Richard Haberman, Southern Methodist University

Published July, 1997 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 736 pp.
Cloth
ISBN 0-13-263807-X

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    Partial Differential Equations-Mathematics

    Partial Differential Equations-Mechanical Engineering

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




Leads readers step-by-step from simple exercises to increasingly powerful mathematical techniques for solving more complicated and realistic physical problems.
Discusses hear flow and vibrating strings and membranes so students can better understand the relationships between mathematics and the physical problems.
Carefully organized, easily readable discussion of the role of partial differential equations in applied mathematics.
Emphasizes examples and problem solving. Provides a thorough and reasoned approach to problem solving, stressing understanding.
Great care in physical and mathematical derivations, ensuring students are aware of assumptions being made.
Clear and lively writing style.
Clearly explains details and ideas with patience and sustained enthusiasm.
Text allows instructor flexibility in the selection of material.
Includes several important pedagogical features.

• More than 200 figures.
• Presents more than 1000 exercises with answers to selected exercises in the back of the book.
• Important equations and statements are frequently boxed.
• Paragraphs are often titled in bold.
• Important formulas are made into tables.
• Inside covers include important tabulated information.

NEW— Includes a new chapter on topics in partial differential equations involving dispersive waves. This self-contained chapter presents stability, nonlinearity, and perturbation methods.
NEW— Includes a short section on fluid flow past a circular cylinder (lift) early in the text, thereby providing a more realistic application of partial differential equations (Laplace's equation).
NEW— Includes a short section on reflection and refraction of light and sound waves that provides a realistic application of partial differential equations (the wave equation).
NEW— Includes a short section on the finite element method in the chapter on numerical methods for partial differential equations.
NEW— Presents a section on partial differential equations with spherical geometry and the required discussion of Legendre polynomials that discusses more realistic physical problems defined on the spherical earth.
NEW— Provides a section on eigenvalue problems with a continuous and discrete spectrum for applicable material on scattering and inverse scattering.
NEW— Includes a section on first-order nonlinear partial differential equations for eikonal equation of geometrical optics.
NEW—Includes many computer generated three-dimensional figures.

1. Heat Equation.
2. Method of Separation of Variables.
3. Fourier Series.
4. Vibrating Strings and Membranes.
5. Sturm-Liouville Eigenvalue Problems.
6. An Elementary Discussion of Finite Difference Numerical Methods for Partial Differential Equations.
7. Partial Differential Equations with at Least Three Independent Variables.
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 Time-Dependent Problems.
12. The Method of Characteristics for Linear and Quasi-Linear Wave Equations.
13. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations.
14. Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods.
Bibliography.
Selected Answers to Starred Exercises.
Index.

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