Course synopsis:
This will be a standard course in multivariable calculus covering vectors and geometry (in two and three dimensions), partial differentiation, multiple integrals, and vector calculus.
Schedule and homework assignments:
| Date | Topic | Problems |
|---|---|---|
| 8/25 (Mon) | Sections 10.1 and 10.2: Euclidean coordinates on R^3 and vectors | 10.1: 6(b), 8, 12, 30, 33, 36 (hint: see problem 7.2.33) |
| 8/27 (Wed) | Section 10.2: Vectors | 10.2: 4, 16, 17, 18, 27 |
| 8/29 (Fri) | Section 10.3: Dot (inner) product | 10.3: 6, 8, 16, 17, 20, 30, 31, 33 |
| 9/1 (Mon) | Labor Day, no class! | no hw! |
| 9/3 (Wed) | Section 10.4: Cross Product | 10.4: 6, 13, 14, 20, 22, 27, 50 |
| 9/5 (Fri) | Section 10.5: Lines and planes | 10.4: 34, 36 10.5: 2, 7, 14, 22, 25, 34, 36 |
| 9/8 (Mon) | Section 10.6: Other surfaces in 3-dimensional space | 10.5: 42, 49, 52 10.6: 6, 7, 11, 12, 15, 21, 25, 28 |
| 9/10 (Wed) | Section 10.7: Vector-valued functions | 10.7: 1, 2, 6, 9, 10, 14, 24, 28 |
| 9/12 (Fri) | Section 10.7: Vector-valued functions(again) | 10.7: 3, 4, 33, 35, 36, 43, 44, 45, 51, 52, 64 |
| 9/15 (Mon) | Section 10.8: Arc length | 10.8: 1, 2, 3, 9, 10, 11 |
| 9/17 (Wed) | Section 11.1: Functions of several variables | 11.1: 2, 13, 15, 16, 18, 24, 25, 41-46 |
| 9/19 (Fri) | Section 11.2: Limits and continuity | 11.2: 3, 5, 6, 9, 10, 13, 26, 27 |
| 9/22 (Mon) | Section 11.3 Partial derivatives | 11.3: 7, 8, 17, 20, 25, 45, 52, 62 |
| 9/24 (Wed) | Section 11.4: Tangent planes | 11.4: 3, 4, 14, 19, 24, 29 |
| 9/26 (Fri) | Section 11.5: Chain rule | 11.5: 4, 8, 9, 11, 20, 25, 30, 32, 41, 42 |
| 9/29 (Mon) | Section 11.6: Directional derivatives | 11.6: 3, 6, 7, 8, 14, 20, 24, 31, 33, 34, 35, 39 |
| 10/1 (Wed) | Midterm Exam 1 | relax! |
| 10/3 (Fri) | Section 11.7: Max/min values | 11.7: 2, 3, 6, 8, 9 (don’t worry about graphing) |
| 10/6 (Mon) | Section 11.7/11.8: Optimization | 11.7: 23, 24, 25, 31, 34, 39, 40 |
| 10/8 (Wed) | Section 11.8: Lagrange multipliers | 11.8: 2, 6, 10, 15, 18, 19, 21, 38 |
| 10/10 (Fri) | Section 12.1: Double integrals | 12.1: 1, 5, 7, 8, 10, 42 |
| 10/13 (Mon) | Section 12.1 Iterated integrals | 12.1: 17, 19, 20, 23, 24, 25, 26, 30 |
| 10/15 (Wed) | Section 12.2: Double integrals over general regions | 12.2: 8, 9, 16, 17, 28, 40, 43, 44, 50 |
| 10/17 (Fri) | Section 12.3: Double integrals in polar coordinates | 12.3: 5, 8, 11, 14, 17, 20, 24, 29 |
| 10/20 (Mon) | Section 12.4: Applications | 12.3: 30 12.4: 1, 3, 5 |
| 10/22 (Wed) | Section 12.5: Triple integrals | 12.5: 4, 7, 12 |
| 10/24 (Fri) | Section 12.5/12.6: Triple integrals and cylindrical coordinates | 12.5: 17, 18, 27 12.6: 4, 8, 10, 12, 17, 18, 20, 21, 24, 29 |
| 10/27 (Mon) | Section 12.7: Spherical coordinates | 12.7: 4, 7, 8, 10, 14, 20, 22, 26, 34, 37 |
| 10/29 (Wed) | Section 13.1: Vector fields | 13.1: 5, 6, 15, 16, 17, 18, 25, 26 |
| 10/31 (Fri) | 13.2: Line integrals | 13.2: 3, 8, 14, 16, 34 |
| 11/3 (Mon) | 13.2/13.3: More on line integrals | 13.2: 21, 22, 37 13.3: 4, 6, 7, 12, 13, 16, 17, 20 |
| 11/5 (Wed) | Exam 2 | relax! |
| 11/7 (Fri) | ||
| 11/10 (Mon) | Section 13.4: Green’s theorem | 13.4: 1, 2, 3, 4, 5, 7, 8, 12, 13, 17, 21 |
| 11/12 (Wed) | 13.5: Curl and divergence | 13.5: 1, 5, 6, 16, 18, 27, 36 |
| 11/14 (Fri) | 13.6: Parametric surfaces | 13.6: 1, 2, 15, 18, 19, 20, 30, 31 (no need to graph in 30 and 31) |
| 11/17 (Mon) | Section 13.6: Surface area | 13.6: 33, 37, 39, 40, 42, 43 |
| 11/19 (Wed) | 13.7: Surface integrals of functions | 13.7: 5, 9, 10, 13, 14, 16, 17 |
| 11/21 (Fri) | 13.7: Surface integrals of vector fields | 13.7 21, 22, 23, 26, 27, 31 |
| 11/24 (Mon) | 13.8: Stokes theorem | |
| 11/26 (Wed) | Thanksgiving break! | |
| 11/28 (Fri) | Thanksgiving break! | |
| 12/1 (Mon) | 13.8: More on Stokes theorem | 13.8: 1, 2, 3, 5, 7, 8, 11, 12, 13, 15 (not to be turned in) |
| 12/3 (Wed) | 13.9 Divergence theorem | |
| 12/5 (Fri) | 13.9: More on the Divergence theorem | 13.9: 1, 2, 3, 6, 7, 9, 10, 12, 17 (not to be turned in) |
| 12/13 (Sat) | Final exam from 2-4pm | 9am section: THH 210 12pm section: THH 301 |