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。

PART ONE   A Library of Elemententary Functions   1

 cHAPTER 1 ABeginningLibraryofElementaryFunctions 3

1．1 Functions 3

1．2 Elementary Functions：Graphs and Transformations 23

1．3 Linear Functions and Straight Lines 36

1。4 Quadratic Functions 53

   Important Terms and Symbols 68

   Review Exercise 69

   Group Activity 1：Introduction to Regression Analysis 74

   Group Activity 2：Mathematical Modeling in Business 75

 cHAPTER 2 AdditionalElementaryFuncUons 79

2．1 Polynomial and Rational Functions 79

2。2 Exponenfial Functions 96

2．3 Logarithmic Functions 110

   ImportantTerms andSymbols 122

   Review Exerdse 122

   Group Activity 1：Comparing the Growth of Exponential and

   P0lvnomiM Functions，and Logarithmic and Root Functions 125

   Group Activity 2：Comparing Regression Models 125

PART TWO  Calculus 129

 CHAPTER 3 The Derivative 131

3．1 Rate of Change and Slope 132

3．2 Limits 144

3．3 The Derivative 162

3．4 Derivatives of Constants，Power Forms，and Sums 175

3．5 Derivatives of Products and Ouotients 189

3。6 Chain Rule：Power Form 197

3。7 Marginal Analysis in Business and Economics 204

   Important Terms and Symbols 216

   Summary of Rules of Differentiation 216

   Review Exercise 217

   Group Activity 1：Minimal Average Cost 221

   Group Activity 2：Numerical Differentiation on a Graphing Utility 222 

 cHAPTER 4 Graphing and Optimization 225

4。1 Continuity and Graphs 226

4。2 First Derivative and Graphs 242

4。3 Second Derivative and Graphs 259

4。4 Curve Sketching Techniques：Unified and Extended 275

4。5 Optimization；Absolute Maxima and Minima 292

   Important Terms and Symbols 308

   Review Exercise 309

   Group Activity 1：Maximizing Profit 313

   Group Activity 2：Minimizing Construction Costs 313

   cHAPT ER 5 Additional Derivative Topics 315

5。1 The Constant e and Continuous Compound Interest 315

5。2 Derivatives of Logarithmic and Exponential Functions 322

5。3 Chain Rule：General Form 334

5。4 Implicit Differentiation 345

5。5 Related Rates 352

   Important TelT／IS and Symbols 358

   Additional Rules of Differentiation 358

   Review Exercise 358

   Group Activity 1：Elasticity ofDemand 360

   Group Activity 2：Point of Diminishing Returns 361

 cHAPTER 6 Integration 363

6。1 Antiderivatives and Indefinite Integrals 363

6。2 Integration by Substitution 378

6。3 Differential Equations；Growth and Decav 390

6。4 Geometric—Numeric Introduction to the Definite Integral 401

6。5 Definite Integral as a Limit of a Sum；Fundamental Theorem of Calculus 417

   Important Terms and Symbols 435

   Integration Formulas and Properties 436

   Review Exercise 436

   Group Activity 1：Simpson"s Rule 440

   Group Activity 2：Bell—Shaped Curves 443

 cHAPTER 7 AdditionalIntegrationTopics 445

7．1 Area Between Curves 445

7。2 Applications in Business and Economics 456

7．3 Integration by Parts 4-69

7。4 Integration Using Tables 477

   Important Terms and Symbols 484

   Review Exercise 485

   Group Activity 1：Analysis of Income Concentration from RawData 487

   Group Activity 2：Grain Exchange 488

 cHAPllIER 8 Multivariable Caleulus 489

8。1 Functions of Several Variables 489

8。2 Partial Derivatives 500

8。3 Maxima and Minima 509

8。4 Maxima and Minima Using Lagrange Multipliers 518

8．5 Method of Least Squares 528

8。6 Double Integrals over Rectangular Regions 539

   Important Terms and Symbols 549  ’

   Review Exercise 550

   Group Activity 1：City Planning 553

   Group Activity 2：Numerical Integration of Multivariable Functions 554

 cHAPllIER 9 Trigonometric Functions 557

9。1 Trigonometric Functions Review 558

9．2 Derivatives of Trigonometric Functions 566

9。3 Integration of Trigonometric Functions 572

   Important Terms and Symbols 577

   Review Exercise 578

   Group Activity 1：SeasonM Business Cycles 579

   Group Activity 2：Heating Degree Days 580

 APPENDlxA BasicAlgebraReview 581

Self-rest on Basic Algebra 581

A。1 Sets 583

A。2 Algebra and Real Numbers 589

A。3 Operations on Polynomials 596

A。4 Factoring Polynomials 603

A。5 Operations on Rational Expressions 609

A。6 Integer Exponents and Scientific Notation 615

A。7 Rational Exponents and Radicals 621

A。8 Linear Equations and Inequalities in One Variable 628

A。9 Quadratic Equations 638

 APPENDlX B SpecialTopics 649

B。1 Sequences．Series．and Sunlmation Notation 649

B。2 Arithmetic and Geometric Sequences 656

B．3 The Binomial Theorem 664

 APPENDlxc Tables 669

Table I Basic Geometric Formulas 669

Table II Integration Formulas 671

Answers A1

Index II

Library of Elementary Functions Inside front cover

Applications Index Inside back cover

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．      （P3）

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高等教育出版社

2004年4月20日