One of the most widely used reference books on applied mathematics for a generation, distributed in multiple languages throughout the world, this text is geared toward use with a one-year advanced course in applied mathematics for engineering students. The treatment assumes a solid background in the theory of complex variables and a familiarity with complex numbers, but it includes a brief review. Chapters are as self-contained as possible, offering instructors flexibility in designing their own courses. The first eight chapters explore the analysis of lumped parameter systems. Succeeding topics include distributed parameter systems and important areas of applied mathematics. Each chapter features extensive references for further study as well as challenging problem sets. Answers and hints to select problem sets are included in an Appendix. This edition includes a new Preface by Dr. Lawrence R. Harvill.