Course Syllabus for Poolesville ODE

The syllabus of the course consists of Chapters 1-3 and 7-9 in B&DiP as well as all of DEwM except Chapters 10 & 11, and Problem Set E. Specifically, the ODE topics in B&DiP that will be covered include:

First Order Ordinary Differential Equations
- Mathematical Modeling
- Four Methods
  - Symbolic or Algebriac (Linear, Separable, Exact)
  - Graphical/Geometric (Vector Fields)
  - Numerical (Euler, others, NDSolve)
  - Qualitative
- Autonomous Equations
- Stability
- Existence and Uniqueness
Second Order Equations
- General -- Existence and Uniqueness
- Linear
  - Homogeneous
    - Exponential Substitution
    - Roots of the Characteristic Polynomial
  - Inhomogeneous
    - Undetermined Coefficients
    - Variation of Parameters
  - Vibrations
Linear Systems
- Review of Linear Algebra
- Existence and Uniqueness
- Constant Coefficient Homogeneous Equations
  - Eigenvalues and Eigenvectors
  - Phase Plane
Non-Linear Systems
- Phase Plane Revisited
  - Vector Fields
  - Numerically Generated Phase Portraits
- Autonomous Systems and Stability
- Locally Linear Systems
- Population Models
  - Competing Species
  - Predator-Prey

The subject matter of DEwM serves as a complement to the material from B&DiP. It introduces a mathematical software component into the study of ODE, which enables a meaningful treatment of geometric and numerical methods. Without the use of a mathematical software system, ODE courses at this level are restricted exclusively to symbolic methods.