Spring 2006
MA332 Intermediate Differential Equations – Homework
Professor Bollt
Homework Page
Text Used: Nonlinear Dynamics and Chaos, With Applications to Physics, Biology, Chemisstry and Engineering,by S. Strogatz
Homework 1,
due We. Jan 18
Maple
practice-sheet.
Homework 2,
due Th. Jan 26
2.1.1, 2.1.2, 2.1.3,
2.2.1, 2.2.3, 2.2.10H
2.3.1, 2.3.2, Just read 2.3.3
2.4.1, 2.4.2, 2.4.5, 2.4.7
Homework 3, due Th. Feb 2
2.3.3
2.5.2, 2.5.6 (and for this one LOOK at 2.5.3 for partial help)
(The extra problem has been postponed until next week! Saved by the bell!)
Homework 4, due Th. Feb 9
And the extra problem which was postponed: For the general linear system,
.
Find a Lipschitz constant for the function f(z)=Az on R^2 in terms of a,b,c,d. Discuss consequence in terms of existence and uniqueness of solutions, and then also in terms of continuous dependence of solutions upon initial conditions.
2.6.1, 2.6.2
2.7.1, 2.7.2, 2.7.3, 2.7.7
2.8.1, 2.8.2, 2.8.3 and 2.8.4-(Use a spreadsheet, OR write your own program).
Also, read 2.8.5
Homework 5, due Fri. Feb 24
3.1.1, 3.1.4, 3.1.5
3.2.1, 3.2.2, 3.2.4, 3.2.5 (but we will do part of this one in class)
Homework 5, due Th. Mar. 2
3.4.1, 3.4.3, 3.4.4 (Hint: use a geometric series here!), 3.4.5, 3.4.7 (give me a series expansion along the way), 3.4.6 (again, that geometric series...)
3.4.15 (Look at 3.4.14 for hints, and you can use maple command "solve" to help with algebra.)
3.5.6, 3.5.7ab (read 3.5.8 for hints AND remind us in words what the logistic equation is used to model...)
3.6.1
Homework 6, due Th. Mar. 9
3.5.4, (on 3.5.4: read part a carefully, but you can take the equations from the back, and the DO parts b,c,d) and READ 3.5.5.
(Note: I moved 3.6.5 to the read only category due to much excitement on your part, but it is a very cool problem, and extra points will be awarded if you
3.7.1, 3.7.2 (Hint: You can use Maple for 3.7.2 to help), AND READ ONLY 3.7.4, 3.7.5 and 3.7.6.
5.2.1, 5.2.2, 5.2.4, 5.2.5, 5.2.12, (Feel free to use Maple's eigenvalue-vector commands on these), read 5.2.14
Problem 1: Consider the family of matrices parameterized by s: A=s[[1,0],[0,-5]]+(1-s)[[0,2],[-2,0]], for 0<=s<=1. Consider the family of differential equations defined by these A: zdot=A z
Considering the theory of Section 5.2, summarized by figure 5.2.8 on page 137, copy figure 5.2.8 and then use the trace and determinant method to place this entire family onto the figure; thus characterize all the behavior of this
family of systems.
6.1.1, 6.1.9 (Use your computer on these last two: remember the maple scripts I showed you!) 6.1.12
6.3.1, 6.3.2 (Again, besides dong linearization, use Maple to help you plot.) Read 6.3.10 and 6.3.15 which are cool but unassigned problems
6.5.1 (This is an assigned problem, but as an end of the year one time only special...I will do this one in class if someone asks me, but better ask on Monday or Wednesday in time!)
7.1.1 Read 7.1.6 and 7.1.9 which are cool applications problems
7.2.1
Homework 9, due Th. April 27
Hooray! This will be the last homework to be posted, and it will be almost summer, and the weather will be warm and sunny, or at least lest snowy. The birds will be back. And the bees. And shorts. And mosquetoes. And barbeques.
7.3.1, 7.3.2
7.4.2 (Hint: Look at example 7.4.1. It will help!)
8.1.1, 8.1.3
That's all folks!