Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation. Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.