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. 29

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

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

Assigned Sept. 5

Sec. 2.3, problems 17, 19.
Sec. 2.4, problems 1, 3, 5, 9, 11, 13, 15, 16, 17.


Assigned Sept. 7

Pp. 35 - 36, problems d, e, f.
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.
Sec. 2.3, problem 35.

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.

Assigned Sept. 26

Sec. 4.3, odd problems 1 - 17, 21, 23, 25.
Sec. 4.4, odd problems 1 - 15.

Assigned Sept. 28

Sec. 4.4, odd problems 17 - 31.
Sec. 4.5, odd problems 1 - 35.

Assigned Oct. 3

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

Assigned Oct. 10

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 in http://www.courses.ncsu.edu/ma341/lec/003/varpar.pdf, which I corrected today.

Assigned Oct. 17

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

Assigned Oct. 19

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 Oct. 24

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

Assigned Oct. 26

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

Assigned Nov. 2

Sec. 9.3, problems 1, 3, 5.

Assigned Nov. 7

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, 13, 17, 21, 23, 25, 30.

Assigned Nov. 9

Sec. 9.3, problems 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 Nov 14

Sec. 9.5, problems 1, 3, 5, 6, 7, 9, 11, 13, 15, 16. See Hints and answers for answers to 6 and 16.

Assigned Nov 16

Sec. 9.6 problems 1, 3, 13a.
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 Nov 21

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. 9.6, problem 19.
Sec. 9.7, problems 11, 13, 15, 21a.

Assigned Dec 5

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. Use linearization to determine the types of the equilibria, and use this information to improve your phase portrait.
Sec. 12.4, problems 7, 9.

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