This is the second part of a 3-semester sequence in calculus for students of mathematics, natural sciences and engineering. Topics include techniques of integration, applications of integration, parametric equations and polar coordinates, and infinite sequences and series.
Tentative Course Schedule:
| Week | Sections | Topics |
|---|---|---|
| 1 | 5.5, 7.1 | The substitution rule. Integration by parts. |
| 2 | 7.2, 7.3 | Trigonometric integrals. Trigonometric substitution. |
| 3 | 7.3, 7.4 | Trigonometric substitution. Integration of Rational Function by Partial Fractions. |
| 4 | 7.5 | Strategy for integration. |
| 5 | 7.8 | Improper Integrals. |
| 6 | 11.1, 11.2 | Sequences. Series. |
| 7 | 11.3, 11.4 | The integral test. Estimates of Sums. The comparison tests. |
| 8 | 11.5, 11.6 | Alternating Series. Absolute convergence & the ratio and root tests. |
| 9 | 11.7, 11.8 | Strategy for testing series. Power series. |
| 10 | 11.9 | Representation of functions as power series. |
| 11 | 11.10, 11.11 | Taylor & Maclaurin Series. Applications of Taylor polynomials. |
| 12 | 8.1 | Arc length. |
| 13 | 6.1, 6.2 | Areas between curves, volumes. |
| 14 | 10.1, 10.2 | Curves defined by parametric equations. Calculus with Parametric Curves. |
| 15 | 10.3 | Polar Coordinates. |
