Differential Equations TextBook-MA102
Professor of Mathematics Ohio State University
Purpose and Structure of the Book
This book provides a comprehensive, thorough, and up-to-date treatment of engineering mathematics. It is intended to introduce students of engineering, physics, mathematics, computer science, and related fields to those areas of applied mathematics that are most relevant for solving practical problems. A course in elementary calculus is the sole prerequisite. (However, a concise refresher of basic calculus for the student is included on the inside cover and in Appendix 3.)
The subject matter is arranged into seven parts as follows:
A. Ordinary Differential Equations (ODEs) in Chapters 1–6
B. Linear Algebra. Vector Calculus. See Chapters 7–10
C. Fourier Analysis. Partial Differential Equations (PDEs). See Chapters 11 and 12
D. Complex Analysis in Chapters 13–18
E. Numeric Analysis in Chapters 19–21
F. Optimization, Graphs in Chapters 22 and 23
G. Probability, Statistics in Chapters 24 and 25.
These are followed by five appendices: 1. References, 2. Answers to Odd-Numbered Problems, 3. Auxiliary Materials (see also inside covers of book), 4. Additional Proofs, 5. Table of Functions. This is shown in a block diagram on the next page.
The parts of the book are kept independent. In addition, individual chapters are kept as independent as possible. (If so needed, any prerequisites—to the level of individual sections of prior chapters—are clearly stated at the opening of each chapter.) We give the instructor maximum flexibility in selecting the material and tailoring it to his or her need. The book has helped to pave the way for the present development of engineering mathematics. This new edition will prepare the student for the current tasks and the future by a modern approach to the areas listed above. We provide the material and learning tools for the students to get a good foundation of engineering mathematics that will help them in their careers and in further studies.
General Features of the Book Include:
• Simplicity of examples to make the book teachable—why choose complicated examples when simple ones are as instructive or even better?
• Independence of parts and blocks of chapters to provide flexibility in tailoring courses to specific needs.
• Self-contained presentation, except for a few clearly marked places where a proof would exceed the level of the book and a reference is given instead.
• Gradual increase in difficulty of material with no jumps or gaps to ensure an enjoyable teaching and learning experience.