There will be two 50 minute exams and a two hour final exam. The first exam covers Chapter 7. The second exam covers Chapter 9. Each counts for 25% of your grade. The final covers Chapters 7 & 9. It counts for 30% of your grade. Homework will count for 10% of your grade. A project will count for the remaining 10%.
Here are Homework Assignments.
Here are Project Details.
Here are Practice Tests.
Vector Fields Using Matlab
Download Matlab from SIU (optional, free)
Vector Fields Using GeoGebra
Maple Online (free)
Intro to Maple (that I wrote)
Maxima, a free CAS
Maxima by Example: Ordinary Differential Equation Tools
Intro to Maxima (that I wrote)
Desmos (free online CAS)
Wolfram Alpha
Intro and Course Overview
Chapter 7
Section 7.1 Converting systems to single equations
Vector Field for Example 1. GeoGerbra. Maple. Matlab.
Vector Field for Example 2. GeoGerbra. Wolfram Alpha.
Section 7.2 Matrices and Linear Algebra
Section 7.3 Eigenspaces
New Improved Version
Eigenvectors with Matlab Online
Eigenvectors with Maple
Eigenvectors with GeoGebra
Section 7.4 and read On The Wronskian.
Section 7.5 Distinct Real Eigenvalues
Example with Geogerbra
Section 7.6 Complex Eigenvalues
Optional Reading:
Finding an Invariant Plane for Complex Eigenvalues Video
Finding a Pair of Invariant Planes for Complex Eigenvalues
Section 7.7 Fundamental Matrix and Diagonalization (missing page added)
Section 7.8 Repeated Eigenvalues
Example with Maple
Finding Generalize Eigenvectors
Section 7.9 Nonhomogeneous Case
Undertermined Ceofficients Example
Chapter 9
Sections 9.1 & 2
Phase portraits with Wolfram Alpha (Click on the Submit button.)
Section 9.3 Linearization
Example 1.
Example 2.
Bifurcation Example (Need to correct this.)
Bifurcation Animation
Section 9.4 Population models
On Problem 12c (17 min video)
Section 9.5 Foxes and Bunnies
Video for graphs in Example 1 (4.5 min)
Intersecting surfaces
Transversality
Section 9.6 Lyapunov's Second Method
Section 9.7 Periodic Solutions
Poincare-Bendixson Example
More Periodic Solutions!
Section 9.8 Chaos!
Video of Lorenz Attractor
Lorenz video I made (18 min)
Chaos Video Series (Optional)
Additional Topics As Time Permits
Index Theory (Based mostly on Michael Henle's book A Combinatorial Introduction to Topology.)
Index Theory, 1
Index Theory, 2
Index Theory, 3
Index Calculations
Plots for Example 5
Index Theory, 4
Index Theory, 5
Index Theory, 6
Supplemental:Example with six hyperbolic sectors
Index Theory, 7 (Surfaces)
Index Theory, 8
Harry Ball Theorem
Student Presentations
Final Exam is Tuesday 12/13, 8:00 - 10:00 am.
Spiral Vector Field Example
Eigenvalue Zero Example
Maple Plot