微积分及其在商业经济生命科学及社会科学中的应用

出版时间：2004  出版社：高等教育出版社  作者：Raymaond A. Rarnett  页数：742  
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前言

　　在我国已经加入WTO、经济全球化的今天，为适应当前我国高校各类创新人才培养的需要，大力推进教育部倡导的双语教学，配合教育部实施的“高等学校教学质量与教学改革工程”和“精品课程”建设的需要，高等教育出版社有计划、大规模地开展了海外优秀数学类系列教材的弓I进工作。　　高等教育出版社和Pearson Education，John Wiley＆Sons，McGraw-Hill，Thomson L,earning等国外出版公司进行了广泛接触，经国外出版公司的推荐并在国内专家的协助下，提交弓l进版权总数100余种。收到样书后，我们聘请了国内高校一线教师、专家、学者参与这些原版教材的评介工作，并参考国内相关专业的课程设置和教学实际情况，从中遴选出了这套优秀教材组织出版。　　这批教材普遍具有以下特点：（1）基本上是近3年出版的，在国际上被广泛使用，在同类教材中具有相当的权威性；（2）高版次，历经多年教学实践检验，内容翔实准确、反映时代要求；（3）各种教学资源配套整齐，为师生提供了极大的便利：（4）插图精美、丰富，图文并茂，与正文相辅相成；（5）语言简练、流畅、可读性强，比较适合非英语国家的学生阅读。　　本系列丛书中，有Finney、Weir等编的《托马斯微积分》（第10版，Pearson），其特色可用“呈传统特色、富革新精神”概括，本书自20世纪50年代第1版以来，平均每四五年就有一个新版面世，长达50余年始终盛行于西方教坛，作者既有相当高的学术水平，又热爱教学，长期工作在教学第一线，其中，年近90的G.B.Thomas教授长年在MIT工作，具有丰富的教学经验；Finney教授也在MIT工作达10年；Weir是美国数学建模竞赛委员会主任。Stewart编的立体化教材（《微积分》（第5版，Thomson Learning）配备了丰富的教学资源，是国际上最畅销的微积分原版教材，2003年全球销量约40余万册，在美国，占据了约50％～60％的微积分教材市场，其用户包括耶鲁等名牌院校及众多一般院校。本系列丛书还包括Anton编的经典教材《线性代数及其应用》（第8版，Wiley）；Jay L.Devore编的优秀教材《概率论与数理统计》（第5版，Thomson Learning）等。在努力降低弓I进教材售价方面，高等教育出版社做了大量和细致的工作，这套弓l进的教材体现了一定的权威性、系统性、先进性和经济性等特点。　　通过影印、翻译、编译这批优秀教材，我们一方面要不断地分析、学习、消化吸收国外优秀教材的长处，吸取国外出版公司的制作经验，提升我们自编教材的立体化配套标准，使我国高校教材建设水平上一个新的台阶；与此同时，我们还将尝试组织海外作者和国内作者合编外文版基础课数学教材，并约请国内专家改编部分国外优秀教材，以适应我国实际教学环境。　　这套教材出版后，我们将结合各高校的双语教学计划，开展大规模的宣传、培训工作，及时地将本套丛书推荐给高校使用。在使用过程中，我们衷心希望广大高校教师和同学提出宝贵的意见和建议。

内容概要

　　《微积分及其在商业经济生命科学及社会科学中的应用（第9版影印版）》从Pearson出版公司引进，是一本优秀经典教材。《微积分及其在商业经济生命科学及社会科学中的应用（第9版影印版）》从图形、数值、解析式和文字语言的　　不同角度讲解主要概念，并强调应用背景。《微积分及其在商业经济生命科学及社会科学中的应用（第9版影印版）》配备了较为丰富的习题，包括一些思考题供讨论，文中有提醒学生注意的重要内容标记，以及启发学生学习兴趣的数学史的传记；在概念的引入上较有特色，不强调解题技巧。　　《微积分及其在商业经济生命科学及社会科学中的应用（第9版影印版）》内容包括：初等函数，微分，图形和最值，导数，积分，积分的几个专题，多重积分，三角函数的导数与微分等等。　　此书用英语编写了微积分在商业、经济、生命科学及社会科学中的应用，并参考国内相关专业的课程设置和教学实际情况，结合各高校的双语教学，是一本实用性很强的教材。

书籍目录

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

章节摘录

　　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．