

  TABLE OF CONTENTS 

1  Ingredients of Change: Functions and Linear Models 
1.1  Fundamentals of Modeling 
1.2  Functions and Graphs 
1.3  Constructed Functions 
1.4  Linear Functions and Models 
Chapter 1 Summary  
Chapter 1 Review Test  
Chapter 1 Projects: Tuition Fees, Finding Data  
2  Ingredients of Change: NonLinear Models 
2.1  Exponential Functions and Models 
2.2  Exponential Models in Finance 
2.3  Polynomial Functions and Models 
2.4  Choosing a Model 
Chapter 2 Summary  
Chapter 2 Review Test  
Chapter 2 Projects: Compulsory School Laws, FundRaising Campaign  
3  Describing Change: Rates 
3.1  Average Rates of Change 
3.2  Instantaneous Rates of Change 
3.3  Tangent Lines 
3.4  Derivatives 
3.5  Percentage Change and Percentage Rates of Change 
Chapter 3 Summary  
Chapter 3 Review Test  
Chapter 3 Projects: Fee Refund Schedules, Doubling Time  
4  Determining Change: Derivatives 
4.1  Numerically Finding Slopes 
4.2  Drawing Slope Graphs 
4.3  Slope Formulas 
4.4  The Sum Rule 
4.5  The Chain Rule 
4.6  The Product Rule 
Chapter 4 Summary  
Chapter 4 Review Test  
Chapter 4 Projects: Fertility Rates, Superhighway  
5  Analyzing Change: Extrema and Points of Inflection 
5.1  Optimization 
5.2  Inflection Points 
5.3  Approximating Change 
Chapter 5 Summary  
Chapter 5 Review Test  
Chapter 5 Projects: Hunting License Fees, Fundraising Campaign  
6  Accumulating Change: Limits of Sums and the Definite Integral 
6.1  Results of Change 
6.2  Trapezoid and MidpointRectangle Approximations 
6.3  The Definite Integral as a Limit of Sums 
6.4  Accumulation Functions 
6.5  The Fundamental Theorem 
6.6  The Definite Integral 
Chapter 6 Summary  
Chapter 6 Review Test  
Chapter 6 Projects: Acceleration, Velocity, and Distance, Estimating Growth  
7  Analyzing Accumulated Change: More Applications of Integrals 
7.1  Differences of Accumulated Changes 
7.2  Perpetual Accumulation 
7.3  Streams in Business and Biology 
7.4  Integrals in Economics 
7.5  Average Values and Average Rates of Change 
7.6  Probability Distributions and Density Functions (Appears in complete edition only.) 
Chapter 7 Summary  
Chapter 7 Review Test  
Chapter 7 Project: Arch Art  
8  Repetitive Change: Cycles and Trigonometry 
8.1  Functions of Angles: Sines and Cosines 
8.2  Cyclic Functions as Models 
8.3  Rates of Change and Derivatives 
8.4  Extrema and Points of Inflection 
8.5  Accumulation in Cycles 
Chapter 8 Summary  
Chapter 8 Review Test  
Chapter 8 Projects: Seasonal Sales, Lake Tahoe Levels  
9  Ingredients of Multivariable Change: Models, Graphs, Rates 
9.1  CrossSectional Models and Multivariable Functions 
9.2  Contour Graphs 
9.3  Partial Rates of Change 
9.4  Compensating for Change 
9.5  Chapter 9 Summary 
Chapter 9 Review Test  
Chapter 9 Projects: Competitive and Complementary Products  
10  Analyzing Multivariable Change: Optimization 
10.1  Multivariable Critical Points 
10.2  Multivariable Optimization 
10.3  Optimization Under Constraints 
10.4  LeastSquares Optimization 
Chapter 10 Summary  
Chapter 10 Review Test  
Chapter 10 Projects: Snow Covering, Carbonated Beverage Packaging  
11  Dynamics of Change: Differential Equations and Proportionality 
11.1  Differential Equations and Accumulation Functions 
11.2  Separable Differential Equations 
11.3  SecondOrder Differential Equations 
Chapter 11 Summary  
Chapter 11 Review Test  
Chapter 11 Project: Slope Fields  
Appendix: Right Triangle and Unit Circle Trigonometry  
Answer Key  
Index of Applications  
Subject Index  
Glossary  
Index 