Basic technical mathematics PDF
Preview Basic technical mathematics
Basic Technical Mathematics SECOND EDITION Other books by the author Essentials of Basic Mathematics Introduction to Technical Mathematics Basic Technical Mathematics with Calculus Second Edition Technical Calculus with Analytic Geometry Allyn J. Washington Dutchess Community College Poughkeepsie, New York Basic Technical Mathematics SECOND EDITION CUMMINGS PUBLISHING COMPANY Menlo Park, California • Reading, Massachusetts London • Amsterdam • Don Mills, Ontario • Sydney Copyright © 1970 by Cummings Publishing Company, Inc. Philippines Copyright 1970 All rights reserved. No fart of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Published simultaneously in Canada Library of Congress Catalog Card No. 76-112355 ISBN 0-8465-8608-8 FGHIJKLMN-HA-798765 Cummings Publishing Company 2727 Sand Hill Road Menlo Park, California 94025 Preface This book is intended primarily for students in technical or pre-engineering technology programs where a coverage of basic mathematics is required. Chapters 1 through 19 provide the necessary background in algebra and trigonometry for analytic geometry and calculus courses, and Chapters 1 through 20 provide the background necessary for calculus courses. There is an integrated treatment of mathematical topics, primarily algebra and trigonom¬ etry, which have been found necessary for a sound mathematical background for the technician. Numerous applications from many fields of technology are included primarily to indicate where and how mathematical techniques are used. It is assumed that students using this text will have a background including algebra and geometry. However, the material is presented in sufficient detail for use by those whose background is possibly deficient to some extent in these areas. The material presented here is sufficient for two to three semesters. One of the primary reasons for the arrangement of topics in this text is to present material in such an order that it is possible for a student to take courses in allied technical areas, such as physics and electricity, concurrently. These allied courses normally require that a student know certain mathematical topics by certain definite times, and yet, with the traditional mathematical order of topics, it is difficult to attain this coverage without loss of continuity. However, this material can be arranged to fit any appropriate sequence of topics, if this is deemed necessary. Another feature of the material in this text is that certain topics which are traditionally included, primarily for mathematical complete¬ ness, have been omitted. The approach used here is basically an intuitive one. It is not unduly mathe¬ matically rigorous, although all appropriate terms and concepts are introduced as needed and given an intuitive or algebraic foundation. The book’s aim is to help the student develop a feeling for mathematical methods, and not simply to have a collection of formulas when he has completed his work in the text. There is emphasis on the fact that it is essential that the student have a fluent background in algebra and trigonometry if he is to understand and succeed in any subsequent work in mathematics. This second edition includes all of the basic features of the first edition. However, nearly all sections have been rewritten to some degree to include additional explanatory material, examples and exercises. Specifically, among the new features of the second edition are the following: (1) Chapter 15, on determinants and matrices, is new; (2) New sections are Section 2-4, devoted to solving equations graphically, Section 5-6, devoted to equations involving fractions, Section 12-7, which takes up logarithms to bases other than ten, and Appendix D, on a review of geometry. (3) Scientific notation is now included as Section 10-2 in the chapter on exponents and radicals. (4) Fitting nonlinear curves to data is a separate section, Section 21-5. (5) There are now about 700 worked examples, an increase of about 125. (6) There are now about 4500 exercises, an increase of about 1800. (7) The early chapters on basic algebra have been expanded considerably. (8) Exercises are now generally grouped such that there is an even-numbered exercise equivalent to each odd-numbered exercise. One of the unique features of this text is that the topics of significant digits and the slide rule are covered in the Appendix. This allows these topics to be introduced whenever the instructor wishes. At Dutchess Community College, we devote a few minutes each day for the first several weeks to this material. It has been found that this policy of many brief discussions works as well as, if not better than, a concentrated coverage at the beginning. Another feature is that this text contains many more worked examples than are ordinarily included in such a book. These examples are often used advan¬ tageously to introduce concepts, as well as to clarify and illustrate points made in the text. Also, there is extensive use of graphical methods. Other features are (1) stated problems are included a few at a time in order to allow the student to develop techniques of solution; (2) those topics which experience has shown to be more difficult for the student have been developed in more detail, with many examples; (3) the order of coverage can be changed in several places without loss of continuity. Also, certain sections may be omitted without loss of continuity. Any omissions or changes in order will, of course, depend on the type of course and the completeness required. (4) The chapter on statistics is included in order to introduce the student to statistical and empirical methods. (5) Miscellaneous exercises are included after each chapter. These may be used either for additional problems or for review assign¬ ments. (6) The answers to nearly all the odd-numbered exercises are given at the back of the book. Included are answers to graphical problems, and other types which are often not included in textbooks. The author wishes to acknowledge the help and suggestions given him by many of those who have used the first edition of this text. In particular, I wish to thank Harry Boyd, Gail Brittain, Stephen Lange, and Michael Mayer of \
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