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A Mathematics Companion for Science and Engineering Students

2007 Edition, December 26, 2007

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ISBN: 9780195327755
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Product Details:

  • Revision: 2007 Edition, December 26, 2007
  • Published Date: December 26, 2007
  • Status: Active, Most Current
  • Document Language: English
  • Published By: Oxford University Press (OUP)
  • Page Count: 496
  • ANSI Approved: No
  • DoD Adopted: No

Description / Abstract:

Preface

Science and engineering are fields that require both a knowledge of, and a facility in, mathematics. For many careers in these fields, especially the most interesting and those that push forwardthe state of the art, an ability to use mathematics to solve analytical problems andto think creatively is a must.

At most colleges and universities, undergraduate programs in science and engineering begin immediately with rigorous coursework in calculus and differential equations, followed by further study in mathematics. Throughout, a student's adeptness at mathematical analysis can be the difference between success and failure.

The purpose of this book is to provide students in these programs with a convenient andreliable reference on a variety of topics in, andrelatedto, basic mathematics. Professional scientists andengineers, as well as pre-college students who are interestedin these professions, shouldalso findit useful. Besides being a source for self-study, the book can be usedas either a supplemental reader in mathematically intense courses or as a textbook itself (perhaps in conjunction with others). A particularly goodplace for its introduction is a freshman orientation course, to be usedthen andthereafter.

The bulk of the material herein is generally referredto as "precalculus". All major topics are thoroughly covered; but, care has been taken not to overwhelm the reader with mathematical terminology (e.g., "ring", "neighborhood") they are unlikely to encounter in practice. Some additional topics (e.g., Stirling's approximation, uniform convergence) have been included which, though unfamiliar to the typical high school graduate, might well become useful later on; thus, to some extent the book grows along with the reader. Also, the last chapter discusses practical matters regarding the application of mathematics to the measurement andmanipulation of experimental data.

The level of the presentation is such that, upon careful reading, the intended reader should be able to assimilate all that is said. This book differs, though, from other treatments of basic math for nonmathematics students in two significant ways. First, being primarily a reference manual rather than a tutorial, many assertions are made without justification; the writing style is succinct; and, examples are used more to explain than to teach. Second, with few exceptions, all definitions and facts are stated completely, precisely, and in detail; the text does not shield the reader from the full story. (The alternative wouldbe to make the material seem easier than it is, thereby leaving pitfalls for readers to stumble upon later and somehow resolve on their own.1)

On the other hand, more is given here than just a compendium of facts and formulas. Much ancillary information—observations, explanations, warnings, techniques, tips—appears on nearly every page. And, although the book does not coddle the reader, it is not written in the formal theorem-proof style of a typical mathematics text. In a nutshell, rigor is not sacrificed to attain readability; rather, rigorous mathematics is made readable.

A large appendix provides 360 problems ranging from easy to challenging, many of which have arisen in science andengineering courses. Almost entirely, these are not mindless exercises (i.e., "drill" or "plug-in" problems), but opportunities for readers to test both their knowledge of the material and their skill in applying it. Additionally, some problems present facts andterminology beyondwhat is addressedin the chapters themselves, andthus might be readfor that reason alone. Accompanying the problems are complete andfully detailedsolutions, which also serve to demonstrate acceptable mathematical argumentation.

An up-to-date list of errata is maintained online at www.oup.com/us/he/breitenbach

1. As just one case in point, see fn. 21 in Chapter 3.