Mathematics

Homework

Assigned Jan. 9

Sec. 1.1, problems 1, 3, 5, 11, 13, 15. On 1, 3, 5, 11, ignore the question, "Is the equation linear or nonlinear?"
Sec. 1.2, problems 1, 3, 5, 15.

Assigned Jan. 11

Sec. 1.2, problems 9, 11, 16, 22.
Sec. 1.3, problems 1, 3.

Assigned Jan. 13

Sec. 1.2, problems 23, 25, 26, 27.
Sec. 1.3, problems 9efg, 11, 14, 15.

Assigned Jan. 18

Sec. 1.4, problems 1 (just do x = 0.1, 0.2, 0.3), 3 (just do x = 0.1, 0.2, 0.3), 5 (just do x = 1.2, 1.4, 1.6).
Sec. 2.2, odd problems 1 - 9.

Assigned Jan. 20

Sec. 2.2, problems 11, 13, odd 17 - 23.
Sec. 2.3, odd problems 1 - 9, 13, 15.

Assigned Jan. 25

Sec. 2.3, problems 17, 19.
Sec. 2.4, problems 1, 3, 5, 9, 11, 13, 15, 16, 17.
Pp. 35 - 36, problems d, e, f.

Assigned Jan. 27

Sec. 3.2, problems 1, 3, 5, 7, 19. In problem 7, both tanks are initially full, so they both start overflowing immediately. We are not told the amount of salt that is initially in the first tank, so just say the initial amount is A pounds.

Assigned Feb. 1

Sec. 3.4, problems 1, 5, 13, 24 (find v(t) only), 25.

Assigned Feb. 3

Sec. 4.2, odd problems 1 - 19.

Assigned Feb. 10

Sec. 4.3, odd problems 1 - 17, 21, 23, 25.

Assigned Feb. 13

Sec. 4.4, odd problems 1 - 31.

Assigned Feb. 15

Sec. 4.5, odd problems 1 - 35.

Assigned Feb. 17

Sec. 4.8, problems 1, 3, 7, 9.
Sec. 4.9, problem 3, 9. Use undetermined coefficients to do these.

Assigned Feb. 27

Sec. 4.6, problems 1, 5, 7, 11, 13. Use the method for doing these problems that was described in lecture today; it's also described at http://courses.ncsu.edu/ma341/lec/001/varpar.pdf, p. 10.

Assigned Mar. 3

Sec. 7.2, problems 1, 3, 9, odd 13 - 19.
Sec. 7.3, odd problems 1 - 7.

Assigned Mar. 13

Sec. 7.3, problems 9, 25.
Sec. 7.4, odd problems 1 - 9.

Assigned Mar 15

Sec. 7.4, problems 21, 23, 25.
Sec. 7.5, problems 1, 3, 5, 7, 19, 21.

Assigned Mar 17

Sec. 7.6, odd problems 1 - 9.

Assigned Mar 20

Sec. 7.6, problems odd 11 - 19, odd 29 - 37.
Sec. 7.8, problems 1, 3, 7, 13, 15, 17.

Assigned Mar 28

Sec. 9.3, problems 1, 3, 5.

Assigned Mar 29

Sec. 9.2, problems 1, 3, 7, 11, 12b. Use reduction of the augmented matrix to row-echelon form.
Sec. 9.3, problems 9, 11.

Assigned Mar. 31

Sec. 9.3, problems 13, 17, 21, 23, 25, 30, 31, 33, 35, 37, 39.
Sec. 9.4, problems 1, 3, 9, 11.

Assigned Apr 3 (corrected Apr 5)

Sec. 9.4, problems 19, 21. For each problem, (1) check that the given vector functions are linearly independent at t=0 by calculating a determinant; (2) if they are linearly independent, give a general solution to the system.

Assigned Apr 5

Sec. 9.5, odd problems 1 - 7.

Assigned Apr 7

Sec. 9.5, problems 6, 9, 11, 13, 15, 16. See Hints and answers for answers to 6 and 16.


Assigned Apr 10

Sec. 9.6 problems 1, 3, 13a.

Assigned Apr 12

Sec. 5.4, problems 11, 12, 29 a. On 29a, use the directions for 11 and 12.
One more problem: dx/dt = x/2, dy/dt = -2y. Use the directions for 11 and 12.
See Hints and answers.

Assigned Apr 21

Sec. 12.2, problems 1, 3, 5, 13, 15. For 13 and 15, use eigenvalues and eigenvectors to sketch the phase plane. Also, use the same method to sketch the phase plane for problem 3.
For answers to 1, 3, and 5 in the terminology I prefer, see Hints and answers.

Assigned Apr 24

Sec. 12.3, problems 9, 11, 21. Draw the nullclines, find the equilibria, draw the vector field on the nullclines, try to sketch a few typical solution curves. We will analyze the equilibria later, which will help us draw better phase portraits.

Assigned Apr 26

Sec. 12.3, problems 9, 11, 21. This time follow the book's instructions.

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