A supplement for Thomas' Calculus Early Transcendentals, 12th Edition
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| Overview | Overview | Overview | ||||
| 1. Functions | 1.4 | Modeling Change: Springs, Driving Safety, Radioactivity, Trees, Fish, and Mammals |
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| 2. Limits and Continuity | 2.2, 2.3, 2.4, 2.5 | Take It to the Limit |
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Continuous/Discontinuous Curves |
| 2.6 | Going to Infinity |
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| 3. Differentiation | 3.1 | Convergence of Secant Slopes to the Derivative Function |
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Tangents and Secants |
| 3.2, 3.11 | Derivatives, Slopes, Tangent Lines, and Making Movies |
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| 3.4, 3.5 | Motion Along a Straight Line, Part I: Position, Velocity, Acceleration |
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| 3.6 | Use the Fourier Series to Approximate Discontinuous Functions and to Interpret Music |
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| 4. Applications of Derivatives | 4.2 | Rain Catchers, Elevators, and Rockets | N/A |
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| 4.4 | Motion Along a Straight Line, Part I: Position, Velocity, Acceleration |
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| 4.7 | Newton's Amazing Method: Estimate pi to How Many Places? |
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| 5. Integration | 5.1, 5.2, 5.3, 5.4 | Summing It up with Riemann, Definite Integrals, and the Fundamental Theorem of Calculus |
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| 5.3, 5.4 | Rain Catchers, Elevators, and Rockets | N/A |
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| 5.4 | Motion Along a Straight Line, Part II: Acceleration, Velocity, Position | N/A |
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| 5.4 | Using Riemann Sums to Estimate Areas, Volumes, and Lengths of Arc |
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| 5.5 | Bending of Beams or What Does Calculus Have to Do With the Design of Structures? |
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| 6. Applications of Definite Integrals | 6.1, 6.3 | Using Riemann Sums to Estimate Areas, Volumes, and Lengths of Arc |
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| 6.5 | Modeling a Bungee Cord Jump: A Classroom Experiment |
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| 6.6 | Bending of Beams or What Does Calculus Have to Do With the Design of Structures? |
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Minimums, Maximums, and Inflection Points | |
| 7. Integrals and Transcendental Functions | 7.2 | Summing It up with Riemann, Definite Integrals, and the Fundamental Theorem of Calculus |
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| 7.4 | Drug Dosages: Are They Effective? Are They Safe? |
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| 8. Techniques of Integration | 8.6 | Riemann, Trapezoids, and Simpson Approximations |
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| 8.7 | Games of Chance: Exploring the Monte Carlo Technique for Numerical Integration and Computing Probabilities with Improper Integrals |
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| 9. First-Order Differential Equations | 9.1, 9.4 | First-Order Differential Equations and Slope Fields |
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| 9.2 | Drug Dosages: Are They Effective? Are They Safe? |
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| 10. Infinite Sequences and Series | 10.2 | Bouncing Ball |
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| 10.8, 10.9 | Taylor Polynomial Approximations of a Function |
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| End of Chapter | Drug Dosages: Are They Effective? Are They Safe? |
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| 11. Parametric Equations and Polar Coordinates | 11.1, 11.2, 11.4 | Parametric and Polar Equations with a Figure Skater |
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| 11.2, 11.3 | Radar Tracking of a Moving Object |
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Projectile Motion | |
| 12. Vectors and the Geometry of Space | 12.3, 12.5 | Using Vectors to Represent Lines and Find Distances |
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| 12.5 | Putting a Scene in Three Dimensions onto a Two-Dimensional Canvas |
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| 12.5, 12.6 | Getting Started in Plotting in 3D |
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| 13. Vector-Valued Functions and Motion in Space | 13.1 | Parametric and Polar Equations with a Figure Skater |
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| 13.1 | Radar Tracking of a Moving Object |
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Projectile Motion | |
| 13.2, 13.3, 13.4, 13.5 | Moving in Three Dimensions |
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Tangents and Normal Vectors | |
| 14. Partial Derivatives | 14.1 | Plotting Surfaces |
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| 14.5 | Exploring the Mathematics Behind Skateboarding: Analysis of the Directional Derivative |
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| 14.7 | Looking for Patterns and Applying the Method of Least Squares to Real Data |
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| 14.8 | Lagrange Goes Skateboarding: How High Does He Go? |
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| End of Chapter | How Does Heat Dissipate? |
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| 15. Multiple Integrals | 15.1 | Take Your Chances: Try the Monte Carlo Technique for Numerical Integration in Three Dimensions |
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| 15.2, 15.3, 15.5, 15.6 | Means and Moments and Exploring New Plotting Techniques |
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| End of Chapter | Volumes That You Can Use |
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| 16. Integration in Vector Fields | 16.3 | Work in Conservative and Non-Conservative Force Fields |
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| 16.4 | How Can You Visualize Green's Theorem? |
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Concept of the Curl | |
| 16.8 | Visualizing and Interpreting the Divergence Theorem |
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Copyright � 2011 Pearson Education, Inc.
