Introductory Calculus. With Analytic Geometry and Linear Algebra
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Introductory Calculus. With Analytic Geometry and Linear Algebra
INTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra right © 1972, BY Academic Press, Inc.ALL RIGHTS reservedNO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, RETRIEVAL SYSTEM. OR ANY OTHER MEANS. WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.ACADEMIC PRESS. INC.Ill Fifth Avenue, New York, New York 10003United Kingdom Editi Introductory Calculus. With Analytic Geometry and Linear Algebra on published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/2R Oval ROiicl. I ondon NW1 7DDLIBRARY OF Congress Catalog Card Number: 72-182601AMS(MOS) 1970 SIntroductory Calculus. With Analytic Geometry and Linear Algebra
ubject classifications: 26-01,26AO6PRINTED IN THE UNITED STATES OF AMERICATo all my D’$PREFACE TO THE SECOND EDITIONA chemist must be familiar with thINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra ertain essentials, such as limits and the properties of real numbers, must be mastered if one is to understand calculus. We doubt, however, that a study of these rather sophisticated notions will be initially responsible for attracting very many people to the study of calculus. In our view, calculus Introductory Calculus. With Analytic Geometry and Linear Algebra should be presented in a way that appeals to the student’s intuitive feeling of W'hat ought to be. This book represents such an effort.We have wishedIntroductory Calculus. With Analytic Geometry and Linear Algebra
to sacrifice neither accuracy nor honesty in our attempt to be interesting. In fact, the definitions we give for function, graph, linear, derivative,INTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra a proof is not given, its omission is clearly pointed out. Often an example is given to show why careful attention to a proof is warranted in a future course.We said in the preface to the first edition that a conscious effort had been made to reverse the trend of calculus texts to become encycloped Introductory Calculus. With Analytic Geometry and Linear Algebra ic. One concession has been made by including in this edition an introductory chapter on elementary analytic geometry (and a concession of another typIntroductory Calculus. With Analytic Geometry and Linear Algebra
e was made to the editor when we agreed not to title this chapter The Plane Facts). We have also included a separate section to discuss limits more fuINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra ut the subject at hand.The first edition stressed the role of the derivative as a tool of approximation by defining the derivative to be a linear transformation. Though the spirit of this idea is retained in the second edition, formal terminology (and notation toward this end) has been left out of t Introductory Calculus. With Analytic Geometry and Linear Algebra he treatment of one variable except for one optional section. Thus, for a traditional course in one variable calculus, this notion can be ignored by tIntroductory Calculus. With Analytic Geometry and Linear Algebra
hose who choose to do so.Keeping in mind the needs of increasing numbers of social science students appearing in the mathematics classroom, wc have coINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra the presentation is set in this context. The background in linear algebra necessary to this approach, somewhat scattered through the first edition, has in this edition been collected into a separate chapter. It is to be stressed that we have included the linear algebra here for the same reason that Introductory Calculus. With Analytic Geometry and Linear Algebra it was included in the first edition; not because it is the modern thing to do so, but because it plays an essential role in what is to follow.The opeIntroductory Calculus. With Analytic Geometry and Linear Algebra
ning chapter on analytic geometry begins with a discussion of vectors in the plane. By using vectors to develop some of the results of—Xi—analytic geoINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra way for using the same definitions and methods in the later chapter on linear algebra.We distinguish between problems and exercises in this text. Problems are scattered throughout the text and are to be attempted by every reader. Their purpose is to clinch an idea of a previous paragraph or to prep Introductory Calculus. With Analytic Geometry and Linear Algebra are the way for what is to come. They should be attempted immediately when they are met in reading. Because they form an important part of the text, cIntroductory Calculus. With Analytic Geometry and Linear Algebra
omplete solutions arc given in the rear of the book. The reader should not be discouraged if he finds the problems very challenging; some arc given moINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra drill problems, they are arranged in what seems to the author to be ascending order of difficulty. Some sections include starred exercises at the end which arc more difficult and serve to extend the abilities of the more able students. Exercises are arranged so that the same skills are required by Introductory Calculus. With Analytic Geometry and Linear Algebra the even-numbered problems (which have no answers given at the rear) and by the odd-numbered ones (for which the answers arc given). Some sections andIntroductory Calculus. With Analytic Geometry and Linear Algebra
their corresponding exercise lists from the first edition have been broken into two parts so as to correspond more directly with the amount of materiINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra is expected to have proficiency at high school algebra and trigonometry, though specific topics are reviewed in the text where experience suggests this to be helpful. Chapter I includes the analytic geometry so many missed in the first edition. It may be used with an emphasis suited to the preparati Introductory Calculus. With Analytic Geometry and Linear Algebra on of the class. The heart of a traditional one variable calculus course is contained in Chapters 2-8 and 14 with Chapters 9 and 15 being optional. AIntroductory Calculus. With Analytic Geometry and Linear Algebra
third-semester course focusing on functions of several variables would include Chapters 10-13 with Chapters 9 and 15 again optional. In that Chapter 1INTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyr Introductory Calculus. With Analytic Geometry and Linear Algebra apter 10.Once again 1 wish to take the opportunity afforded by a Preface to thank the students and faculty at Macalester College who have now made substantial contributions to two editions of this text. Special thanks are due to Carol Svoboda who helped with many of the mechanical details of the sec Introductory Calculus. With Analytic Geometry and Linear Algebra ond edition, checked all the answers in the back of the book, and read the galley proof of the entire book. Finally, it is a pleasure to acknowledge aIntroductory Calculus. With Analytic Geometry and Linear Algebra
gain the helpfulness and good spirit of the staff of Academic Press.—xii—INTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyrINTRODUCTORYCALCULUSSecond Edition, with Analytic Geometry and Linear AlgebraA. WAYNE ROBERTSMacalester CollegeACADEMIC PRESS New York and LondonCopyrGọi ngay
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