Math 111.001/02 (Applied Mathematical Analysis I)

Fall 1998

Plan for Week 5

This week we continue our study of homogeneous second-order linear DEs. We start by looking at the underlying theory of "fundamental" solutions -- so that we know what to look for when we solve these equations.

Next we discover the oscillatory solutions that occur when there are no real roots of the characteristic equation and the "oscillatory wannabes" associated with one real root.

In lab we study graphical representations of solutions of equations with constant coefficients. While we can easily find symbolic solutions of these equations, we will use numerical solutions instead, because these are quick to compute and easy to plot. Our emphasis will be on determining how the qualitative features of the solutions are related to sizes and signs of the coefficients.

Here is the syllabus for Week 5:

Week 5 Date Topic Reading Activity
M 9/28 Fundamental solutions 3.2
W 9/30 Complex roots,
repeated roots
3.4, 3.5
F 10/2 Second-order linear DEs Lab: Second-Order Linear
Differential Equations
         
     
                    
         
                    


Notes

  1. Your next homework papers will be turned in on Monday, October 5. Those papers should include solutions to all problems in the assignment below. The assignment dates are start dates.
  2. Your textbook has far too many answers in the back of the book. If you look there first, you will subvert the learning process. If you know your answers are correct, you will never need to look there. In general, no homework problem will be given full credit unless you have written an explanation of why you know it is correct. For example, an acceptable explanation for a solution of a differential equation is that you have substituted the proposed solution into the original equation and found that it satisfies the equation -- but you have to show your work. Two examples of unacceptable explanations: (a) It matches the answer in the back of the book. (b) I did the work again and it came out the same.
  3. Submit your Week 5 lab report (the Maple file) via e-mail by the end of the day Wednesday, October 7.
  4. Remember to submit your e-mail journal entry on Friday, October 2.

Assignments


David A. Smith <das@math.duke.edu>

Last modified: July 14, 1998