Description
Problems
One of the most important things about a textbook is the problems. Usually, students will have reason to feel that they truly understand the material while or after they do homework problems based on, or related to, the narrative of the book.
Most of the problems are based on what is discussed in the narrative; these may be called “exercises.” A few problems provide a structured way of filling in some of the details in the narrative. Other problems explore topics related to, but not directly based on, the material in the narrative; these problems are referred to as “complements.”
I believe students will find that the problems vary in difficulty, point of view, and style. This will help them learn thoroughly and assess their learning, and this will make the book good preparation for their use of mathematics in engineering courses.
Some of the problems are derivations, usually requiring manipulations of formulas as students do in science and engineering courses to get new, useful formulas. While this may strike some as being “theory,” asking students to derive things is essential to measuring their understanding of what they have learned and determining if they are likely to be able to use that knowledge in future courses.
Appendices
There are three appendices. Appendix A develops the technique of partial fractions that are useful (a) in solving problems using Laplace transforms in Sections 4.4 and 4.5 and (b) in calculating contour integrals in the complex plane in Sections 15.8, 15.9, and 17.3. Students will also be familiar with using partial fractions to evaluate integrals in calculus courses.
Appendix B provides the definition of the Laplace transform and the derivations of its properties that are used in Sections 4.4 and 4.5.
Appendix C discusses series solutions of ordinary differential equations. Bessel func-tions and Legendre polynomials discussed in this appendix are used in solving partial differential equations in Sections 11.5 and 11.6.
Developmental Plan
Over the past 14 years, I have been either developing or teaching new courses of mathe-matics for graduate students of engineering, in consultation with professors of mechanical engineering. Also, I have taught much of that material in other courses, at both the undergraduate and graduate levels, for decades.
Many colleagues and independent reviewers have helped me in developing this book. I also appreciate help from my MTH 399/599, MTH 699, and MTH 304/504 and 305/605 students. Professors Antonio Mastroberardino and Peter Olszewski, both from Penn State Erie, The Behrend College, assisted with accuracy checking.
Most of the book’s chapters underwent classroom testing by one or more professors, including Professors Lop-Fat Ho, David Miller, and me at Wright State University, as well as by Professor Paul Eloe at the University of Dayton.
Professors Vasilios Alexiades, University of Tennessee–Knoxville; Markus Bussmann, University of Toronto; Paul Eloe, University of Dayton; Harry Hardee, New Mexico State University; Allen Hunt, Wright State University; Thomas Pence, Michigan State University; Allen Plotkin, San Diego State University; Carl Prather, Virginia Polytechnic Institute; Scott Strong, Colorado School of Mines; Hooman Tafreshi, Virginia Common-wealth University; Thad Tarpey, Wright State University; James T. Vance, Jr., Wright State University; Aleksandra Vinogradov, Montana State University; and Dr. Glenn Stoops reviewed and commented on early drafts of the chapters of the book.
Professors Yuqing Chen, Weifu Fang, Ann Farrell, Qingbo Huang, Terry McKee, Munsup Seoh, and James T. Vance, Jr., all from Wright State University, helped me check the first page proofs.
Scott Isenberg served as developmental editor for the project. The feedback he and the reviewers gave me were essential in improving the book. It was helpful for me to get con-structive criticism, and it was heartening for me to read some good reviews. I appreciate early encouragement and help from Bill Stenquist.