Prof. Nyikos's Office: LeConte 406. Phone: 7-5134
Email: nyikos @ math.sc.edu
Special office hours Monday, Dec. 8: 10:00 - 10:45 am, 2:00 - 3:45 pm; Tuesday, Dec. 9 and Wednesday, Dec. 10: : 10:00 - 12:00 and 1:30 - 3:45; Thursday, Dec. 11: 2:00 - 5:30 pm; Friday, Dec. 12: 9:30 - 11:40 am.
A fact sheet will be distributed along with the final exam. These two things, plus writing instruments and low-tech calculators are the only things you should have on your desks during the exam. An electronic copy of the fact sheet can be found here.
The final exam is on Friday, December 12, at 12:30pm. Information on all final exam times can be found outside of "Self Service Carolina" at this good old fashioned Registrar's website.
The textbook for this course is Differential Equations, Computing and Modeling, by C. Henry Edwards & David E. Penney, 4th edition, Pearson/Prentice Hall, 2008.
The course covers the following chapters and sections:
Chapter 1, with emphasis on Sections 1.4, 1.5, and 1.6
Sections 2.1, 2.2, and material from other sections of Chapter 2 as
time permits
Sections 3.1 through 3.5, and material from other sections of Chapter 3 as
time permits
Chapter 7
Sections 4.1 and 4.2
Only simple calculators (in other words, those that may be used in taking SAT tests) are needed for this course, and they will be needed only a small fraction of the time, outside of class. Neither the quizzes, nor the hour tests, nor the final exam will require their use, although they may save some time on a few problems. Programmable calculators are not permitted for quizzes, hour tests, or the final exam.
The course grade will be based on quizzes, homework, 3 one-hour tests, a final exam, and attendance. Details on this and on various policies can be found here.
Learning Outcomes: Students will master concepts and solve problems based upon the topics covered in the course, including general and particular solutions to ordinary differential equations of the following types: separable, exact, nonlinear homogeneous, first- and higher order linear equations (both homogeneous and inhomogeneous, especially those with constant coefficients), systems of two equations. They will use solution methods such as: integrating factors, substitution, variation of parameters, undetermined coefficients, Laplace transforms. They will employ approximation methods such as Euler or Runge-Kut ta, and use differential equations in application to population biology, cooling, mechanical vibrations and/or electrical circuits.
There was a quiz on Section 2.2 on Friday, October 10. It
involved finding critical points of first order equations and telling
whether they are stable or unstable.
There was a quiz on Section 2.1 on Wednesday, October 1. It was
similar to Example 3 on page 83, and the equations (3) [p. 81] and
(7) [p. 82] will be provided.
There will be a quiz Monday, November 24, on Laplace transforms.
The first hour test was on Wednesday, September 24. It covered
Sections 1.2, 1.4, 1.5 and 1.6.
The second hour test was on Wednesday, October 29. It covered exact
equations (Section 1.6, covered by practice problems 31 and 39) and
sections 2.1 (with a problem similar to the quiz 4 problem), 2.2,
3.1, and 3.2, with problems similar to the practice problems and quiz problems for these sections.
The third hour test was on Friday, November 21. It covers Sections 3.3
through 3.6, and 7.1. Besides questions similar to those on quizzes and
practice problems (see below) for these sections, you were expected to identify
oscillation problems as Forced undamped, Forced damped, Free overdamped,
Free critically damped, or Free underdamped.
Homework due Friday, November 14:
Give the general solution to:
1. y'' + y' + 7y = 0
2. y''' - 3y'' + 3y' -y =0 [Hint: what integers divide the coefficient of y evenly?]
3. Find the particular solution to y''-y' -6y =0 that satisfies y(0) = -1, y(1) = 1
4. Find a particular solution to y'' - 5y' +4y = 3 + 2e^x
5.Find a particular solution to y'' + y = sec x [This requires variation of parameters.]
Practice problems, not to be handed in:
Section 1.2: 14, 24, 27, 28
Section 1.4: 1, 3, 19, 34, 38, 41
Section 1.5: 1, 5, 19
Section 1.6: 8, 9, 21, 22, 23, 31, 39.
Section 2.1: 1, 3, 17, 19
Section 2.2: 2, 3, 8, 21
Section 3.1: 2, 3, 5, 11, 13
Section 3.2: 1, 5, 13, 17, 21, 23
Section 3.3: 2, 8, 11, 15, 24
Section 3.4: 1, 2, 3
Section 3.5: 1, 3, 4, 10, 11, 21, 22, 23
Section 3.6: 1, 4 [graphs optional], 15 [solve equation, the rest is optional]
Section 7.1: 1, 2, 3
Section 7.2: 1, 5, 19, 21
Section 7.3: 1, 3, 7, 9
There is no due date for extra credit, but once a fully correct solution
is handed back, the problem is no longer eligible for extra credit.
This is true of any problem crossed out below
If you can't quite get the solution but have some ideas, hand them in for partial credit. I will keep adding to your score as you improve your work on it.
To get full credit, it is not enough to get the correct answer. You need to get it in such a way that someone who has not seen the problem before can tell that you did, indeed, get the right answer.
2. Problem 58, p.211
3. Problem 4, p. 231
4. Problem 6, p. 231