Preface -- Introduction -- Activities -- Projects -- A Modern Calculus Course -- Course Logistics -- About Using Projects -- Questions About Using Student Groups -- Questions About Using Activities -- Questions About Course Organization and Content -- Unifying Threads -- To the Student -- Acknowledgments -- Contents -- Part I Activities -- 1 Graphical Calculus -- Introduction -- 1.1 Chalk Toss -- 1.2 Classroom Walk -- 1.3 Biking to School -- 1.4 Raising a Flag -- 1.5 Library Trip -- Airplane Flight with Constant Velocity -- 1.7 Projected Image -- 1.8 A Formula for a Piecewise-Linear Graph -- 1.9 Water Balloon -- 1.10 Graphical Estimation of Slope -- 1.11 Linear Approximation -- 1.12 Slope with Rulers -- 1.13 Examining Linear Velocity -- 1.14 More Airplane Travel -- 1.15 Dallas to Houston -- 1.16 Given Velocity Graph, Sketch Distance Graph -- 1.17 Function- Derivative Pairs -- 1.18 Water Tank Problem -- 1.19 Tax Rates and Concavity -- 1.20 Water Container -- 1.21 Testing Braking Performance -- 1.22 The Start-up Firm -- 1.23 Graphical Composition -- 1.24 The Leaky Balloon -- Inverse Function from Graphs -- 2 Functions, Limits, and Continuity -- Introduction -- 2.1 Introduction to Functions -- 2.2 Postage -- 2.3 What is Continuity? -- 2.4 Limits and Continuity from a Graph -- 2.5 Slopes and Difference Quotients -- 2.6 Sequences -- 2.7 Can We Fool Newton? -- 3 Derivatives -- Introduction -- 3.1 Estimating Cost -- 3.2 Finite Differences -- 3.3 Using the Derivative -- 3.4 Gotcha -- 3.5 Animal Growth Rates -- 3.6 The Product Fund -- 3.7 Exchange Rates and the Quotient Rule -- 3.8 Using the Product Rule to Get the Chain Rule -- 3.9 Magnification -- 4 Integration -- Introduction -- 4.1 Time and Speed -- 4.2 Oil Flow -- 4.3 Can the Car Stop in Time? -- 4.4 Fundamental Theorem of Calculus -- 4.5 Comparing Integrals and Series.

4.6 Graphical Integration -- 4.7 How Big Can an Integral Be? -- 4.8 Numerical Integration -- 4.9 Verifying the Parabolic Rule -- 4.10 Finding the Average Rate of Inflation -- 4.11 Cellular Phones -- 4.12 The Shorter Path -- 4.13 The River Sine -- 4.14 Improper Integrals -- 5 Transcendental Functions -- Introduction -- 5.1 Ferris Wheel -- 5.2 Sunrise-Sunset -- 5.3 Why Mathematicians Use ex -- 5.4 Exponential Differences -- 5.5 Inverse Functions -- 5.6 Fitting Exponential Curves -- 5.7 Log-Log Plots -- 5.8 Using Scales -- 6 Differential Equations -- Introduction -- 6.1 Direction Fields -- 6.2 Using Direction Fields -- 6.3 Drawing Solution Curves -- 6.4 Cooling and Heating Models -- 6.5 The Hot Potato -- 6.6 Spread of a Rumor: Discrete Logistic Growth -- 6.7 Population -- 6.8 Save the Perch -- 6.9 Systems of Differential Equations -- 6.10 Visualizing Solutions to 2nd-order Differential Equations -- 6.11 Phase Plane Practice -- 7 Series -- Introduction -- 7.1 Investigating Series -- 7.2 Space Station -- 7.3 Convergence -- 7.4 Salt Spill -- 7.5 Decimal of Fortune -- 7.6 Approximating Functions with Polynomials -- 7.7 Introduction to Power Series -- 7.8 Graphs of Polynomial Approximations -- 7.9 Taylor Series -- 7.10 Approximating Logs -- 7.11 Approximating pi -- 7.12 Using Series to Find Indeterminate Limits -- 7.13 Using Power Series to Solve a Differential Equation -- 7.14 Second Derivative Test -- 7.15 Padé Approximation -- 7.16 Using Taylor Polynomials to Approximate Integrals -- Complex Power Series -- Part II Projects -- 1. Designing a Roller Coaster -- 2. Tidal Flows -- 3. More Tidal Flows -- 4. Designing a Cruise Control -- 5. Designing a Detector -- 6. Gasoline and Advertising -- 7. Taxes -- 8. Water Evaporation -- 9. Glen Canyon Dam -- 10. Real Estate Investor -- 11. How Much Curve? -- 12. Mutual Funds -- 13. Rescuing a Satellite.

