Traditional
(Boyce/diPrima)
| Reform
(Blanchard, Devaney & Glen)
|
First-order DEQs
- Linear DEQs
- Separable DEQs
- Exact DEQs
- Homogeneous DEQs
- Bernoulli DEQs
- Integrating factors
- Slope fields
- Applications (free fall with air resistance, tanks, Newton's law of cooling)
- Existence and Uniqueness
| First-order DEQs
- Linear DEQs
- Separable DEQs
- Slope fields
- Euler's Method
- Bernoulli DEQs, Homogeneous DEQs (project)
- Autonomous DEQs (equilibrium analysis, phase line, bifurcation)
- Modeling (population models, free fall, tanks, Newton's law of cooling)
- Existence and Uniqueness
|
Second-order DEQs
- Linear DEQs with constant coefficients (via characteristic polynomial)
- d'Alembert's Reduction of Order
- Variation of Parameters
- Method of Undetermined Coefficients
- Series solutions
- Applications (harmonic oscillator, forcing)
| Systems of DEQs
- Graphical analysis of (non-linear) autonomous DEQs (phase portraits, time series, Euler's method, nullcline analysis)
- Systems of (2 autonomous) linear DEQs with constant coefficients (via eigenvectors)
- Second-order DEQs as systems of first-order DEQs
- Bifurcation for systems of DEQs
- Applications (Predator-prey, harmonic oscillator)
- Linearization (simple and simple linear pendulum)
- Equilibrium-point analysis
|
Laplace Transforms
- Linear DEQs with forcing
- Discontinuous forcing functions
- Impulse forcing functions
| Laplace Transforms
- Linear DEQs with forcing
- Discontinuous forcing functions
- Impulse forcing functions
|
