Ordinary Differential Equations
Math 520 -- Spring 2008

Professor Doug Meade
meade@math.sc.edu
Department of Mathematics
University of South Carolina

Homework Assignments

Date Assigned
 Date Due
 Assignment
 Comments
14 Jan 18 Jan §1.1 (p. 12) # 3, 7, and 8a
  • #8 is easier than it might appear at first; the idea is to determine the differential equation satisfied by Q(t) using only the fact that y'(t)=Q(t).
16 Jan 25 Jan §1.2 (p. 27) # 9, 14, 17, 22, 30, 31
  • Read each question carefully. Be sure you answer the question(s) asked.
  • Many of these questions introduce ideas that we will explore in much greater detail later in the course. Do not worry about trying to do more than you are asked to do - yet.
23 Jan 1 Feb §2.1 (p. 58) # 2
23 Jan 1 Feb §2.2 (p. 72) # 10, 15, 16
  • [ Maple ] [ MapleNet ] Practice solving Separable Differential Equations
25 Jan 1 Feb §2.3 (p. 83) # 8, 11, 12, 18
  • Do not worry about determining the behavior of the solutions as t—>∞.
  • We do not know how to find the exact solution to #18. For this problem, just create the slope field and draw three representative solutions.
  • A worksheet to help create slope fields with Maple.
  • [ Maple ] [ MapleNet ] Identifying direction fields for a DE.
28 Jan 4 Feb §2.4 (p. 93) # 4, 7, 10
30 Jan 4 Feb §2.5 (p. 106) # 8, 9
  • This assignment is due on Monday, so you can have it back to prepare for the exam on Friday.
  • The differential equations in these problems were seen in sections 2.2 and 2.3. You should not have to do any additional work to find the exact solution.
  • A Maple worksheet for Euler's method.
8 Feb 8 Feb Exam 1
4 Feb 15 Feb §3.1 (p. 135) # 1, 2, 4, 8
  • Hint: For #8, the information that the mass oscillates with period 1s means the solution looks like y(t)=c1sin(2πt)+c2cos(2πt). Use this information to determine k.
---- 15 Feb §3.2 (p. 147) # 4, 7, 8, 14, 20
  • Solution for #20 [PDF]
13 Feb 22 Feb §3.3 (p. 160) # 11, 18, 21
15 Feb 22 Feb §3.4 (p. 168) # 5, 8
  • For the long-time approximation, determine which term of the solution (if the solution has more than one term) is the largest when t is large.
15 Feb 22 Feb §3.5 (p. 177) # 5, 8, 12
  • #12 can become a little messy. Your answer should involve t. It is not appropriate to choose a convenient value for t. It is not unreasonable to use Maple (for example) to compute the derivatives.
  • Solution for #12 [PDF]
18 Feb 29 Feb §3.6 (p. 186) # 3, 4, 6, 7
20 Feb 29 Feb §3.7 (p. 198) # 3, 6
25 Feb 3 Mar §4.2 (p. 226) # 2, 4, 12
27 Feb 3 Mar §4.3 (p. 239) # 7, 8, 10, 16, 20, 23
7 Mar 7 Mar Exam 2
29 Feb 21 Mar §4.5 (p. 260) # 2, 4, 11, 18, 33
  • Solution for #33 [PDF]
29 Feb 21 Mar §4.6 (p. 270) # 1, 2, 4, 12, 18
21 Mar 28 Mar §5.1 (p. 286) # 1, 2
  • Variation of Parameters practice: # 3 (p. 271)
24 Mar 28 Mar §5.2 (p. 295) # 1, 2, 4, 6
26 Mar 4 Apr §5.3 (p. 308) # 2, 5, 7, 8
  • Solution to Exercise #4 [Maple Worksheet]
  • Variation of Parameters practice: #10 (p. 271) [EXTRA CREDIT]
28 Mar 4 Apr §5.4 (p. 318) # 4, 6, 9, 13
31 Mar 4 Apr §5.5 (p. 326) # 2, 7
2 Apr 7 Apr §6.1 (p. 341) # 2, 5, 11
  • Variation of Parameters practice: #11 (p. 271) [EXTRA CREDIT]
  • Solution to #17 and #18 (an interesting model of lead in the bloodstream) [Maple Worksheet]
4 Apr 7 Apr §6.2 (p. 354) # 3, 6, 7, 10, 13, 16
11 Apr 11 Apr Exam 3
  • §§ 4.4 -- 4.6 Chapter 5, and §§ 6.1 -- 6.2
  • Solution Key
7 Apr 18 Apr §6.3 (p. 364) # 2, 3, 14, 16
  • Variation of Parameters practice: #19 (p. 272) [EXTRA CREDIT]
14 Apr 25 Apr §6.4 (p. 375) # 2, 4, 12, 14
  • Variation of Parameters practice: #20 (p. 272) [EXTRA CREDIT]
  • You do not need to sketch the phase portrait for these systems.
18 Apr 25 Apr §6.5 (p. 385) # 4, 7
21 Apr 25 Apr §6.6 (p. 395) # 2, 9
23 Apr 25 Apr §6.7 (p. 408) # 2, 3, 6
  • Three examples [Maple Worksheet]
  • Graph the nullclines and identify the equilibrium solutions. You can use my worksheet to give you a picture of the phase portrait.
  • Solutions [PDF]
30 Apr 30 Apr Final Exam
  • Chapters 1 -- 6 (comprehensive)

Notes:

  • Maple worksheets (.mw files) should be downloaded to your local computer (I recommend creating a folder called, say, MapleFiles.)
  • Portable Document Format (PDF) files are viewable with acroread, a publicly available PDF viewer by Adobe.
  • PostScript (PS) files are viewable with ghostview, the public domain PS viewer.

    • If you have any questions, please send e-mail to meade@math.sc.edu
    Last modified: 29 November 2006