# Calendar

Calendar schedule.
Lec # | Topics | KEY DATES
--- | --- | ---
1 | Metric Spaces, Continuity, Limit Points |
2 | Compactness, Connectedness |
3 | Differentiation in n Dimensions |
4 | Conditions for Differentiability, Mean Value Theorem | Graded assignment 1 out
5 | Chain Rule, Mean-value Theorem in n Dimensions |
6 | Inverse Function Theorem |
7 | Inverse Function Theorem |
8 | Reimann Integrals of Several Variables, Conditions for Integrability |
9 | Conditions for Integrability (cont.), Measure Zero | Graded assignment 1 due 2 days after Lec #9
10 | Fubini Theorem, Properties of Reimann Integrals | Graded assignment 2 out
11 | Integration Over More General Regions, Rectifiable Sets, Volume |
12 | Improper Integrals |
13 | Exhaustions |
| Midterm |
14 | Compact Support, Partitions of Unity |
15 | Partitions of Unity (cont.), Exhaustions (cont.) |
16 | Review of Linear Algebra and Topology, Dual Spaces | Graded assignment 2 due
17 | Tensors, Pullback Operators, Alternating Tensors |
18 | Alternating Tensors (cont.), Redundant Tensors |
19 | Wedge Product |
20 | Determinant, Orientations of Vector Spaces | Graded assignment 3 out
21 | Tangent Spaces and k-forms, The d Operator |
22 | The d Operator (cont.), Pullback Operator on Exterior Forms |
23 | Integration with Differential Forms, Change of Variables Theorem, Sard's Theorem |
24 | Poincare Theorem |
25 | Generalization of Poincare Lemma |
26 | Proper Maps and Degree |
27 | Proper Maps and Degree (cont.) |
28 | Regular Values, Degree Formula | Graded assignment 3 due
29 | Topological Invariance of Degree | Graded assignment 4 out
30 | Canonical Submersion and Immersion Theorems, Manifolds |
31 | Examples of Manifolds |
32 | Tangent Spaces of Manifolds |
33 | Differential Forms on Manifolds |
34 | Orientations of Manifolds |
35 | Integration on Manifolds, Degree on Manifolds |
36 | Degree on Manifolds (cont.), Hopf Theorem | Graded assignment 4 due
37 | Integration on Smooth Domains |
38 | Integration on Smooth Domains (cont.), Stokes’ Theorem |
| Final Exam |