## Homepage for Math 417: Advanced Calculus

## SECTION 002 ONLY!!

Here is the syllabus (for section 2 only!).
**HOMEWORK**

(I include notes after each problem so you can make sure that the numbering
in your edition matches that in mine.)

**HW 1** (due Friday, 9/6):

- 1-7: norm-preserving vs. inner product-preserving.
- 1-10: There is a number M....
- 1-12: Dual spaces: Show someting is 1-1, linear, and something is unique.
- 1-13: perpendicular (orthogonal)
- 1-14: Union of open sets is open....
- 1-16: Exterior, interior, boundary of 3 sets.

**HW 2** (due Friday, 9/13):
- 1-21: PARTS a AND c ONLY!! Distance between a point and a set.
- 1-22: U open, subset C is compact, there exists D such that....

READ (don't do) 1-23, 1-24.
- 1-25: Use problem 1-10. (!)
- 1-29: Every continuous function on a compact set A takes on a max and a min value.

READ (don't do) 2-1.

**HW 3** (due Friday, 9/27):
- 2-7

READ (don't do, unless you want to) 2-10
- 2-16
- 2-19
- 2-23a
- 2-38 (Mean Value Theorem could help for (a).)

**HW 4** (due Friday, 10/11):
- 3-1 (use Theorem 3-3)
- 3-2 (feel free to use Theorem 3-8)
- 3-5
- 3-12 (use the hint in the book; no need to prove 1-30)
- 3-14
- 3-36

**HW 5** (due Monday, 10/21):
- 3-41 EXCEPT part b. Just that one (5-1=4-part) problem! I suggest
reading through the full (page-long) problem statement so that you can
see the final target of all the parts before you begin.

(Exam 1 given in late October.)

**HW 6** (due Monday, 11/11):

- Prove that (w1+w2)^w3 = w1^w3 + w2^w3 (where ^ is the wedge product; w1 and w2 are alternating k-tensors; and w3 is an alternating m-tensor).
- Prove that
**v** x (a**w**) x **z** = a(**v** x **w** x **z**) (where x is the cross product; a is a real number; and **v**, **w**, and **z** are vectors).
- 4-1a. Read b, but don't bother doing it.
- 4-9ab (not c-e).

**HW 7** (due Friday, 11/22):
- 4-13b.

READ 4-14 through 4-16.
- 4-17b.
- 4-23.

**HW 8** (due Friday, 12/13):
- 5-5.
- 5-6: backwards direction only.
- 5-8a: think about thickening the manifold by an arbitrarily small amount.