MATH 331: Ordinary differential equations
Summer 2007

• The information sheet
• Week 1
• Week 2
• Week 3
• Week 4

• Download the Excel file Euler2.xls   (This file illustrates the Euler method on a simple initial value problem.)

• The Book of Beautiful Matrices consists of two-by-two matrices whose entries and eigenvalues are integers between -9 and 9. I consider only the matrices with the nonnegative top-left entry. In addition, I consider only matrices with the relatively prime entries. To get matrices that are omitted in this way you just multiply one of the given matrices by an integer. You need to adjust the eigenvalues by multiplying them with the same integer. The eigenvectors remain unchanged.
I divided the Book in three volumes: Volume 1 contains matrices with real distinct eigenvalues, Volume 2 contains matrices with non-real eigenvalues (whose real and imaginary part are integers between -9 and 9) and Volume 3 contains matrices with a repeated eigenvalue. The eigenvalues and a corresponding eigenvector (and a root vector for repeated eigenvalues) are given for each matrix. Three volumes in pdf format are here:
• There are 4292 matrices in Volume 1.   Here you can find Volume 1   ordered by eigenvalues.
• There are 1164 matrices in Volume 2.   Here you can find Volume 2   ordered by the complex eigenvalues.
• There are 270 matrices in Volume 3.   Here you can find Volume 3   ordered by repeated eigenvalues.

• Download the Mathematica notebook that I used to create the Book of Beautiful Matrices here.