Mathematics

Homework

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Assigned Jan. 11

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, 9, 11, 15, 16, 22. See Hints and answers for answers to even problems.

Assigned Jan. 13

Sec. 1.3, problems 1, 3, 9efg, 11, 14, 15, 18.
Sec. 1.2, problems 23, 25, 27, 28, 31.
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).

Assigned Jan. 18

Sec. 1.3, problem 17.
Sec. 2.2, odd problems 1 - 23 (omit 15).
Sec. 2.3, odd problems 1 - 9.

Assigned Jan. 25

Sec. 2.3, odd problems 13 - 19. Note that in problem 13, the roles of x and y are reversed: x is to be a function of y.
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, 25a - e.

Assigned Feb. 8

Sec. 4.2, odd problems 1 - 19.
Sec. 4.3, odd problems 1 - 17, 21, 23, 25.

Assigned Feb. 10

Sec. 9.2, problems 1, 3, 7, 11, 12b. Use row operations to convert the augmented matrix to reduced row-echelon form.
Sec. 4.4, problems 9, 11, 13, 25.

Assigned Feb. 15

Sec. 4.4, odd problems 1 - 7, 15 - 23, 27 - 31.
Sec. 4.5, odd problems 1 - 35.

Assigned Feb. 17

Sec. 4.6, problems 1, 5, 7, 11, 13.

Assigned Feb. 22

Sec. 4.9, problems 1, 3, 7, 9.
Sec. 4.10, problems 3, 9. Use undetermined coefficients to do these. For problem 9, first read p. 245 in the text and Example 3 on p. 246.

Assigned Feb. 24

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

Assigned Mar. 1

Sec. 7.3, problems 9, 25.
Sec. 7.4, problems 1, 3, 5, 7, 9, 21, 23, 25.
Sec. 7.5, problems 1, 3, 5, 7, 19, 21.

Assigned Mar. 4

Sec. 7.6, odd problems 1 - 7, 11 - 19, 29 - 37.

Assigned Mar. 15

Sec. 7.8, problems 1, 3, 5, 7, 13, 15, 17.

Assigned Mar. 24

Sec. 9.3, problems 1, 3, 5, 9, 11, 13, 21, 23, 25.

Assigned Mar. 29

Sec. 9.3, problems 17, 30, 31, 33, 35, 37, 39.
Sec. 9.4, problems 1, 3, 9, 11, 19, 21. For problems 19 and 21, (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 Mar. 31

Sec. 9.4, problem 23.
Sec. 9.5, problems 1, 3, 5, 6, 7, 11, 13, 15, 16. See Hints and answers for answers to 1, 6, and 16.

Assigned Apr. 5

Sec. 9.5, problem 9.
Sec. 9.6, problems 1, 3, 13a, 19.

Assigned Apr 7

Sec. 9.7, problems 11, 13, 15.

Assigned Apr. 19

Sec. 5.4, problems 11, 12, 29a. 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.
For solutions to 12 and the extra problem, see Hints and answers.
Sec. 12.2, problems 1, 3, 5, 13, 15. For 1, 3, and 5, classify the origin as an attracting or repelling node, attracting or repelling spiral, or saddle. 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, see Hints and answers.

Assigned Apr 26

Sec. 12.3, problems 9, 11, 21. Ignore the directions. Draw the nullclines, find the equilibria, draw the vector field on the nullclines and show typical vectors in the regions determined by the nullclines, try to sketch a few typical solution curves. Then use linearization to determine the types of the equilibria, and use this information to improve the phase portraits. For answers see Hints and answers.