Crowhurst Norman - Mastering Technical Mathematics

Mastering Technical Mathematics

ABOUT THE AUTHORS

Stan Gibilisco is one of McGraw-Hill's most prolific and popular authors. His clear, reader-friendly writing style makes his books accessible to a wide audience, and his experience as an electronics engineer, researcher, and mathematician makes him an ideal editor for reference books and tutorials. Stan has authored several titles for the McGraw-Hill Demystified library of home-schooling and self-teaching volumes, along with more than 30 other books and dozens of magazine articles. His work has been published in several languages. Booklist named his McGraw-Hill Encyclopedia of Personal Computing one of the Best References of 1996, and named his Encyclopedia of Electronics one of the Best References of the 1980s.

Norman Crowhurst (deceased) originated the concept of Mastering Technical Mathematics. He authored the first edition.

Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.

ISBN: 978-0-07-159542-1

MHID: 0-07-149448-0

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To Tim, Samuel, and Tony

Contents

Introduction

This book is intended as a refresher course for scientists, engineers, and technicians. It begins with a review of basic calculation techniques and progresses through intermediate topics in applied mathematics. This edition contains new or revised material on scientific notation, geometry, trigonometry, vectors, coordinate systems, logarithms, exponential functions, propositional logic, truth tables, statistics, and probability.

Youll notice that some of the discussions, especially in the early chapters, deal with archaic units such as feet and pounds. This isnt sheer madness or nostalgia for the olden days; there is a reason for it! The unfamiliarity (and in some cases strangeness) of these English units can help you more fully grasp the principles relating the phenomena the units describe.

Ideally, youll have worked with all the material youll see in this book, or at least seen it in some form. If something here is alien to youfor example, propositional logicconsider taking a formal course on that subject, using this book as a supplement. What if you took logic from your Alma Mater 20 years ago? Are the concepts still in your mind but no longer fresh? In that sort of situation, this book can bring things back into focus, so you can again work easily with concepts you learned long ago.

Each chapter ends with a Questions and Problems section. Refer to the text when solving these problems. Answers are in an appendix at the back of the book. In some cases, descriptions of the problem-solving processes are given in the answer key. Of course, many problems can be solved in more than one way. If you get the right answer by a method that differs from the scheme in the answer key, you might have found a better way!

In recent years, electronic calculators have rendered much of the material in this book academic. To find the sine of an angle, for example, you can punch it up on a calculator you bought at a grocery store and get an answer accurate to 10 significant figures. Personal computers have calculator programs that can go to many more digits than that. Nevertheless, its helpful to understand the theory involved. You should at least read (if not painstakingly study) every chapter in this book.

Most people are strong in certain areas of mathematics and weak in others. If your job involves the use of math, youll need proficiency in some fields more than in others. When you use this book as a refresher course, keep in mind that you might need intensive work on subjects that you dont like or that you have trouble grasping.

The material here is presented in a condensed format. Youll sometimes think that your progress must be measured in hours per page. If you get stuck someplace, skip ahead, work on something else for awhile, and then come back to the trouble spot. Of course, you can always refer to more basic or subject-intensive texts to reinforce your knowledge in those areas where you are not confident.

Suggestions for future editions are welcome.

Stan Gibilisco

Weve all seen or heard people count. You put a number of things in a group, move them to another group one at a time, and count as you go. One, two, three We learn to save time when counting by making up groups. shows four different ways in which seven items, in this case coins, can be grouped.