The second edition of this book contains several major improvements over the first edition.
Some of these improvements involve format and presentation philosophy, and some of the
changes involve old material which has been deleted and new material which has been
added.
Each chapter begins with a chapter table of contents. The first figure carries a sketch
of the application used as the example problem in the chapter. Section 1 of each chapter is
an introduction to the chapter, which discusses the example application, the general subject
matter of the chapter, special features, and solution approaches. The objectives of the
chapter are presented, and the organization of the chapter is illustrated pictorially. Each
chapter ends with a summary section, which presents a list of recommendations, dos and
don'ts, and a list of what you should be able to do after studying the chapter. This list is
actually an itemization of what the student should have learned from the chapter. It serves
as a list of objectives, a study guide, and a review guide for the chapter.
Chapter 0, Introduction, has been added to give a thorough introduction to the book
and to present several fundamental concepts of relevance to the entire book.
Chapters 1 to 6, which comprise Part I, Basic Tools of Numerical Analysis, have
been expanded to include more approaches for solving problems. Discussions of pitfalls of
selected algorithms have been added where appropriate. Part I is suitable for second-
semester sophomores or first-semester juniors through beginning graduate students.
Chapters 7 and 8, which comprise Part II, Ordinary Differential Equations, have
been rewritten to get to the methods for solving problems more quickly, with less emphasis
on theory. A new section presenting extrapolation methods has been added in Chapter 7.
All of the material has been rewritten to flow more smoothly with less repetition and less
theoretical background. Part II is suitable for juniors through graduate students.