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Assignments

There are two kinds of assignments for this course: Problem Sets and Daily Homework. The problem sets will be handed in and graded. The daily homework assignments will not be handed in, but some problems will show up in the midterm and the final.

Textbooks

Munkres, James R. Analysis on Manifolds. CO: Westview Press, June 1997. ISBN: 0201315963.

Spivak, Michael. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. Boulder, CO: Westview Press, June 1, 1965. ISBN: 0805390219.

Problem Sets

The assignments are due during the class sessions listed.

SES #	ASSIGNMENTS
10	Munkres Chapter 1, Section 4: 3 Munkres Chapter 1, Section 6: 10 Munkres Chapter 1, Section 8: 3 Spivak Chapter 2: 2.4
14	All problems are from Munkres Section 12: 2 Section 13: 2 Section 15: 3 Section 16: 3
23	Problem Set 3 (PDF)
30	Supplementary Notes, Section 2: 2 Supplementary Notes, Section 4: 8 Supplementary Notes, Section 6: 6 Munkres, Section 24: 6

Daily Homework

SES #	PROBLEMS
1	Munkres Chapter 1, Section 3: 2, 3, 4, 6, 8, and 9 Prove the following statement (PDF)
2	Munkres Chapter 1, Section 4: 1-4 Prove that every closed interval [a,b] is compact in the set of real numbers
3	Munkres Chapter 2, Section 5: 2, 3, 4, 6
4	Munkres Chapter 2, Section 6: 1, 2, 5, 6, 7
5	Munkres Chapter 2, Section 7: 1, 2, 3
6	Munkres Chapter 2, Section 8: 1, 2, 4, 5
7	Spivak Chapter 2: 2.37, 2.38, 2.39
8	Munkres, Section 10: 1, 2, 3, 4, 5
9	Munkres, Section 11: 1, 2, 3, 6, 8
10	Munkres, Section 12: 1, 4 Remark: Problem 4 is also problem 3.28 in Spivak chapter 3. Spivak gives you a hint that is very useful
11	Munkres, Section 14: 1, 2, 5, 6, 7
12	Munkres, Section 15: 1, 2, 4, 5 and Section 16: 1
13	Section 40: 1, 2
14	Munkres, Section 26: 1, 2
15	Munkres, Section 26: 3, 4, 5 Munkres, Section 27: 1, 2
16	Munkres, Section 26: 6, 8 Munkres, Section 27: 4
17	Munkres, Section 28: 1 (part a and c), 5, 6
18	Munkres, Section 29: 1, 2 Prove the following properties of the pull-back operation A* (PDF)
19	Munkres, Section 30: 1, 2, 3, 4
20	Munkres, Section 30: 5
21	Munkres, Section 32: 1, 2, 3, 4
22	Supplementary Notes, Section 1: 1, 3, 6, 7 (PDF)
23	Supplementary Notes, Section 2: 2, 3
24	Supplementary Notes, Section 4: 4, 5, 6, 7 (PDF)
25	Supplementary Notes, Section 4: 2 (PDF) Supplementary Notes, Section 5: 2, 3 (PDF)
26	Supplementary Notes, Section 4: 3 (PDF) Supplementary Notes, Section 6: 5, 6 (PDF)
27	Supplementary Notes, Section 6: 1, 2, 3, 4 (PDF)
28	Munkres, Section 24: 5
29	Munkres, Section 34: 6
30	Munkres, Section 35: 3

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Assignments