Partial Differential Equations with Fourier Series and Boundary Value Problems Third Edition

by Asmar, Nakhle H.

• ISBN13: 9780486807379
• ISBN10: 0486807371
• Edition: 3rd
• Format: Paperback
• Copyright: 2016-09-21
• Publisher: Dover Publications

Summary

This text provides an introduction to partial differential equations and boundary value problems, including Fourier series. The treatment offers students a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations. This widely adopted and successful book also serves as a valuable reference for engineers and other professionals. The approach emphasizes applications, with particular stress on physics and engineering applications. Rich in proofs and examples, the treatment features many exercises in each section.
Relevant Mathematica files are available for download from author Nakhlé Asmar's website; however, the book is completely usable without computer access. The Students' Solutions Manual can be downloaded for free from the Dover website, and the book includes information on how instructors may request the Instructor Solutions Manual.
The text is suitable for undergraduates in mathematics, physics, engineering, and other fields who have completed a course in ordinary differential equations.

Author Biography

Nakhlé H. Asmar is Professor of Mathematics at the University of Missouri, Columbia. He is also the author of Applied Complex Analysis with Partial Differential Equations.

Table of Contents

Preface

1. A Preview of Applications and Techniques

2. Fourier Series, plus Supplement on Convergence

3. Partial Differential Equations in Rectangular Coordinates

4. Partial Differential Equations in Polar and Cylindrical Coordinates, plus Supplement on Bessel Functions

5. Partial Differential Equations in Spherical Coordinates, plus Supplement on Legendre Functions

6. Sturm-Liouville Theory with Engineering Applications

7. The Fourier Transform and Its Applications

8. The Laplace and Hankel Transforms with Applications

9. Finite Difference Numerical Methods

10. Sampling and Discrete Fourier Analysis with Applications to Partial Differential Equations

11. An Introduction to Quantum Mechanics, plus Supplement on Orthogonal Polynomials

12. Green's Functions and Conformal Mappings

Appendixes

A. Ordinary Differential Equations: Review of Concepts and Methods

B. Tables of Transforms

References

Answers to Selected Exercises

Index