This textbook is in two parts. The first part contains Chapters 1-7 and
is subtitled Finite Difference Methods. The second part contains Chapters
8-11 and is subtitled Conservation Laws and Elliptic Equations. This text
was developed from material presented in a year long, graduate course on
using difference methods for the numerical solution of partial differential
equations. Writing this text has been an iterative process, and much like the
Jacobi iteration scheme presented in Chapter 10, it has been a slow iterative
process. The course at Colorado State University is designed for graduate
students in both applied mathematics and engineering. The students are
required to have at least one semester of partial differential equations and
some programming capability. Generally, the classes include a broad spectrum of types of students, ranging from first year mathematics graduate students with almost no physical intuition into the types of problems we
might solve, to third year engineering graduate students who have a lot of
physical intuition and know what types of problems they personally want. to solve and why they want to solve them. Since the students definitely help shape the class that is taught, they probably have also helped to shape this text.