| Class | Text Reading | Due |
|---|---|---|
| 1. Wed 8/27 | Ch. 1: differentials | |
| 2. Fri 8/29 | Ch. 1: forms on a vector space |
| Mon 9/1 | LABOR DAY. | |
| 3. Wed 9/3 | Ch. 1: transf. of k-forms by linear maps. | |
| 4. Fri 9/5 | Ch. 1: exterior differential |
| 5. Mon 9/8 | Ch. 2: line integrals. | H01 |
| 6. Wed 9/10 | Ch. 2: homotopy invariance. | |
| 7. Fri 9/12 | No Class |
| 8. Mon 9/15 | Ch. 3: Diff. manifold. | H02 |
| 9. Wed 9/17 | Ch. 3: maps, functions & tangent vectors | |
| 10. Fri 9/19 | Ch. 3: tangent vectors, diffeos |
| 11. Mon 9/22 | Ch. 3: Vector fields, Lie bracket | |
| 12. Wed 9/24 | Ch. 3: Orientation | |
| 13. Fri 9/26 | Ch. 4.1: Integration of forms | H03 |
| 14. Mon 9/29 | Ch. 4.1: Partition of unity | |
| 15. Wed 10/1 | Ch. 4.2: Stokes Theorem | H04 |
| 16. Fri 10/3 | Ch. 4.2: Stokes Theorem |
| 17. Mon 10/6 | Ch. 4.2: Divergence Theorem | |
| 18. Wed 10/8 | Ch. 4.3: Poincare Lemma | H05 |
| 19. Fri 10/10 | Closed 2-form on S3 is exact |
| 20. Mon 10/13 | Midterm Exam | Chapters 1 - 4 |
| 21. Wed 10/15 | Ch. 5.1: Moving frames in Rn | |
| 22. Fri 10/17 | Ch. 5.1: Moving frame on a surface |
| 23. Mon 10/20 | Ch. 5.2: Gauss map & Theorema Egregium | H06 |
| 24. Wed 10/22 | Ch. 5.2: Levi-Civita form | |
| Thur-Fri 10/23-10/24 | FALL BREAK |
| 25. Mon 10/27 | Lie groups & Lie algebras | H07 |
| 26.Wed 10/29 | Maurer-Cartan form | |
| 27. Fri 10/31 | Ch. 5.2: Bonnet's Theorem |
| 28. Mon 11/3 | Ch. 5.3: Instrinsic Riemannian geometry | |
| 29. Wed 11/5 | Ch. 5.3: Covariant derivative | H08 |
| 30. Fri 11/7 | Ch. 5.3: Parallel translation |
| 31. Mon 11/10 | Ch. 6.1: Geodesic curvature, examples | H09 |
| 32. Wed 11/12 | Ch. 6.1: Index of a vector field | |
| 33. Fri 11/14 | Ch. 6.1: Gauss-Bonnet Theorem |
| 34. Mon 11/17 | Gauss-Bonnet with boundary | |
| 35. Wed 11/19 | The Hessian and Morse theory | H10 |
| 36. Fri 11/21 | Flow of a vector field |
| 37. Mon 11/24 | Exponential map of a Lie group | |
| Wed 11/26 | THANKSGIVING BREAK | |
| Fri 11/28 | THANKSGIVING BREAK |
| 38. Mon 12/1 | Frobenius Theorem | |
| 39. Wed 12/3 | Frobenius Theorem | H11 |
| 40. Fri 12/5 | Cartan-Darboux Theorem |
| 41. Mon 12/8 | Cartan-Darboux Theorem | |
| Wed 12/10 | NO CLASS | H12 (due by noon) |
| Wed 12/17 | Final Exam 8-10 am |
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Gary Jensen
Last modified: Thu Nov 20 16:09:25 CST 2003