Partial Differential Equations Theory and Completely Solved Problems Thomas Hillen, I. Ed Leonard, Henry van Roessel
This textbook on linear partial differential equations (PDEs) consists of two parts.
In Part I we present the theory, with an emphasis on completely solved examples and intuition. In Part II we present a collection of exercises containing over 150 explicitly solved problems for linear PDEs and boundary value problems. These problems are based on more than 30 years of collective experience in teaching introductory PDE courses at several North American universities. Here we address exactly this need. While Part I presents the theory behind linear PDEs and introduces methods and techniques for solving them.
The problems in Part II allow students to learn and repeat arguments in hands-on exercises. The problems in Part II are all completely solved and explained in great detail. The final two chapters contain four sample midterm examinations and four sample final examinations. These sample examinations are actual exams given between 2004 and 2009 at the University of Alberta.
They provide students with a useful guideline as to what to expect as well as an opportunity to test their abilities. Topics are category by as follow as:
1.Introduction
2 Fourier Series
3 Separation of Variables
4 Sturm-Liouville Theory
5 Heat, Wave, and Laplace Equations
6 Polar Coordinates
7 Spherical Coordinates
8 Fourier Transforms
9 Fourier Transform Methods In PDEs
10 Method of Characteristics
PART II EXPLICITLY SOLVED PROBLEMS
11 Fourier Series Problems
12 Sturm-Liouville Problems
13 Heat Equation Problems
14 Wave Equation Problems
15 Laplace Equation Problems
16 Fourier Transform Problems
17 Method of Characteristics Problems
18 Four Sample Midterm Examinations
18.1 Midterm Exam 1
18.2 Midterm Exam 2
18.3 Midterm Exam 3
18.4 Midtenn Exam 4
19 Four Sample Final Examinations
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