ABSTRACT

With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs). The text represents a new approach to PDEs at the undergraduate level by presenting computation as an integral part of the study of differential equations. The authors use the computer software Mathematica (R) along with graphics to improve understanding and interpretation of concepts. The book also presents solutions to selected examples as well as exercises in each chapter. Topics include Laplace and Fourier transforms as well as Sturm-Liuville Boundary Value Problems.

chapter 1|82 pages

Fourier Series

chapter 2|62 pages

Integral Transforms

chapter 3|59 pages

Sturm{liouville Problems

chapter 4|39 pages

Partial Dierential Equations

chapter 5|83 pages

The Wave Equation

chapter 6|57 pages

The Heat Equation

chapter 7|68 pages

Laplace And Poisson Equations

chapter 8|71 pages

Finite Dierence Numerical Methods

chapter |2 pages

A. Table Of Laplace Transforms

chapter |2 pages

B. Table Of Fourier Transforms

chapter C|3 pages

Series And Uniform Convergence Facts

chapter |7 pages

E. Vector Calculus Facts

chapter |3 pages

G. Euler Gamma And Beta Functions

chapter |15 pages

H. Basics Of Mathematica

chapter |1 pages

Bibliography

chapter |55 pages

Answers to the Exercises