Homework assignments for MAT-157Y: Analysis I, Sep 2006 - April 2007

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# Assigned: Due date: Comments, corrections, etc.

1 Sep 19 Sep 29 Problem 1: The final answer should be expressed just in terms of square roots and the four basic operations. (No numerical value.) Problem 2: Simplify so that the final answer is in terms of cosines, no sines.

2 Sep 26 Oct 6 ..

3 Oct 3 Oct 13 ..

4 Oct 10 Oct 20 In problem 1, X and Y can be arbitrary sets -- not necessarily intervals of real numbers.

5 Oct 17 Oct 27 The "required reading" should also include chapter 5.

5a Oct 24 never This week, the problem set consists only of "recommended problems"!

6 Oct 31 Nov 10 ..

7 Nov 7 Nov 17 ..

8 Nov 14 Nov 24 ..

9 Nov 21 Dec 1 ..

10 Nov 28 Dec 8 ..

11 Jan 9 Jan 19 ..

12 Jan 16 Jan 26 Please note that I've corrected problems 1 and 2 -- you are supposed to do the even parts, not the odd parts. Also, it was pointed out that Spivak, chapter 14, problem 6(ii) (= our problem 3) has no solution g(x) defined for all real x. Please restrict to the region where x is non-negative. (Or else give a good, solid argument *why* it does not have a solution defined for all x. Or even better, do both!)

13 Jan 23 Feb 2 ..

14 Jan 30 Feb 9 ..

15 Feb 6 Feb 16 ..

16 Feb 27 March 9 ..

17 March 6 March 16 ..

18 March 13 March 23 Problem 3(a) is correct only if one allows improper limits (e.g. minus infinity). To correct the problem, assume that the series is bounded.

19 March 20 March 30 ..

20 March 27 April 5** Initially, I had indicated a due date of April 6. This does not work since the University of closed on that day. You can either return the problem set by April 5th, or (better) hand them back during the tutorial on Monday, April 9.

20a April 3 never The problem set only consists of (highly) recommended problems. Note: Kejia remarked that the function in 1(b) actually *is* integrable. To make the problem meaningful, take g to be a function that is equal to 1 on the rationals, equal to $0$ on the irrationals. (Hint: the set of rational numbers is countable.)

#	Assigned:	Due date:	Comments, corrections, etc.
1	Sep 19	Sep 29	Problem 1: The final answer should be expressed just in terms of square roots and the four basic operations. (No numerical value.) Problem 2: Simplify so that the final answer is in terms of cosines, no sines.
2	Sep 26	Oct 6	..
3	Oct 3	Oct 13	..
4	Oct 10	Oct 20	In problem 1, X and Y can be arbitrary sets -- not necessarily intervals of real numbers.
5	Oct 17	Oct 27	The "required reading" should also include chapter 5.
5a	Oct 24	never	This week, the problem set consists only of "recommended problems"!
6	Oct 31	Nov 10	..
7	Nov 7	Nov 17	..
8	Nov 14	Nov 24	..
9	Nov 21	Dec 1	..
10	Nov 28	Dec 8	..
11	Jan 9	Jan 19	..
12	Jan 16	Jan 26	Please note that I've corrected problems 1 and 2 -- you are supposed to do the even parts, not the odd parts. Also, it was pointed out that Spivak, chapter 14, problem 6(ii) (= our problem 3) has no solution g(x) defined for all real x. Please restrict to the region where x is non-negative. (Or else give a good, solid argument why it does not have a solution defined for all x. Or even better, do both!)
13	Jan 23	Feb 2	..
14	Jan 30	Feb 9	..
15	Feb 6	Feb 16	..
16	Feb 27	March 9	..
17	March 6	March 16	..
18	March 13	March 23	Problem 3(a) is correct only if one allows improper limits (e.g. minus infinity). To correct the problem, assume that the series is bounded.
19	March 20	March 30	..
20	March 27	April 5**	Initially, I had indicated a due date of April 6. This does not work since the University of closed on that day. You can either return the problem set by April 5th, or (better) hand them back during the tutorial on Monday, April 9.
20a	April 3	never	The problem set only consists of (highly) recommended problems. Note: Kejia remarked that the function in 1(b) actually is integrable. To make the problem meaningful, take g to be a function that is equal to 1 on the rationals, equal to $0$ on the irrationals. (Hint: the set of rational numbers is countable.)