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  • 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)[平装]
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  • 作者:巴尼特(作者),等(作者)
  • 出版社:高等教育出版社;第9版(2005年4月1日)
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  • ISBN:9787040162318

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    《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)》高等教育出版社出版发行。

    作者简介

    作者:( )Raymond A.Barnett等[著]

    目录

    PART ONE A Library of.Elementary Functions1
    CHAPTER 1. A Beginning Library of Elementary Functions3
    1-1 Functions 3
    1-2 Elementary Functions: Graphs and Transformations23
    1-3 Linear Functions and Straight Lines36
    1-4 Quadratic Functions53
    Important Terms and Symbols 68
    Review Exercise69
    Group Activity 1: Introduction to Regression Analysis74
    Group Activity 2: Mathematical Modeling in Business75

    CHAPTER 2Additional Elementary Functions79
    2-1 Polynomial and Rational Functions79
    2-2 Exponential Functions96
    2-3Logarithmic FUnctions110
    Important Terms and Symbols 122
    Review Exercise122
    Group Activity 1: Comparing the Growth of Exponential and
    Polynomial Functions, and Logarithmic and Root Functions125
    Group Activity 2: Comparing Regression Models125

    PART TWO Calculus 129
    CHAPTER 3The Derivative131
    3-1 Rate of Change and Slope132
    3-2Limits144
    3-3 The Derivative162
    3-4 Derivatives of Constants,Power Forms, and Sums175
    3-5 Derivatives of Products and Quotients189
    3-6 Chain Rule: Power Form197
    3-7 Marginal Analysis in Business and Economics204
    Important Terms and Symbols216
    Summary of Rules of Differentiation 216
    Review Exercise217
    Group Activity 1: Minimal Average Cost221
    Group Activity 2: Numerical Differentiation on a Graphing
    Utility 222

    CHAPTER 4Graphing and Optimization225
    4-1 Continuity and Graphs226
    4-2 First Derivative and Graphs242
    4-3 Second Derivative and Graphs259
    4-4 Curve Sketching Techniques: Unified and Extended275
    4-5 Optimization; Absolute Maxima and Minima292
    Important Terms and Symbols,:.308
    Review Exercise309
    Group Activity 1:Maximizing Profit 313
    Group Activity 2: Minimizing Construction Costs313

    CHAPTER 5Additional Derivative Topics 315
    5-1 The Constant e and Continuous Compound Interest315
    5-2 Derivatives of Logarithmic and Exponential Functions322
    5-3 Chain Rule: General Form334
    5-4 Implicit Differentiation345
    5-5 Related Rates352
    Important Terms and Symbols358
    Additional Rules of Differentiation 358
    Review Exercise358
    Group Activity 1 : Elasticity of Demand360
    Group Activity 2: Point of Diminishing Returns361

    CHAPTER 6 Integration363
    6-1 Antiderivatives and Indefinite Integrals363
    6-2 Integration by Substitution378
    6-3 Differential Equations; Growth and Decay390
    6-4 Geometric-Numeric Introduction to the Definite Integral401
    6-5 Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus417
    Important Terms and Symbols 435
    Integration Formulas and Properties436
    Review Exercise436
    Group:Activity 1: Simpson's Rule 440
    Group Activity 2: Bell-Shaped Curves443

    CHAPTER 7 Additional Integration, Topics445
    7-1 Area Between Curves 445
    7-2 Applications in Business and,Economics456
    7-3Integration by Parts 469
    7-4 Integration Using Tables 477
    Important Terms and Symbols484
    Review Exercise485
    Group Activity 1: Analysis of Income Concentration from
    Raw Data 487
    Group Activity 2: Grain Exchange488

    CHAPTER 8 Multivariable Calculus489
    8-1 Functions of Several Variables 489
    8-2 Partial Derivatives 500
    8-3Maxima and Minima 509
    8-4 Maxima and Minima Using Lagrange Multipliers518
    8-5 Method of Least Squares528
    8-6 Double Integrals over Rectangular Regions539
    Important Terms and Symbols549
    Review Exercise550
    Group Activity 1: City Planning 553
    Group Activity 2: Numerical Integration of Multivariable
    Functions554

    CHAPTER 9 Trigonometric Functions557
    9-1 Trigonometric Functions Review558
    9-2 Derivatives of Trigonometric Functions566
    9-3 Integration of Trigonometric Functions572
    Important Terms and Symbols577
    Review Exercise578
    Group Activity 1: Seasonal Business Cycles579
    Group Activity 2: Heating Degree Days580

    APPENDIX A Basic Algebra Review581
    Self-Test on Basic Algebra581
    A-1 Sets 583
    A-2 Algebra and Real Numbers589
    A-3 Operations on Polynomials596
    A-4 Factoring Polynomials 603
    A-5 Operations on Rational Expressions609
    A-6Integer Exponents and Scientific Notation 615
    A-7 Rational Exponents and Radicals621
    A-8 Linear Equations and Inequalities in One Variable628
    A-9 Quadratic Equations638

    APPENDIX B Special Topics649
    B-1 Sequences, Series, and Summation Notation649
    B-2 Arithmetic and Geometric Sequences656
    B-3 The Binomial Theorem664

    APPENDIX C Tables669
    Table I Basic Geometric Formulas669
    Table II Integration Formulas671
    Answers A1
    Index I1
    Library of Elementary Functions Inside front cover
    Applications Index Inside back cover

    序言

    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。
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    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。

    文摘

    插图:


    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.