applied partial differential equations

Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics.

Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.

Contents

• Heat Equation
• Method of Separation of Variables
• Fourier Series
• Wave Equation : Vibrating Strings and Membranes
• Sturm-Liouville Eigenvalue Problems
• Finite Difference Numerical Methods for Partial Differential Equations
• Higher Dimensional Partial Differential Equations
• Nonhomogeneous Problems
• Green's Functions for Time-Independent Problems
• Infinite Domain Problems-Fourier Transform Solutions of Partial Differential Equations
• Green's Functions for Wave and Heat Equations
• The Method of Characteristics for Linear and Quasi-Linear Wave Equations
• Laplace Transform Solution of Partial Differential Equations
• Dispersive Waves : Slow Variations, Stability, Nonlinearity, and Perturbation Methods

• Bibliography
• Answers to Starred Exercises
• Index