This book evolved from lecture notes developed over the past 20+ years of teaching this material, mostly in Applied Mathematics 585–6 at the University of Washington. The course is taken by first-year graduate students in our department, along with graduate students from mathematics and a variety of science and engineering departments.

Exercises and student projects are an important aspect of any such course and many have been developed in conjunction with this book. Rather than lengthening the text, they are available on the book's Web page:

Along with exercises that provide practice and further exploration of the topics in each chapter, some of the exercises introduce methods, techniques, or more advanced topics not found in the book.

The Web page also contains MATLAB� m-files that illustrate how to implement finite difference methods, and that may serve as a starting point for further study of the methods in exercises and projects. A number of the exercises require programming on the part of the student, or require changes to the MATLAB programs provided. Some of these exercises are fairly simple, designed to enable students to observe first hand the behavior of numerical methods described in the text. Others are more open-ended and could form the basis for a course project.

The exercises are available as PDF files. The LATEX source is also provided, along with some hints on using LATEX for the type of mathematics used in this field. Each exercise is in a separate file so that instuctors can easily construct customized homework assignments if desired. Students can also incorporate the source into their solutions if they use LATEX to typeset their homework. Personally I encourage this when teaching the class, since this is a good opportunity for them to learn a valuable skill (and also makes grading homework considerably more pleasurable).