Math 322

Spring 2018
Instructor: David Perkinson (schedule)
General info: Course description, office hours, grading, etc.
Text: Differential equations and dynamical systems, by Lawrence Perko.
LaTeX: getting started
Handouts: first recipes.

Collected notes: 4/28/2018.

Final week
☛ Monday ☚
Hamiltonian systems.
Homework due Monday
  • Reading: Section 2.14.
☛ Wednesday ☚
Gradient systems.
Homework due Wednesday
  • Reading: Section 2.14.
☛ Friday ☚
Review.
Homework due Friday
  • Reading: None.
  • Turn in: Here is a final assignment, due by 4 pm, Monday, May 7. H13F (tex file: H13F.tex).

Previous classes

Week 1
☛ Monday ☚
Separable equations. First recipes.
Homework due Monday
  • None.
☛ Wednesday ☚
Logistic equation. Homogeneity trick for separable equations. Exact equations (if time). The wikipedia page for the logistic function is worth reading. (Take a look at the history section, for instance.)
Homework due Wednesday
☛ Friday ☚
Exact equations. Integrating factors.
Homework due Friday
Week 2
☛ Monday ☚
First-order linear. Linear homogeneous constant coefficients.
Homework due Monday
☛ Wednesday ☚
Bernoulli equation motivation. Linear homogeneous constant coefficients: complex roots and repeated roots. Method of undetermined coefficients.
Homework due Wednesday
☛ Friday ☚
Special second-order equations.
Homework due Friday
Week 3
☛ Monday ☚
Matrix exponentiation.
Homework due Monday
  • Reading: Sections 1.1–1.3.
☛ Wednesday ☚
Fundamental theorem for linear systems.
Homework due Wednesday
  • Reading: Section 1.4.
☛ Friday ☚
Fundamental theorem for linear systems. Linear systems in \(\mathbb{R}^2\).
Homework due Friday
Week 4
☛ Monday ☚
Linear systems in \(\mathbb{R}^2\).
Homework due Monday
  • Reading: Section 1.5.
☛ Wednesday ☚
Jordan form.
Homework due Wednesday
  • Reading: Sections 1.6–1.8.
☛ Friday ☚
Exponentiating Jordan matrices. Algorithm for computing Jordan form.
Homework due Friday
Week 5
☛ Monday ☚
Stability theory. Linear systems in \(\mathbb{R}^3\). Nonhomogeneous equations.
Homework due Monday
  • Reading: Sections 1.9 and 1.10.
☛ Wednesday ☚
Nonhomogeneous equations.
Homework due Wednesday
  • Reading: Section 1.10 (and the lecture notes).
☛ Friday ☚
Higher-order homogeneous linear equations with constant coefficients.
Homework due Friday
Week 6
☛ Monday ☚
Higher-order homogeneous linear equations with constant coefficients.
Homework due Monday
  • Reading: last Friday's worksheet and today's lecture notes.
☛ Wednesday ☚
Existence and uniqueness for non-linear systems.
Homework due Wednesday
  • Reading: Sections 2.1 and 2.2.
☛ Friday ☚
Existence and uniqueness for non-linear systems.
Homework due Friday
  • Reading: Sections 2.1 and 2.2 (and the lecture notes).
  • Turn in: H06F (tex file: H06F.tex, solutions: H06Fsol).
Week 7
☛ Monday ☚
Existence and uniqueness for non-linear systems.
Homework due Monday
  • Reading: Sections 2.1 and 2.2 (and the lecture notes).
☛ Wednesday ☚
Existence and uniqueness for non-linear systems.
Homework due Wednesday
  • Reading: Sections 2.1 and 2.2 (and the lecture notes).
☛ Friday ☚
Linearization.
Solutions.
Homework due Friday
Week 8
☛ Monday ☚
Dependence on parameters, maximal interval. Begin stable manifold theorem.
Homework due Monday
  • Reading: Sections 2.3–7.
☛ Wednesday ☚
Stable manifold theorem.
Homework due Wednesday
  • Reading: Section 2.6–7.
☛ Friday ☚
Stable manifold theorem. Solutions.
Homework due Friday
Week 9
☛ Monday ☚
Global stable and unstable manifolds. The Hartman-Grobman theorem.
Homework due Monday
  • Reading: Sections 2.7 and 2.8.
☛ Wednesday ☚
Stability and Liapunov functions.
Homework due Wednesday
  • Reading: Section 2.9.
☛ Friday ☚
Liapunov functions.
Homework due Friday
Week 10
☛ Monday ☚
Planar systems.
Homework due Monday
  • Reading: Sections 2.10 and 2.11.
☛ Wednesday ☚
Global theory for nonlinear systems: index theory.
Homework due Wednesday
  • Reading: Section 3.12.
☛ Friday ☚
Global theory for nonlinear systems: index theory.
Homework due Friday
Week 11
☛ Monday ☚
Global theory for nonlinear systems: index theory.
Homework due Monday
  • Reading: Section 3.12.
☛ Wednesday ☚
Global theory for nonlinear systems: index theory.
Homework due Wednesday
  • Reading: Section 3.12.
☛ Friday ☚
Critical points at infinity, and global phase portraits.
Homework due Friday
Week 12
☛ Monday ☚
Critical points at infinity, and global phase portraits.
Homework due Monday
  • Reading: Section 3.10.
☛ Wednesday ☚
Critical points at infinity, and global phase portraits.
Homework due Wednesday
  • Reading: Lecture notes.
☛ Friday ☚
Resolution of singularities.
Homework due Friday
Week 13
☛ Monday ☚
Hamiltonian systems.
Homework due Monday
  • Reading: Section 2.14.
☛ Wednesday ☚
Gradient systems.
Homework due Wednesday
  • Reading: Section 2.14.
☛ Friday ☚
Review.
Homework due Friday
  • Reading: None.
  • Turn in: Here is a final assignment, due by 4 pm, Monday, May 7. H13F (tex file: H13F.tex).