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
Chapter 7 Summary
Chapter 7 Review Test
Chapter 7 Project: Arch Art
Appendix: Right Triangle and Unit Circle Trigonometry
Answer Key
Index of Applications
Subject Index

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