syllabus. Here are the math department policies and the university policies that are technically part of the syllabus.
Instructor information, including contact information. My office hours are MWF 10:30-12:30 in AMB 110. Here is my weekly schedule. You can always send me e-mail, drop in, or make an appointment if these times aren't convenient.
This is a great webcast introducing you to Mathematica. I suggest you look at it even if you know about Mathematica.
Here are some graphical resources for differential equations:
Slope Field and Vector Field applet by Darryl Nester of Bluffton University.
Hint: For 2D phase portraits, use "System", open "Numerical..." and uncheck "lock t=0 on the left".
Vector Field applet written by Ariel Barton of the University of Arkansas.
Numerical solutions of nonlinear ODEs
Mathematica notebook DrivenDampedPendulum.nb. This produced the following animations with c = 1/2 and omega/omega_0 = 2/3 with increasing rho:
Symmetric Period 1 rho = 0.9
Asymmetric Period 1 rho = 1.06
Period 2 rho = 1.078
See some of the animations produced by my MAT 667 class (near the bottom of the page).
Section 1.8: What are the JCFs of these two matrices with eigenvalues 5?
Here is my Jordan Canonical Form algorithm.
Here are some scanned
Examples From Perko.
The general solution for a 4x4 matrix with repeated complex conjugate eigenvalues.
Section 1.7 and beyond: You can use mathematica (or matlab) to do matrix operations. Here is the notebook I made in class, matrixOperationsClass.nb, finding the S+N decomposition of a matrix.
Section 1.6: General solution and phase portrait for an example where A has complex eigenvalues. Here is a worked example, finishing the example I started in class with eignvalues -1 +/- 2i. Here's another example, with the phase portraits drawn by computer.
Section 1.3:
Here is a proof of Corollary 4 that is different from the book.
Here's a notebook of what I asked you to do on problem 1.3 1b: prob1.3-1b.nb. Nobody did it!
Maybe I was too polite, calling it a hint and saying "I'd like you to find the function...".
Section 1.1: Here are some examples of three-dimensional phase portraits of uncoupled linear systems in R3. I notice that the homework on section 1.1 doesn't need this type of phase portraits. I will write extra problems with this. Nothing yet
