APPLIED CALCULUS, 3/E brings together the best of both new and traditional curricula to meet the needs of today's students. The author team's extensive teaching experience and proven ability to write innovative and relevant problems has made this text a true bestseller. Exciting new real-world applications make this new edition even more meaningful to students in management, life and social sciences. This book will work well for those departments seeking a middle ground for their instructors.

Chapter 1 FUNCTIONS AND LINEAR MODELS 2

1.1 Functions from the Numerical and Algebraic Viewpoints

1.2 Functions from the Graphical Viewpoint 17

1.3 Linear Functions 30

1.4 Linear Models 41

1.5 Linear Regression 59

 Case Study: Modeling Spending on Internet Advertising 74

 Optional lnternet Topic:New Functions from Old:Scaled and Shifted Functions

Chapter 2 NONLINEAR MODELS 80

2.1 Quadratic Functions and Models 81

2.2 Exponential Functions and Models 94

2.3 Logarithmic Functions and Models 110

2.4 Logistic Functions and Models 121

 Case Study: Checking Up on Malthus 133

 Optional Internet Topics:Inverse Functions

 Linear and Exponential Regression

 Using and Deriving Algebraic Properties of Logarithms

Chapter 3 INTRODUCTION TO THE DERIVATIVE 138

3.1 Average Rate of Change 139

3.2 The Derivative: Numerical and Graphical Viewpoints 154

3.3 The Derivative: Algebraic Viewpoint 177

3.4 Derivatives of Powers, Sums, and Constant Multiples 186

3.5 A First Application: Marginal Analysis 198

3.6 Limits: Numerical & Graphical Approaches (Optional) 209

3.7 Limits and Continuity (Optional) 219

3.8 Limits and Continuity: Algebraic Approach (Optional) 225

 Case Study: Redudng Sulfur Emissions 235

 Optional Internet Topics:

 Proof of the Power Rule

 Sketching the Graph of the Derivative

 Continuity and Differentiability

Chapter4 TECHNIQUES OF DIFFERENTATION 240

4.1 The Product and Quotient Rules 241

4.2 The Chain Rule 251

4.3 Derivatives of Logarithmic and Exponential Functions 261

4.4 Implicit Differentiation 273

 Case Study: Projecting Market Growth 280

 Optional lnternet Topic: Linear Approximation and Error Estimation

Chapter 5 APPLICATIONS OF THE DERIVATIVE 29o

5.1 Maxima and Minima 291

5.2 Applications of Maxima and Minima 304

5.3 The Second Derivative and Analyzing Graphs 317

5.4 Related Rates 329

5.5 Elasticity 337

 Case Study: Production Lot-Size Management 346

Chapter 6 THE INTEGRAL 352

6.1 The Indefinite Integral 353

6.2 Substitution 364

6.3 The Definite Integral as a Sum: A Numerical Approach 373

6.4 The Definite Integral as Area: A Geometric Approach 384

6.5 The Definite Integral: An Algebraic Approach and the Fundamental Theor of Calculus 391

 Case Study: Wage Inflation 403

 Optional lnternet Topic:Numerical Integration

Chapter 7 FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL 408

7.1 Integration by Parts 409

7.2 Area between Two Curves and Applications 416

7.3 Averages and Moving Averages 430

7.4 Continuous Income Streams 438

7.5 Improper Integrals and Applications 442

7.6 Differential Equations and Applications 450

 Case Study: Estimating Tax Revenues 458

Chapter 8 FUNCTIONS OF SEVERAL VARIABLES 466

8.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints 467

8.2 Three-Dimensional Space and the Graph of a Function of Two Variables 479

8.3 Partial Derivatives 490

8.4 Maxima and Minima 498

8.5 Constrained Maxima and Minima and Applications 508

8.6 Double Integrals 518

 Case Study: Modeling Household Income 527

Chapter 9 TRIGONOMETRIC MODELS 538

9.1 Trigonometric Functions, Models, and Regression 539

9.2 Derivatives of Trigonometric Functions and Applications 555

9.3 Integrals of Trigonometric Functions and Applications 563

 Case Study:Predicting Cocoa Inventories 569

Chapter5 CALCULUS APPLIED TO PROBABILITY AND STATISTIC&(OPTIONAL INTERNET TOPIC)

S.1 Continuous Random Variables and Histograms

S.2 Probability Density Functions: Uniform, Exponential, Normal, and Beta

S.3 Mean, Median, Variance and Standard Deviation Case Study: Creating a Family Trust

Appendix A ALGEBRA REVIEW A1

A.1 Real Numbers A1

A.2 Exponents and Radicals A6

A.3 Multiplying and Factoring Algebraic Equations A16

A.4 Rational Expressions A20

A.5 Solving Polynomial Equations A22

A.6 Solving Miscellaneous Equations A28

ANSWERS TO SELECTED EXERCISES A33

INDEX A65