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.

Assigned Jan. 11

Sec. 1.2, problems 9, 11, 15, 16, 22. See Hints and answers for answers to even problems.
Sec. 1.3, problem 11.

Assigned Jan. 14

Sec. 1.2, problems 23, 25, 26, 27, 31.
Sec. 1.3, problems 1, 3, 9efg, 14, 15, 17, 18.


Assigned Jan. 16

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. 2.2, odd problems 1 - 23 (omit 15).
Sec. 2.3, odd problems 1 - 9, 13, 15, 17, 19.

Assigned Jan. 23

Sec. 2.4, problems 1, 3, 5, 9, 11, 13, 15, 16, 17.


Assigned Jan. 25

Pp. 35 - 36, problems d, e, f.


Assigned Jan. 28

Sec. 3.2, problems 1, 3, 5, 7. 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. 2

Sec. 3.2, problem 19.
Sec. 3.4, problems 1, 5, 13, 25a - e.

Assigned Feb. 11

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

Assigned Feb. 13

Sec. 4.4, odd problems 9 - 25.

Assigned Feb. 15

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

Assigned Feb. 18

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

Assigned Feb. 20

Sec. 4.8, problem 1.

Assigned Feb. 22

Sec. 4.8, problems 3, 7, 9.

Assigned Feb. 27

Sec. 4.9, problems 3, 9. Use undetermined coefficients to do these. For problem 9, see pages 225 (bottom) to 227 for how to determine the spring constant k.
Sec. 7.2, problems 1, 3, 9, odd 13 - 19.

Assigned Feb. 29

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

Assigned Mar. 10

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

Assigned Mar. 12

Sec. 7.6, odd problems 1 - 7.

Assigned Mar. 14

Sec. 7.6, odd problems 11 -19, odd 29 - 37.
Sec. 7.8, problems 1, 3, 5, 7, 13, 15, 17.

Assigned Mar. 24

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

Assigned Mar. 26

Sec. 9.3, problems 1, 3, 5.

Assigned Mar. 28

Sec. 9.3, problems 9, 11, 13, 21, 23, 25, 30.

Assigned Mar. 31

Sec. 9.3, problems 17, 31, 33, 35, 37, 39.
Sec. 9.4, problems 1, 3, 9, 11, 19, 21, 23. 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 Apr. 2

Sec. 9.5, problems 1, 3, 5, 7, 11, 13, 15.

Assigned Apr. 4

Sec. 9.5, problems 6, 9, 16. See Hints and answers for answers to 6 and 16.
Sec. 9.6, problems 1, 3, 13a.

Assigned Apr. 7

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.
Warnings! (1) If a solution curve of the phase plane equation goes through an equilibrium, then it contains several trajectories. For example, in Figure 5.10 on p. 267, the solutions of the phase plane equation are y=Cx^2. Each consists of three trajectories: one with x<0, one with x>0, and the origin. (2) If dx/dt = 0 on a vertical line x=c, then x=c is a trajectory or a union of trajectories, but the general solution of the phase plane equation misses it. For example, in Figure 5.10 on p. 267, dx/dt = 0 on the vertical line x=0. This is not one of the solutions of the phase plane equation.
For solutions to 12 and the extra problem, see Hints and answers.

Assigned Apr 9

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 11

Sec. 9.7, problems 11, 13, 15.

Assigned Apr 21

Sec. 12.3, problems 9, 11, 21. Ignore the directions. Draw the nullclines, find the equilibria, draw the vector field on 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.


Assigned Apr 23

Sec. 12.4, problems 7, 9.

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