Topics for midterm 1
- Separation of Variables
- Method of Undetermined Coefficients (lucky guess)
- Integration Factors
- Direction Fields
- Equilibria and Classification
- Phaselines
- Bifurcations
- Modeling
- Populations - Exponential and Logistic
- Mixing Problems
- Existence and Uniqueness
- Euler's Method
- Systems of Differential Equations
- Phase Planes
- Nullclines
- Equillibria
- Conversion of 2nd order ODE to 1st order systems
Topics for Midterm 2
- Systems of Differential Equations
- Phase Planes
- Nullclines
- Equillibria
- Conversion of 2nd order ODE to 1st order systems
- Linear Systems
- Eigenvalues and Eigenvectors and their relation to the phase
plane
- Complex, repeated Eigenvalues and all the special cases
- General solutions and solutions to initial value problems
(IVP)
- Trace-determinant plane
- 2 - parameter bifurcation diagrams for systems of linear ODE
- 3-D Linear Systems
Topics for Final
Review topics from previous midterms
1-D
- 2nd order ODE
- Conversion of 2nd order ODE to 1st order systems
- Non-homogeneous 2nd order ODE
- Method of undetermined coefficients
- Damped and un-damped harmonic oscillators
- Forced oscillators and resonance.
2-D
- Non-linear Systems
- Equilibria
- Linearization
- Phase Planes
- Nullclines
- Hamiltonian Systems