14. Spread of a Disease -- 15. Designing an Arch -- 16. Cleopatra's Oar -- 17. Differential Equations -- 18. How Many Deer Are There? -- 19. Tax Assessment -- 20. The Fish Pond -- 21. Drug Dosage -- 22. Investigating Series -- 23. Topographical Maps -- Part III Instructor Notes for Activities -- 1 Graphical Calculus -- 1.1 Chalk Toss -- 1.2 Classroom Walk -- 1.3 Biking to School -- 1.4 Raising a Flag -- 1.5 Library Trip -- 1.6 Airplane Flight with Constant Velocity -- 1.7 Projected Image -- 1.8 A Formula for a Piecewise-Linear Graph -- 1.9 Water Balloon -- 1.10 Graphical Estimation of Slope -- 1.11 Linear Approximation -- 1.12 Slope with Rulers -- 1.13 Examining Linear Velocity -- 1.14 More Airplane Travel -- 1.15 Dallas to Houston -- 1.16 Given Velocity Graph, Sketch Distance Graph -- 1.17 Function- Derivative Pairs -- 1.18 Water Tank Problem -- 1.19 Tax Rates and Concavity -- 1.20 Water Container -- 1.21 Testing Braking Performance -- 1.22 The Start-up Firm -- 1.23 Graphical Composition -- 1.24 The Leaky Balloon -- 1.25 Inverse Function from Graphs -- 2 Functions, Limits, and Continuity -- 2.1 Introduction to Functions -- 2.2 Postage -- 2.3 What is Continuity? -- 2.4 Limits and Continuity from a Graph -- 2.5 Slopes and Difference Quotients -- 2.6 Sequences -- 2.7 Can We Fool Newton? -- 3 Derivatives -- 3.1 Estimating Cost -- 3.2 Finite Differences -- 3.3 Using the Derivative -- 3.4 Gotcha -- 3.5 Animal Growth Rates -- 3.6 The Product Fund -- 3.7 Exchange Rates and the Quotient Rule -- 3.8 Using the Product Rule to Get the Chain Rule -- 3.9 Magnification -- 4 Integration -- 4.1 Time and Speed -- 4.2 Oil Flow -- 4.3 Can the Car Stop in Time? -- 4.4 Fundamental Theorem of Calculus -- 4.5 Comparing Integrals and Series -- 4.6 Graphical Integration -- 4.7 How Big Can an Integral Be? -- 4.8 Numerical Integration -- 4.9 Verifying the Parabolic Rule.

4.10 Finding the Average Rate of Inflation -- 4.11 Cellular Phones -- 4.12 The Shorter Path -- 4.13 The River Sine -- 4.14 Improper Integrals -- 5 Transcendental Functions -- 5.1 Ferris Wheel -- 5.2 Sunrise-Sunset -- 5.3 Why Mathematicians Use ex -- 5.4 Exponential Differences -- 5.5 Inverse Functions -- 5.6 Fitting Exponential Curves -- 5.7 Log-Log Plots -- 5.8 Using Scales -- 6 Differential Equations -- 6.1 Direction Fields -- 6.2 Using Direction Fields -- 6.3 Drawing Solution Curves -- 6.4 Cooling and Heating Models -- 6.5 The Hot Potato -- 6.6 Spread of a Rumor: Discrete Logistic Growth -- 6.7 Population -- 6.8 Save the Perch -- 6.9 Systems of Differential Equations -- 6.10 Visualizing Solutions to 2nd-order Differential Equations -- 6.11 Phase Plane Practice -- 7 Series -- 7.1 Investigating Series -- 7.2 Space Station -- 7.3 Convergence -- 7.4 Salt Spill -- 7.5 Decimal of Fortune -- 7.6 Approximating Functions with Polynomials -- 7.7 Introduction to Power Series -- 7.8 Graphs of Polynomial Approximations -- 7.9 Taylor Series -- 7.10 Approximating Logs -- 7.11 Approximating pi -- 7.12 Using Series to Find Indeterminate Limits -- 7.13 Using Power Series to Solve a Differential Equation -- 7.14 Second Derivative Test -- 7.15 Padé Approximation -- 7.16 Using Taylor Polynomials to Approximate Integrals -- 7.17 Complex Power Series -- Part IV Instructor Notes for Projects -- 1. Designing a Roller Coaster -- 2. Tidal Flows -- 3. More Tidal Flows -- 4. Designing a Cruise Control -- 5. Designing a Detector -- 6. Gasoline and Advertising -- 7. Taxes -- 8. Water Evaporation -- 9. Glen Canyon Dam -- 10. Real Estate Investor -- 11. How Much Curve? -- 12. Mutual Funds -- 13. Rescuing a Satellite -- 14. Spread of a Disease -- 15. Designing an Arch -- 16. Cleopatra's Oar -- 17. Differential Equations -- 18. How Many Deer Are There? -- 19. Tax Assessment.

20. The Fish Pond -- 21. Drug Dosage -- 22. Investigating Series -- 23. Topographical Maps -- Part V Appendices -- Sample Curriculum -- Calculus 1 -- Calculus 2 -- "Sample Guidelines for Projects'' -- Guide to the Threads -- Graphical calculus -- Distance and velocity -- Multiple representation of Functions -- Modeling -- Approximation and estimation -- About the Authors.