Course
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part 1, part 2, part 3, part 4, part 5, part 6, part 7, part 8, part 9, part 10,
| Homeworks | Solutions | Graded Problems |
|---|---|---|
| 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3. | Solution #1 | 1.1, 1.2, 1.3, 1.5, 2.1 |
| 1.7, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9. | Solution #2 | 1.7, 2.4, 2.5, 2.6, 2.7 |
| 2.10, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6. | Solution #3 | 2.10, 3.1, 3.3, 3.4, 3.5 |
| 3.7, 3.8, 3.9, 3.10, 3.11, 3.12, 4.1, 4.2. | Solution #4 | 3.8, 3.10, 3.12, 4.1 |
| 4.5, 4.6, 4.8, 4.9, 4.10, 4.11, 5.1, 5.2, 5.4. | Solution #5 | 4.6, 4.8, 4.10, 4.11, 5.4 |
| 4.12, 4.13, 4.14, 4.15, 5.3, 5.6, 5.7. | Solution #6 | 4.12, 4.13, 5.6, 5.7 |
| 5.8, 5.9, 5.10, 5.11, 5.12, 6.1, 6.2, 6.3. | Solution #7 | 5.9, 5.10, 5.11, 6.2, 6.3 |
| 6.5, 6.6, 6.7, 6.11, 7.7, 8.1, 8.2, 8.4. | Solution #8 | 6.5, 6.7, 6.11, 7.7, 8.2 |
| 6.4, 6.8, 6.10, 8.3, 8.5, 8.6, 8.8, 8.9. | Solution #9 | 6.4, 6.8, 8.3, 8.5, 8.9. |
| 10.1, 10.3, 10.4, 11.6, 11.7 | Solution #10 | 10.1, 10.3, 10.4, 11.6, 11.7 |
The graphs in solution 9 can not be properly displayed for some reason. But it's not hard to program Mathematica to get the graphs. If you want my Mathematica code for these graphs, please email me.
| Date | Contents |
|---|---|
| 08/29, Thursday | Review of multivariable calculus: implicit fuction theorem, chain rule of differentiation, etc. |
| 09/05, Thursday | We'll work out sample problems similar to those of HW#1. |
| 09/12, Thursday | We'll talk about configuration space, in particular, example 1.4 and problem 1.7. |
| 09/19, Thursday | We'll talk about HW#3, in particular, problem 2.10 and problem 3.6 |
| 09/26, Thursday | We'll talk about problem 3.14, as well as problems in HW#4. |
| 10/02, Thursday | I'll present the solutions to the practice problems, as well as Exercise 3.13 and a 2-dim version of 3.12. If time allows, I'll spend a little time on part of 4.7. |
| 10/10, Thursday | The emphasis of this recitation would be on problem 4.5, 4.6, 4.8 and 4.11. |
| 10/17, Thursday | We'll see what questions may arise from the homework problems. If time allows, we'll also prove the fact that every permutation is a product of transpositions. |
| 10/25, Thursday | We'll cover three topics: determinants and permutations, pullbacks, and line intergrals. More specifically, we'll cover the Coxeter relations, some problems on path integrals (Marsden-Tromba, section 7.1-2), as well as problems on pullbacks. |
| 10/31, Thursday | Practice problems from notes, 7.1--7.6. |
| 11/07, Thursday | Homework #8 |
| 11/14, Thursday | An example of nonorientable manifold, as well as the homework due on Friday. |
| 11/21, Thursday | Problems 9.2, 9.3, 9.5, 9.6 |
| 12/06, Friday | HW 10 |
Last modified: 12/13/2002