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Messages - Yanyuan Jing

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MAT 244 Misc / Re: Comparison of 9th and 10th textbook editions
« on: January 30, 2013, 02:14:52 AM »
Hey guys,

Here are the suggested questions for those using the 9th edition. Again, I only compared the suggested problems listed on the course website, not all the questions in the textbook.

Sections 7.1-7.7: same
Section 7.8: 4, 5, 16, 18, 20, with the following changes to #18:

Quote from: 10th edition
(c) Equation (iii) is satisfied if ξ is an eigenvector, so one way to proceed is to choose ξ to be a suitable linear combination of ξ(1) and ξ(2) so that Eq. (iv) is solvable, and then to solve that equation for η. However, let us proceed in a different way and follow the pattern of Problem 17. First, show that η satisfies $$(A-I)^2η=0$$ Further, show that (A-I)2=0. Thus η can be chosen arbitrarily, except that it must be independent of ξ(1) and ξ(2).
(d) A convenient choice for η is η=(0, 0, 1)T. Find the corresponding ξ from Eq. (iv). Verify that ξ is an eigenvector.
(f) Form a matrix T with the eigenvector ξ(1) in the first column and with the eigenvector ξ from part (d) and the generalized eigenvector η in the other two columns. Find T-1 and form the product J=T-1AT. The matrix J is the Jordan form of A.

(Note: 18(e) is unchanged)

Section 7.9: same
Sections 9.1-9.6: same
Section 9.7: same, with slight difference in the prompt

Quote from: 10th edition
Determine all periodic solutions, all limit cycles, and the stability characteristics of all periodic solutions.

Sections 5.2-5.5: same
Section 6.1: Questions 21-24 in the 10th edition are not included in the 9th edition, and #27 is actually #23 in the 9th edition. Here are questions 21-24:

Quote from: 10th edition
21. $$f(t)= \left\{\begin{array}{ll}
1, & 0 \le t < \pi\\
0, & \pi \le t < \infty
\end{array}
\right.$$
22. $$f(t)= \left\{\begin{array}{ll}
t, & 0 \le t < 1\\
0, & 1 \le t < \infty
\end{array}
\right.$$
23. $$f(t)= \left\{\begin{array}{ll}
t, & 0 \le t < 1\\
1, & 1 \le t < \infty
\end{array}
\right.$$
24. $$f(t)= \left\{\begin{array}{ll}
t, & 0 \le t < 1\\
2-t, & 1 \le t < 2\\
0, & 2 \le t < \infty
\end{array}
\right.$$

Section 6.2: #35 is #34 in the 9th edition. Also, the prompt for #25 should read:
Quote from: 10th edition
A method of determining the inverse transform is developed in Section 6.3. You may wish to refer to Problems 21 through 24 in Section 6.1.

That's all! Hope that's helpful for everyone using the 9th edition!

P.S. This is my first time using LaTeX/MathJax. Please let me know if there are formatting/coding improvements I can make :)

2
MAT 244 Misc / Re: Comparison of 9th and 10th textbook editions
« on: January 23, 2013, 02:16:06 PM »
Good job, Brian and Yanyuan. I think you need to state explicitly that you are comparing only problems given as a home work, not all problems in general (may be I am mistaken).

Thanks for the suggestion, Dr. Ivrii. I added a clarification in my previous post.

3
MAT 244 Misc / Re: Comparison of 9th and 10th textbook editions
« on: January 23, 2013, 12:11:33 AM »
Hey guys,

*EDIT*
Here are the differences in the homework questions for those using the 9th Edition. Since there aren't that many changes, I won't bother retyping all the individual question numbers, so I guess you can all refer to this page for specifics: http://www.math.toronto.edu/courses/mat244h1/20131/homeassignments.html

PLEASE NOTE: We didn't check ALL the questions in the textbook, only the suggested ones listed in the above link.

Sections 1.1-2.2: same
Section 2.3 had one difference, which Brian has already posted (see 2 posts above)
Sections 2.4-3.3: same.
Section 3.4: 6, 14, 22, 27, 43
Section 3.5: 2, 12, 13, 22, 25
Section 3.6-4.2: same
Section 4.3: #19 does not have any parts (it doesn't have parts in the 10th edition either...)
Section 4.4: #1, the restriction is $$-\pi/2 < t < \pi/2$$

Brian and I are meeting up next week to do the rest of the suggested problems. I'll update this post when we do!

4
MAT 244 Misc / Re: Comparison of 9th and 10th textbook editions
« on: January 06, 2013, 09:13:30 PM »
I wouldn't mind helping, though I haven't bought the book yet. Also, I don't think it'll need to be a weekly thing. I think all the assigned questions have already been posted, and there aren't any evaluated problem sets, just suggested practice problems.

I'll private message you to set up meeting times?

Yan

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