Advanced Engineering Mathematics (2nd Edition)

Book Preface

Purpose and Prerequisites

This book is written primarily for a single- or multi-semester course in applied mathematics for students of engineering or science, but it is also designed for self-study and reference. By self-study we do not necessarily mean outside the context of a formal course. Even within a course setting, if the text can be read independently and understood, then more pedagogical options become available to the instructor.

The prerequisite is a full year sequence in calculus, but the book is written so as to be usable at both the undergraduate level and also for first-year graduate students of engineer­ing and science. The flexibility that permits this broad range of use is described below in the section on Course Use.

Changes from the First Edition
Principal changes from the first edition are as follows:

1 Part I on ordinary differential equations. In the first edition we assumed that the reader had previously completed a first course in ordinary differential equations. How­ever, differential equations is traditionally the first major topic in books on advanced engineering mathematics so we begin this edition with a seven chapter sequence on or­dinary differential equations. Just as the book becomes increasingly sophisticated from beginning to end. these seven chapters are written that way as well. with the final chapter on nonlinear equations being the most challenging.
2. Incorporation of a computer-algebra-system. Several powerful computer environ­ments are available, such as Maple, Mathematica, and MATLAB. We selected Maple, as a representative and user-friendly software. In addition to an Instructor’s Manual, a brief student supplement is also available, which presents parallel discussions of Math­ematica and MATLAB.
3. Revision of existing material and format. Pedagogical improvements that evolved through eight years of class use led to a complete rewriting rather than minor modifica­tions of the text. The encl-of-section exercises are refined and expanded.