Judith L. Gersting - Technical Calculus with Analytic Geometry

Judith L. Gersting University of Hawaii at Hilo DOVER PUBLICATIONS, INC. New York Copyright 1984 by Judith L. Gersting All rights reserved. This Dover edition, first published in 1992, is an unabridged and corrected republication of the work first published by the Wadsworth Publishing Company, Belmont, California, in 1984. 1, 66, 182, 246, 286, 340, and 374; Tim Yates, p. 33; Image Bank West/Grafton Marshall Smith, p. 81; NASA, p. 136. Library of Congress Cataloging-in-Publication Data Gersting, Judith L. Library of Congress Cataloging-in-Publication Data Gersting, Judith L.

Technical calculus with analytic geometry / Judith L. Gersting.
p. cm. Unabridged and corrected republication of the work first published by the Wadsworth Publishing Company, Belmont, California, in 1984T.p. verso. Includes index.

ISBN 0-486-67343-X 1. Calculus. 2. Geometry, Analytic. I. Title.
QA303.G43 1992 515M5dc20 92-34100 CIP Manufactured in the United States by Courier Corporation
67343X04
www.doverpublications.com To John, my favorite engineer

This text is intended for a two-semester course in calculus for technology students.

The prerequisites for the course are college algebra and trigonometry. The expected student audience has influenced the choice of topics covered, the style of presentation, and the types of examples and exercises. In my teaching experience I have found technology students to be strongly career oriented; they sincerely work hard to understand material that they feel is pertinent to their goals. This text has been written to attract students interest by providing motivating examples, by giving them an intuitive understanding of the concepts behind what they are doing, and by providing much opportunity to gain proficiency in techniques and skills.

The topics in the table of contents are quite standard, but there are some variations from other books as to where or how a particular topic is covered. A brief but thorough review of the concept of a function is done in the first sections.

Polar coordinates, partial derivatives, and double integrals are presented where they are natural extensions of rectangular coordinate work, but they can be left for later or omitted entirely if the instructor desires. The definite integral as the limit of a sum is stressed (in an intuitive way) so that the student gets a good idea of how to use the definite integral in a variety of situations. There is an emphasis on matching an integration problem with the pattern for a given integration rule, and a section is included on partial fractions as an integration technique.

Numerous features are built into the book in an effort to make it a useful learning tool for students. First and foremost, the writing style has been kept clear and readable, informal and conversational. I have tried to write as if I were giving a lecture in class, avoiding the stuffiness that can all too easily slip into written material and cause the students to have to ask for an interpretation of what theyve read.

The book talks with students and acts as their aid and advocate in conquering the calculus.

Examples are abundant. Each example shows the complete solution method without skipping any intermediate steps. Occasionally alternate solutions to the same problem are given. When a new technique is being demonstrated, a reason is given for each step in the solution process. Many examples and exercises are drawn from various fields of technology, as well as such fields as ecology, economics, and physiology.

The value of student motivation generated in this manner can be great. I remember a student in my early teaching career who came to ask me about an example that he did not understand. The example was phrased in terms of electronics technology, and the student said, I want to be an electronics technician, so I figure I really need to understand this example. As teachers, we can capitalize on this sort of interest.

Practice problems appear in the body of the text in each section of the book. These problems are relatively easy and are intended to be worked by the student as soon as they are encountered.

Each new type of example in the text is followed by a practice problem that allows the student to gain immediate reinforcement in applying the problem-solving technique illustrated by the example. Answers to all practice problems are given at the back of the book, many with worked-out solution steps. This sets the method in the students mind so that when the exercises at the end of the section are worked, the student does not have to begin by searching for an appropriate example and wondering if he or she really understands it once it is located. Students find the practice problems to be extremely helpful.

Other learning aids are incorporated in the book. Many Words of Advice are scattered throughout.

These messages from a wise old owl caution the student against common errors. Complex problem-solving processes are broken down into a series of step-by-step tasks. Numerous exercises appear at the end of each section. The exercises, for the most part, are paired into odd-even problems that are very similar. Answers to all odd exercises are given at the back of the book, some with expanded solutions. A Status Check at the end of each chapter gives the chapter objectives to help the students review (and to aid the instructor in making out exams).

The chapter Status Check is immediately followed by a section of additional review exercises. A glossary, with definitions and page references, is included at the back of the book.

The book assumes that the student has a scientific calculator available to use. There are several consequences of this assumption. First, and perhaps most obvious, is that no trigonometric or logarithmic tables appear in the book. (In computing answers I have used exact values, such as , throughout a computation and converted them at the end to decimal equivalents when required. (In computing answers I have used exact values, such as , throughout a computation and converted them at the end to decimal equivalents when required.

I have used no standard rule, however, for the number of decimal places of accuracy and have simply rounded off answers as seemed appropriate. Thus students should be aware that their answers may differ slightly in numerical value if they have carried more decimal places.) Third, the most interesting consequence of having the calculator available is that it is used to suggest patterns and illustrate concepts such as limit, slope, and convergence of series. A calculator is also useful in approximation techniques for integration and solution of differential equations. Virtually all examples and exercises use SI (metric) units. An appendix of common metric units and their notation is included at the back of the book. Other appendices give common geometric formulas and a table of integrals.

My thanks to the many reviewers whose helpful suggestions smoothed out the rough spots. In particular, Mr. Blin Scatterday of the Univesity of Akron and Mr. Henry Davison of St. Petersburg Junior College helped in reading proof and checking answers, and I especially appreciate their work. Mr.

Scatterday has also prepared a solutions manual for all the even-numbered exercises. Miss Linda Knabe worked wonders in creating typescript out of handwritten manuscript, and I thank her for her always cheerful help. I would also like to express my appreciation to Rich Jones of Wads worth, who originally thought of this project and had the patience to see me through it. Finally, my special thanks to my family for their support and encouragement, including their willingness to endure my long periods of reclusion in the den. Judith L. J. J.