Calculus for business, economics, life sciences, and social sciences = 微积分及其在商业、经济、生...

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