Mathematics

Homework

Assigned Aug. 24

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.

Assigned Aug. 27

Sec. 1.2, problems 23, 25, 26, 27, 31.
Sec. 1.3, problems 1, 3, 9efg, 11, 14, 15, 17, 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).

Assigned Aug. 29

Sec. 2.2, odd problems 1 - 23 (omit 15).

Assigned Aug. 31

Sec. 2.3, odd problems 1 - 9, 13, 15, 17, 19.

Assigned Sept. 5

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


Assigned Sept. 7

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


Assigned Sept. 10

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 Sept. 12

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

Assigned Sept. 21

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

Assigned Sept. 24

Sec. 4.4, odd problems 9 - 23.

Assigned Sept. 26

Sec. 4.4, odd problems 1 - 7, 25 - 31.
Sec. 4.5, odd problems 3 - 7, 17 - 29.

Assigned Sept. 28

Sec. 4.5, odd problems 1, 9 - 15, 31 - 35.
Sec. 4.6, problems 1, 5, 7, 11, 13.

Assigned Oct. 3

Sec. 4.8, problems 1, 3, 7, 9.


Assigned Oct. 5

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.

Assigned Oct. 8

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

Assigned Oct. 10

Sec. 7.3, problems 9, 25.
Sec. 7.4, problems 1, 3, 5, 7, 9.

Assigned Oct. 15

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

Assigned Oct. 19

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

Assigned Oct. 26

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

Assigned Oct. 29

Sec. 9.3, problems 1, 3, 5.

Assigned Oct. 31

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

Assigned Nov. 2

Sec. 9.4, problems 1, 3, 9, 11.

Assigned Nov. 5

Sec. 9.4, problems 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.
Sec. 9.5, problems 1, 3, 5, 7, 11, 13, 15.

Assigned Nov 7

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 Nov 9

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.
Warning! 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.
For solutions to 12 and the extra problem, see Hints and answers.

Assigned Nov 12

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.
Sec. 9.7, problems 11, 13, 15.

Assigned Nov 26

Sec. 9.6, problem 19.
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. For answers see Hints and answers.


Assigned Nov 28

Sec. 12.3, problems 9, 11, 21. Use linearization to determine the types of the equilibria, and use this information to improve the phase portraits you drew for the previous assignment.

Assigned Dec 3

Sec. 12.4, problems 7, 9.

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