微積分及其在商業(yè)經(jīng)濟生命科學及社會科學中的應用

前言

　　在我國已經(jīng)加入WTO、經(jīng)濟全球化的今天，為適應當前我國高校各類創(chuàng)新人才培養(yǎng)的需要，大力推進教育部倡導的雙語教學，配合教育部實施的“高等學校教學質(zhì)量與教學改革工程”和“精品課程”建設的需要，高等教育出版社有計劃、大規(guī)模地開展了海外優(yōu)秀數(shù)學類系列教材的弓I進工作?！　「叩冉逃霭嫔绾蚉earson Education，John Wiley＆Sons，McGraw-Hill，Thomson L,earning等國外出版公司進行了廣泛接觸，經(jīng)國外出版公司的推薦并在國內(nèi)專家的協(xié)助下，提交弓l進版權總數(shù)100余種。收到樣書后，我們聘請了國內(nèi)高校一線教師、專家、學者參與這些原版教材的評介工作，并參考國內(nèi)相關專業(yè)的課程設置和教學實際情況，從中遴選出了這套優(yōu)秀教材組織出版?！　∵@批教材普遍具有以下特點：（1）基本上是近3年出版的，在國際上被廣泛使用，在同類教材中具有相當?shù)臋嗤?；?）高版次，歷經(jīng)多年教學實踐檢驗，內(nèi)容翔實準確、反映時代要求；（3）各種教學資源配套整齊，為師生提供了極大的便利：（4）插圖精美、豐富，圖文并茂，與正文相輔相成；（5）語言簡練、流暢、可讀性強，比較適合非英語國家的學生閱讀。　　本系列叢書中，有Finney、Weir等編的《托馬斯微積分》（第10版，Pearson），其特色可用“呈傳統(tǒng)特色、富革新精神”概括，本書自20世紀50年代第1版以來，平均每四五年就有一個新版面世，長達50余年始終盛行于西方教壇，作者既有相當高的學術水平，又熱愛教學，長期工作在教學第一線，其中，年近90的G.B.Thomas教授長年在MIT工作，具有豐富的教學經(jīng)驗；Finney教授也在MIT工作達10年；Weir是美國數(shù)學建模競賽委員會主任。Stewart編的立體化教材（《微積分》（第5版，Thomson Learning）配備了豐富的教學資源，是國際上最暢銷的微積分原版教材，2003年全球銷量約40余萬冊，在美國，占據(jù)了約50％～60％的微積分教材市場，其用戶包括耶魯?shù)让圃盒＜氨姸嘁话阍盒?。本系列叢書還包括Anton編的經(jīng)典教材《線性代數(shù)及其應用》（第8版，Wiley）；Jay L.Devore編的優(yōu)秀教材《概率論與數(shù)理統(tǒng)計》（第5版，Thomson Learning）等。在努力降低弓I進教材售價方面，高等教育出版社做了大量和細致的工作，這套弓l進的教材體現(xiàn)了一定的權威性、系統(tǒng)性、先進性和經(jīng)濟性等特點?！　⊥ㄟ^影印、翻譯、編譯這批優(yōu)秀教材，我們一方面要不斷地分析、學習、消化吸收國外優(yōu)秀教材的長處，吸取國外出版公司的制作經(jīng)驗，提升我們自編教材的立體化配套標準，使我國高校教材建設水平上一個新的臺階；與此同時，我們還將嘗試組織海外作者和國內(nèi)作者合編外文版基礎課數(shù)學教材，并約請國內(nèi)專家改編部分國外優(yōu)秀教材，以適應我國實際教學環(huán)境?！　∵@套教材出版后，我們將結(jié)合各高校的雙語教學計劃，開展大規(guī)模的宣傳、培訓工作，及時地將本套叢書推薦給高校使用。在使用過程中，我們衷心希望廣大高校教師和同學提出寶貴的意見和建議。

內(nèi)容概要

　　《微積分及其在商業(yè)經(jīng)濟生命科學及社會科學中的應用（第9版影印版）》從Pearson出版公司引進，是一本優(yōu)秀經(jīng)典教材?！段⒎e分及其在商業(yè)經(jīng)濟生命科學及社會科學中的應用（第9版影印版）》從圖形、數(shù)值、解析式和文字語言的　　不同角度講解主要概念，并強調(diào)應用背景。《微積分及其在商業(yè)經(jīng)濟生命科學及社會科學中的應用（第9版影印版）》配備了較為豐富的習題，包括一些思考題供討論，文中有提醒學生注意的重要內(nèi)容標記，以及啟發(fā)學生學習興趣的數(shù)學史的傳記；在概念的引入上較有特色，不強調(diào)解題技巧?！　　段⒎e分及其在商業(yè)經(jīng)濟生命科學及社會科學中的應用（第9版影印版）》內(nèi)容包括：初等函數(shù)，微分，圖形和最值，導數(shù)，積分，積分的幾個專題，多重積分，三角函數(shù)的導數(shù)與微分等等。　　此書用英語編寫了微積分在商業(yè)、經(jīng)濟、生命科學及社會科學中的應用，并參考國內(nèi)相關專業(yè)的課程設置和教學實際情況，結(jié)合各高校的雙語教學，是一本實用性很強的教材。

