MACS 315F Study Problems, Homework, and Quizzes

Study Problems

1.2 #1a, 3, 6, 8, 12, 13, 15
1.3 #1-8, 15, 16
2.1 #6, 9, 13-16, 28, 30
2.2 #1-8, 21, 23, 27, 28
2.3 #1, 4, 7, 14, 15, 24, 27
2.4 #1, 5, 13, 15, 22
3.1 #1-6, 9, 14, 29, 32, 35
3.2 #1-6, 9, 11. 21, 22, 23, 25
3.3 #1-10
3.4 #1, 5, 7, 9, 10, 20, 21, 24, 25
3.5 #1-10, 12, 14, 18, 23, 25, 27
3.6 #1-8, 13-18
3.7 #1-8, 13, 14
3.8 #1, 2, 6, 8, 11, 12. 13. 17, 29ab
3.9 #5-8, 10-12
6.1 #1, 5, 6, 9, 11, 15, 16, 21
6.2 #1-10, 11, 13, 14, 15, 17, 18, 20, 22, 29 (32), 30
6.3 #2, 4, 8, 10-18
6.4 #1, 3, 8, 10, 16
6.5 #1, 3, 5, 7, 10, 13
6.6 #4, 5, 8, 9, 11, 13, 15, 16
7.1 #1-4
7.2 #1, 4, 21, 22, 23
7.3 #6, 15, 18, 21
7.4
7.5 #1, 5, 7, 9, 14, 15, 16
7.6 #1, 5, 7, 9
7.7
7.8 #1-9 odd
7.9 #1-5, 12

Homework

  1. 01/14/02 2.1 #7, 25 (Must approximate local max), 2.2 #7, 17
  2. 01/21/02 HW2
  3. 01/28/02 3.1 #32, 3.2 #22, 3.4 #21, 24
  4. 02/04/02 (1) 3.5.15 (2) y'' + 3y = -48x2 e3x (3) y'' + 2y' = 2x + 5 - e-2x (4) y'' + y = sec x (by Variation of Parameters)
  5. 02/18/02 (1) 3.8.7, (2) 3.8.18 (Hints: p.196 and E = 0), (3) A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially the mass is released 1 foot below the equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to two times the the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 12 cos 2t + 3 sin 2t. (b) Graph the transient and steady-state solutions on the same coordinate axes. (4) 6.1.10
  6. 02/25/02 (1) 6.2.12 (2) 6.2.16 (Hint: Thm 6.3.2) (3) 6.3.7 (4) 6.3.10
  7. 03/04/02 (1) 6.4.2 (2) 6.4.5 (3) 6.5.14ab (4) 6.6.14
  8. 03/25/02 (1) 7.1.3 (2) 7.2.23 (3) 7.3.16 (4) 7.3.22
  9. 04/01/02 (Skip plots but not limits in all problems) (1) 7.5.4 (2) 7.5.13 (3) 7.6.3 (4) 7.8.4
  10. 04/12/02 Note later due date! (1) 7.9.7 (2) 7.9.8 (3) 9.1.2 (a)-(c) (4) 9.1.3 (a)-(c)

Quizzes

  1. (1/23/2) On terms defined in lecture (e.g., "order", "linearly independent") and study problems: 1.3 #1-6, 3.2 #1-6, 3.3 #1-10.
  2. (1/30/02) Guess particular solutions for the method of undetermined coefficients, as in section 3.6 Study Problems, but don't solve. Example trial solutions.
  3. (2/13/02) On spring-and-mass vocabulary: amplitude, phase, period, frequency, underdamped, overdamped, critically damped.
  4. (2/20/02) 6.2.1-10. You will need a table of Laplace Transforms.
  5. (3/20/02) 7.1 study problems and 7.2 terminology and operations covered in class.
Last modified $Date: 2002/04/09 22:33:40 $ -07:00/06:00 MST/MDT by Glenn Murray