Calculus Concepts: An Informal Approach to the Mathematics of Change, 1e

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: Non-Linear 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, Fund-Raising 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, Fund-raising Campaign
6 Accumulating Change: Limits of Sums and the Definite Integral
6.1 Results of Change
6.2 Trapezoid and Midpoint-Rectangle 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 Cross-Sectional 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 Least-Squares 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 Second-Order 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

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