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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:

(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

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:

Section 6.2: #35 is #34 in the 9th edition. Also, the prompt for #25 should read:

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

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 ifÎ¾is an eigenvector, so one way to proceed is to choose Î¾ to be a suitable linear combination ofÎ¾and^{(1)}Î¾so that Eq. (iv) is solvable, and then to solve that equation for^{(2)}Î·. However, let us proceed in a different way and follow the pattern of Problem 17. First, show thatÎ·satisfies $$(A-I)^2Î·=0$$ Further, show that (A-I)^{2}=0. ThusÎ·can be chosen arbitrarily, except that it must be independent ofÎ¾and^{(1)}Î¾.^{(2)}

(d) A convenient choice forÎ·isÎ·=(0, 0, 1)^{T}. Find the correspondingÎ¾from Eq. (iv). Verify thatÎ¾is an eigenvector.

(f) Form a matrixTwith the eigenvectorÎ¾in the first column and with the eigenvector^{(1)}Î¾from part (d) and the generalized eigenvectorÎ·in the other two columns. FindTand form the product^{-1}J=T^{-1}AT. The matrixJis the Jordan form ofA.

(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