Mathematics

Homework

Assigned Jan. 10

Sec. 1.1, problems 1, 3, 5, 11, 13, 15. On 1, 3, 5, 11, ignore the question, "Is the equation linear or nonlinear?" (1, 3, 5 correspond to 2, 4, 6 in the 5th edition.)
Sec. 1.2, problems 1, 3, 5, 9, 11, 15, 16. See Hints and answers for answers to even problems. (1, 3, 5, 9 correspond to 2, 4, 6, 10 in the 5th edition.)

Assigned Jan. 12

Sec. 1.2, problems 22, 23, 25, 27, 28, 31.
Sec. 1.3, problems 1, 3, 9efg, 11, 14, 15, 18. (1 corresponds to 2 in the 5th edition.)

Assigned Jan. 17

Sec. 1.3, problem 17.
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 = 1.1, 1.2, 1.3). (Problems correspond to 2, 4, 6 in the 5th edition.)
Sec. 2.2, odd problems 1 - 23 (omit 5, 15). (In the 5th edition, 1 and 3 correspond to 2 and 4; 7 corresponds to 10; 9 does not have a corresponding problem; 11 corresponds to 11; 13 approximately corresponds to 13; 17, 19 correspond to 17, 19; 21 and 23 do not have corresponding problems.)


Assigned Jan. 19

Sec. 2.3, odd problems 1 - 9, 13 - 19. Note that in problem 13, the roles of x and y are reversed: x is to be a function of y. (In the 5th edition, 1, 3, 5, 7, 9 correspond to 2, 4, 6, 8, 10.)


Assigned Jan. 24

Sec. 2.4, problems 1, 3, 5, 7, 11, 13, 15, 16, 17, 19. (In the 5th edition, 1, 3, 5, 7 correspond to 2, 4, 6, 8.)
P. 33, problems d, e, f. (In the 5th edition, these problems are on pp. 35 - 36.)


Assigned Jan. 31

Sec. 3.2, problems 1, 3, 5, 7, 19. In problem 7, assume that 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. 3.4, problems 1, 5, 13, 25a - e.

Assigned Feb. 9

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

Assigned Feb. 14

Sec. 9.2, problems 1, 3, 7, 11, 12b. Do the problems by using row operations to convert the augmented matrix to reduced row-echelon form. (In the 5th edition, 3 corresponds to 8.)
Sec. 4.4, odd problems 1 - 9, 13 - 31. (In the 5th edition, 3, 5, and 9 correspond to 4, 6, and 10.)

Assigned Feb. 16

Sec. 4.5, odd problems 1 - 35. (In the 5th edition, 1, 3, 5, 7, 9 corresponds to 2, 4, 6, 8, 10.)
Sec. 4.6, problems 2, 3, 4, 7, 11, 13. (In the 5th edition, 2, 3, 4, 7 corresponds to 1, 6, 5, 10.)

Assigned Feb. 23

Sec. 4.9, problems 1, 3, 7, 9. (In the 5th edition, 1 corresponds to 2.)
Sec. 7.2, problems 1, 3, 9, odd problems 13 - 19.
Sec. 7.3, odd problems 1 - 7.

Assigned Feb. 28

Sec. 4.10, problems 3, 9. Use undetermined coefficients to do these. For problem 9, first read pp. 228-229 in the text and Example 3 on p. 229. (In the 5th edition, p. 245 and Example 3.)
Sec. 7.3, problems 9, 25.

Assigned Mar. 1

Sec. 7.4, problems 1, 3, 5, 7, 9, 21, 23, 25.
Sec. 7.5, problems 1, 3, 5, 7, 19, 21.
Sec. 7.6, odd problems 1 - 7.

Assigned Mar. 13

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

Assigned Mar. 16

Sec. 7.8, problems 13, 15, 17.

Assigned Mar. 27

Sec. 9.3, problems 1, 3, 5, 9, 11, 13, 17, 21, 23, 25, 30, 31, 33.


Assigned Mar. 29

Sec. 9.3, problems 35, 37, 39.
Sec. 9.4, problems 1, 3, 9, 11, 21, 23, 25. For problems 21 and 23, (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. (In the 5th edition, 21, 23, 25 correspond to 19, 21, 23.)

Assigned April 3

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. 10

Sec. 9.5, problem 9.
Sec. 9.6, problems 1, 3, 13a.
Sec. 9.7, problems 11, 13, 15.

Assigned Apr. 12

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.

Assigned Apr. 19

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. 12.3, problems 9, 11, 21. Ignore the directions. Draw the nullclines, find the equilibria, show typical vectors in the regions determined by the nullclines, try to sketch a few typical solution curves. See Hints and answers for complete phase portraits, but your answers will not be this complete yet. We'll improve your answers next week.

Assigned Apr 24

Sec. 12.3, problems 9, 11, 21. Ignore the directions. Finish these problems by using linearization to determine the types of the equilibria, and using this information to improve your phase portraits. For answers see Hints and answers.

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