Lecture Notes
Tip: for the videos, you can change the playback speed… and little is lost by speeding them up to 1.4x speed.
- Lecture 13: Two Dimensional Models: SIR model for closed population. Nullcline/phase plane analysis. Basic reproductive number as a threshold for an outbreak. Vaccination. Outbreak size (not on tests). Brief mention of SIR model with births/deaths.
- Lectures 12 and 13: Two Dimensional Models and Lotka-Volterra Predator-Prey Model. Two dimensional models: velocity vectors and phase plane. PPLANE. Lotka-Volterra Predator-Prey model. Nullclines. More realistic predator-prey model.
- Lecture 10: Two Dimensional Models and Linear First Order Differential Equations. Two dimensional models: velocity vectors and phase plane. Pro drug model. Linear first order differential equations.
- Lecture 9: Bifurcations. Harvesting models (more realistic and even more realistic). Bistability, tipping points and hysteresis.
- Lecture 8: Bifurcations. Transcritical (SIS epidemic model) and Saddle-Node (simplest harvesting model).
- Lecture 7: Sketching Solutions of Differential Equations
For those of you who took MA 231, this should be revision of material you saw there.- 8.4.2 Preparing for Sketching Solutions
- 8.4.3 Method for Sketching Solutions Notes One page guide
- 8.4.4 Continuation of First Example Notes
- 8.5.1 Second Example of Sketching, part 1 Notes
- 8.5.2 Second Example of Sketching, part 2 (uses same notes as previous video)
- 8.5.3 Third Example of Sketching Notes
- 8.5.4 Concavities on Solution Curves (no notes)
- Lecture 6: Euler’s Method and Qualitative Theory (Sketching Solutions)
- 8.4.1 Intro to Qualitative Theory Notes One page version of notes
- Note: the following videos were made by another faculty member… they might not do things exactly the same way that I did them.
- Lecture 5: Slope Fields
- Lecture 3: Population Models
- Lecture 2: Separation of Variables Videos here go through the method in more detail and some of them provide additional examples.
- Separation of variables handout
- Notes on setting up Newton’s Law of Cooling model
- Video on Separable Differential Equations. Notes
- Video: Method of Separation of Variables. Notes
- Another example of separation of variables. Notes
- Video: Solving exponential growth model. Notes
- Solving the logistic growth model:
- Video: Warm up for solving logistic growth… Partial Fractions. Notes
- Video: Solving the logistic growth model. (Long video!) Notes
- Finishing the solution: use initial condition. Notes
- Lecture 1