| 6. Applications of Integration | ||
|---|---|---|
| 6.1 |
More About Areas | 2, 7, 23, 29, 34, 41, 45 |
| 6.2 |
Volume | 3, 21, 34, 46, 49, 68 |
| 6.3 |
Volumes by Cylindrical Shells | 2, 5, 15, 26, 33, 38, 43 |
| 6.5 |
Average Value of a Function | 1, 7, 10, 15, 16, 22 |
| 8. Techniques Of Integration | ||
| 8.1 |
Integration by Parts | 1, 15, 20, 23, 34, 46, 55, 62 |
| 8.2 |
Trigonometric Integrals | 3, 8, 13, 31, 52, 55, 57, 62 |
| 8.3 |
Trigonometric Substitution | 1, 12, 22, 32, 36, 40 |
| 8.4 |
Integration of Rational Functions by Partial Fractions | 2, 7, 23, 35, 44, 51, 54, 55, 62 |
| 8.5 |
Strategy for Integration | 2, 9, 25, 30, 41, 48, 52 |
| 8.6* |
Integration Using Tables and
Computer Algebra Systems (*To be covered as part of general discussion of methods of integration) |
1, 7, 14, 31, 37 |
| 8.7 |
Approximate Integration | 1, 2, 10, 19, 26, 29, 32, 37 |
| 8.8 |
Improper Integrals | 2, 4, 6, 21, 35, 47, 50, 57, 67 |
| 9. Further Applications Of Integration | ||
| 9.1 |
Arc Length | 3, 8, 13, 17, 19, 22, 26, 31, 34, 39 |
| 9.2 |
Area of a Surface of Revolution | 1, 6, 15, 17, 28 |
| 9.3 |
Applications to Physics and Engineering | 1, 4, 13, 18, 19, 21, 26, 31, 35, 41 |
| 9.4 |
Applications to Economics and Biology | 1,4,7,9,14,18 |
| 9.5 |
Probability | 2, 5, 8, 10, 13 |
| 12. Infinite Sequences And Series | ||
| 12.1 |
Sequences | 1, 3, 8, 9, 13, 19, 23, 28, 36, 41, 50, 55, 59, 62 |
| 12.2 |
Series | 1, 4, 7, 8, 11, 14, 23, 29, 35, 38, 42, 47, 58, 64 |
| 12.3 |
The Integral Test and Estimates of Sums | 1, 5, 9, 11, 19, 21, 28 |
| 12.4 |
The Comparison Tests | 1, 2, 4, 9, 18, 22, 28, 34, 37, 40, 45 |
| 12.5 |
Alternating Series | 1, 5, 11, 17, 19, 21, 24, 29, 32, 35 |
| 12.6 |
Absolute Convergence and the Ratio and Root Tests | 1, 2, 7, 11, 14, 17, 25, 29, 38 |
| 12.7 |
Strategy for Testing Series | 1, 7, 9, 14, 20, 25, 26, 35 |
| 12.8 |
Power Series | 1, 2, 3, 9, 13, 21, 24, 27, 29, 31, 33, 37 |
| 12.9 |
Representations of Functions as Power Series | 1, 2, 5, 9, 11, 13, 16, 20, 28, 35 |
| 12.10 |
Taylor and Maclaurin Series | 1, 2, 3, 4, 9, 13, 17, 27, 25, 30, 34, 39, 49, 56, 60 |
| 12.11 |
Applications of Taylor Polynomials | 2, 5, 23, 28 |
| 10. Differential Equations | ||
| 10.1 |
Modeling with Differential Equations | 2, 3, 6, 7, 9, 11, 14 |
| 10.2 |
Direction Fields and Euler's Method | 2, 3, 4, 5, 6, 11, 18, 23, 28 |
| 10.3 |
Separable Equations | 3, 9, 12, 16, 21, 23, 27, 30, 35, 38, 41 |
| 10.4 |
Models for Population Growth | 1, 3, 4, 5, 7, 12, 15, 19 |