### Author Topic: Comparison of 9th and 10th textbook editions  (Read 31467 times)

#### Yanyuan Jing

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##### Re: Comparison of 9th and 10th textbook editions
« Reply #15 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 Î¾ is an eigenvector, so one way to proceed is to choose Î¾ to be a suitable linear combination of Î¾(1) and Î¾(2) so that Eq. (iv) is solvable, and then to solve that equation for Î·. However, let us proceed in a different way and follow the pattern of Problem 17. First, show that Î· satisfies $$(A-I)^2Î·=0$$ Further, show that (A-I)2=0. Thus Î· can be chosen arbitrarily, except that it must be independent of Î¾(1) and Î¾(2).
(d) A convenient choice for Î· is Î·=(0, 0, 1)T. Find the corresponding Î¾ from Eq. (iv). Verify that Î¾ is an eigenvector.
(f) Form a matrix T with the eigenvector Î¾(1) in the first column and with the eigenvector Î¾ from part (d) and the generalized eigenvector Î· 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

#### Victor Ivrii

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##### Re: Comparison of 9th and 10th textbook editions
« Reply #16 on: January 30, 2013, 05:03:03 AM »
Amazing job!

I noticed you typed bold $\xi$ without using MathJax and this was a correct decision as you wanted bold and upright.

Unfortunately MathJax does not support upright Greek fonts (LaTeX does through package upgreek)

#### Victor Ivrii

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##### Re: Comparison of 9th and 10th textbook editions
« Reply #17 on: January 30, 2013, 05:18:38 PM »
Added 4 numbers to sect. 3.3 of home assignments (in red). Please check them (9th vs 10th)