書籍目錄

PART ONE A Library of.Elementary Functions1CHAPTER 1. A Beginning Library of Elementary Functions31-1 Functions 31-2 Elementary Functions: Graphs and Transformations231-3 Linear Functions and Straight Lines361-4 Quadratic Functions53Important Terms and Symbols 68Review Exercise69Group Activity 1: Introduction to Regression Analysis74Group Activity 2: Mathematical Modeling in Business75CHAPTER 2Additional Elementary Functions792-1 Polynomial and Rational Functions792-2 Exponential Functions962-3Logarithmic FUnctions110Important Terms and Symbols 122Review Exercise122Group Activity 1: Comparing the Growth of Exponential andPolynomial Functions, and Logarithmic and Root Functions125Group Activity 2: Comparing Regression Models125PART TWO Calculus 129CHAPTER 3The Derivative1313-1 Rate of Change and Slope1323-2Limits1443-3 The Derivative1623-4 Derivatives of Constants,Power Forms, and Sums1753-5 Derivatives of Products and Quotients1893-6 Chain Rule: Power Form1973-7 Marginal Analysis in Business and Economics204Important Terms and Symbols216Summary of Rules of Differentiation 216Review Exercise217Group Activity 1: Minimal Average Cost221Group Activity 2: Numerical Differentiation on a GraphingUtility 222CHAPTER 4Graphing and Optimization2254-1 Continuity and Graphs2264-2 First Derivative and Graphs2424-3 Second Derivative and Graphs2594-4 Curve Sketching Techniques: Unified and Extended2754-5 Optimization; Absolute Maxima and Minima292Important Terms and Symbols,:.308Review Exercise309Group Activity 1:Maximizing Profit 313Group Activity 2: Minimizing Construction Costs313CHAPTER 5Additional Derivative Topics 3155-1 The Constant e and Continuous Compound Interest3155-2 Derivatives of Logarithmic and Exponential Functions3225-3 Chain Rule: General Form3345-4 Implicit Differentiation3455-5 Related Rates352Important Terms and Symbols358Additional Rules of Differentiation 358Review Exercise358Group Activity 1 : Elasticity of Demand360Group Activity 2: Point of Diminishing Returns361CHAPTER 6 Integration3636-1 Antiderivatives and Indefinite Integrals3636-2 Integration by Substitution3786-3 Differential Equations; Growth and Decay3906-4 Geometric-Numeric Introduction to the Definite Integral4016-5 Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus417Important Terms and Symbols 435Integration Formulas and Properties436Review Exercise436Group:Activity 1: Simpsons Rule 440Group Activity 2: Bell-Shaped Curves443CHAPTER 7 Additional Integration, Topics4457-1 Area Between Curves 4457-2 Applications in Business and,Economics4567-3Integration by Parts 4697-4 Integration Using Tables 477Important Terms and Symbols484Review Exercise485Group Activity 1: Analysis of Income Concentration fromRaw Data 487Group Activity 2: Grain Exchange488CHAPTER 8 Multivariable Calculus4898-1 Functions of Several Variables 4898-2 Partial Derivatives 5008-3Maxima and Minima 5098-4 Maxima and Minima Using Lagrange Multipliers5188-5 Method of Least Squares5288-6 Double Integrals over Rectangular Regions539Important Terms and Symbols549Review Exercise550Group Activity 1: City Planning 553Group Activity 2: Numerical Integration of MultivariableFunctions554CHAPTER 9 Trigonometric Functions5579-1 Trigonometric Functions Review5589-2 Derivatives of Trigonometric Functions5669-3 Integration of Trigonometric Functions572Important Terms and Symbols577Review Exercise578Group Activity 1: Seasonal Business Cycles579Group Activity 2: Heating Degree Days580APPENDIX A Basic Algebra Review581Self-Test on Basic Algebra581A-1 Sets 583A-2 Algebra and Real Numbers589A-3 Operations on Polynomials596A-4 Factoring Polynomials 603A-5 Operations on Rational Expressions609A-6Integer Exponents and Scientific Notation 615A-7 Rational Exponents and Radicals621A-8 Linear Equations and Inequalities in One Variable628A-9 Quadratic Equations638APPENDIX B Special Topics649B-1 Sequences, Series, and Summation Notation649B-2 Arithmetic and Geometric Sequences656B-3 The Binomial Theorem664APPENDIX C Tables669Table I Basic Geometric Formulas669Table II Integration Formulas671Answers A1Index I1Library of Elementary Functions Inside front coverApplications Index Inside back cover

章節(jié)摘錄

　　1．l FunCtions1．2 Elementary Functions：Graphs and Transformations1．3 Linear Functions and Straight Lines1．4 Quadratic Functionslmportant Terms and SymbolsReview ExerciseGroup Activity 1：Introduction to Regression Analysis ．Group Activity 2：Mathematical Modeling in BusinessINTRODUCTIONThe function concept is one of the most important ideas in mathematics．The study of mathematics beyond the elementary level requires a firm under"standing of a basic list of elementary functions，their properties，and their graphs．See the inside front cover of this book for a list of the functions that form our library of elementary functions．Most functions in the fist will be introduced to you by the end of Chapter 2 and should become a part of your mathematical toolbox for use in this and most future courses or activities that involve mathematics．A few more elementary functions may be added to these in other courses，but the functions listed inside the front cover are more than sufficiant for all the applications in this text．Functions口CARTESIAN COORDINATE SYSTEM口GRAPHING：POINT-BY-POINT口DEHNITION OF A FuNCTION口FuNCTIONS SPECIFIED BY EQUATIONS口FUNCTION NOTATION口 APPLICATIONS After a brief review of the Cartesian(rectangular)coordinate system in the plane and point-by-point graphing，we discuss the concept of function，one of the most important ideas in mathematics．

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