This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked.
Week #1:
Aug. 27 - 31 Homework |
Structures on Rn
Manifolds as subspaces of Rn Abstract Manifolds |
Week #2:
Sept. 3 - 7 Homework |
Differentiability of functions of Several Variables
Administrative Note: Monday, September 3 is Labor Day. No Class. |
Week #3:
Sept. 10 - 14 Homework |
The space of Tangent Vectors at a Point of Rn
Another Definition of Ta(Rn) Vector Fields on Open Subsets of Rn |
Week #4:
Sept. 17 - 19 Homework |
The Definition of a Differentiable Manifold
Further Examples Differentiable Functions and Mappings |
Week #5:
Sept. 24 - 28 Homework |
The Tangent Space at a Point of a Manifold
The Inverse Function Theorem The Rank of a Mapping |
Week #6:
Oct. 1 - 5 Homework |
Rank of a Mapping: Immersions
Submanifolds |
Week #7:
Oct. 8 - 12 Homework |
Submanifolds
Exam #1 will be given in class on Friday, October 12. Here is some more information about the exam |
Week #8:
Oct. 15 - 19 |
Lie Groups
Administrative note: Friday, October 19 is the Mid-Semester Break. No Class. |
Week #9:
Oct. 22 - 26 Homework |
Lie Groups
Vector Fields Administrative Note: Monday, October 22 is the Mid-Semester Break. No Class. |
Week #10:
Oct. 29 - Nov. 2 Homework |
Vector Fields(The Tangent Bundle)
One Parameter Groups and Local One Parameter Groups Acting on Manifolds The Existence Theorem for Ordinary Differential Equations |
Week #11:
Nov. 5 - 9 Homework |
The Lie Algebra of Vector Fields on a Manifold
Tangent Covectors Bilinear Forms: The Riemannian Metric |
Week #12:
Nov. 12 - 16 Homework |
Riemannian Manifolds as Metric Spaces
Differentiation of Vector Fields along Curves in Rn |
Week #13:
Nov. 19 - 23 |
Differentiation of Vector Fields along Submanifolds in Rn
Administrative note: Wednesday, November 21 through Friday, November 23 is the Thanksgiving Break. No Class. |
Week #14:
Nov. 26 - 30 |
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Week #15:
Dec. 3 - 7 |
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Final Exam:
Dec. 10 - 14 |
Administrative Note: Monday, Dec. 10 is the last day of Classes. |