Book Preface

Today’s engineering and science students routinely confront problems involving numerical solution techniques. Sometimes these solutions are “automatically” generated by a software package. In other cases, students must use programming skills to devise their own solutions. In either case, knowledge of numerical methods is absolutely necessary for developing and interpreting such solutions with wisdom and insight.

This book is written to support a one-semester course in numerical methods. The book’s primary audience are students who want to learn numerical methods to solve problems in engineering and science. As such, the methods are motivated by problems rather than by mathematics. That said, sufficient theory is provided so that students come away with insight into the techniques and their shortcomings.

MATLAB® provides a great environment for such a course. Although other environments (e.g., Excel/VBA, Mathcad) or languages (e.g., Fortran 90, C++) could have been chosen, MATLAB presently offers a nice combination of handy programming features with powerful built-in numerical capabilities. On the one hand, its M-file programming environment allows students to implement moderately complicated algorithms in a structured and coherent fashion. On the other hand, its built-in numerical capabilities empower students to solve more difficult problems without trying to “reinvent the wheel.”

The first chapters provide introductory material including background on mathematical modeling, MATLAB fundamentals, and error analysis. This is followed by chapters dealing with several major areas of numerical methods: root location, linear algebraic equations, least-squares regression, interpolation, integration, ordinary differential equations, and eigenvalues.

I have made a concerted effort to make this book as student-friendly as possible. Thus, I’ve tried to keep my explanations straightforward and oriented practically. Although my primary intent is to empower students by providing them with a sound introduction to numerical problem solving, I have the ancillary objective of making this introduction exciting and pleasurable. I believe that motivated students who enjoy engineering and science, problem solving, and—yes—programming, will ultimately make better professionals. If my book fosters enthusiasm and appreciation for this subject, I will consider the effort a success.