Lecture Notes for Systems of Differential Equations
MATH 405
Summer 2024
I'll be adding some examples and videos as time premits.
Week 1
Intro and Course Overview
Video
Section 7.1
Converting Systems To Single Higher Order Equations.
Video
Section 7.2
Matrices and Linear Algebra
Section 7.3
Eigenspaces
Video: Eigenvectors and Eigenvalues with Wolfram Alpha
Video: Eigenvectors and Eigenvalues with GeoGebra
Week 2
Section 7.4
Fundemental Solutions and The Wronskian
Section 7.5
Systems With Real Distinct Eingenvalues
Video: Plots with Wolfram Alpha and GeoGebra
Example with GeoGerbra
Week 3
Section 7.6
Systems With Complex Eigenvalues
Finding an Invariant Plane for Complex Eigenvalues
Video
Finding a Pair of Invariant Planes for Complex Eigenvalues
Section 7.7
Fundamental Matrix and Diagonalization
Section 7.8
Repeated Eigenvalues
Week 4
Section 7.9
Nonhomogeneous Case
Undertermined Ceofficients Example
Test 1 on Chapter 7.
Week 5
Sections 9.1 & 2
Stability and Intro to Nonlinear Systems
Finding Critical Points For #7 With Wolfram Alpha
Vector Field for #7 with Wolfram Alpha
Not very good! Divide by magnitude to get direction field:
Direction Field
A Different Example:
Phase portraits with Wolfram Alpha
(Click on the Submit button.)
Section 9.3
Linearization
Example 1 with more details:
Notes.
Video.
An Example of a Bifurcation:
Notes.
Animation.
Section 9.4
Population Models
Video
Example 1 in Maple
Example 2 in Maple
Section 2.5 notes for review
Week 6
Section 9.5
Foxes and Bunnies
Video for graphs in Example 1
(4.5 min)
Intersecting surfaces image
Transversality
(External Link)
Section 9.6
Lyapunov's Second Method
Video
Section 9.7
Periodic Solutions
Poincare-Bendixson Example
Equation's of Liénard and van der Pol
Week 7
Section 9.8: Lorenz Equations and Chaos
Video.
Video of Lorenz Attractor
Video of Lorenz Attractor
(External. Just for fun.)
Talks on Geometric Lorenz Attractor
Chaos Video Series
(Optional. For general audience.)
Week 8
Test 2 on Chapter 9.
Project Due.
Final Exam.
