Math 218 Course Outline
Fall 2009






Week Starts Section(s) Topic
1
Tue, Sep 1 Keshet: Section 1.1-1.3, 1.5 Comments about modeling phenomena and the scientific method.
Discrete linear, deterministic models.
Application: Propagation of Annual Plants.
2
Tue, Sep 8 Keshet: Section 1.4, 1.6-1.10 and Problem 20 in Chapter 1. Basics of eigenvalues and eigenvectors.
Application: Leslie Matrices and Demographics of populations.
3
Tue, Sep 15 Keshet: Section 3.6 and Problems 18, 19, 20 in Chapter 3. Example of a nonlinear, discrete model: Population Genetics and the Hardy-Weinberg Law.
4
Tue, Sep 22 Keshet: Section 6.1. Continuous linear, deterministic models.
Population models: Exponential growth and Logistic growth.
Allee Effect.
Gompertz Growth in Tumors.
5
Tue, Sep 29 Keshet: Section 6.2, 6.3. Autonomous systems, steady states and stability analysis.
Predator-Prey systems and the Lotka-Volterra equations.
Competitive populations and the principle of competitive exclusion (and the resultant adaptations).
FALL BREAK: Monday, Oct 5
6
Tue, Oct 6 Keshet: Section 6.6. Compartmental Models in Epidemiology (Infectious Diseases).
The SIR-model of Kermack-McKendrick.
7
Tue, Oct 13 Keshet: Section 6.7. The SIR(S)-model with vital dynamics.
Herd Immunity and intrinsic reproduction numbers.
MIDTERM EXAM:
Wed, Oct 21, 7:30-10:30 PM in Hylan 1101 and 1104.
(Covers Material covered in HW1-4.)
(No calculator but a 8 x 11 inch sheet of notes (both sides) is OK.)
8
Tue, Oct 20 Olinick Chapter 9 I and II, A-D. Basics of Probability.
Conditional Probability, Bayes Theorem, Independence of Events.
9
Tue, Oct 27 Olinick Chapter 9 II, E-F and III. Random variables, expected values and variance.
Probabilistic model: Pure Birth Process.
10
Tue, Nov 3 Olinick Chapter 9 IV. Stochastic Processes.
11
Tue, Nov 10 Olinick Chapter 10 I and II. Markov chains.
12
Tue, Nov 17 Olinick Chapter 10 III and IV. Regular and Absorbing Markov chains.
THANKSGIVING BREAK: Nov 25 (Starts at Noon) - Nov 29
13
Tue, Nov 24 Olinick Chapter 10. Applications of Markov chains to Biology.
14
Tue, Dec 1 Olinick Chapter 13. A stochastic model of simple epidemics.
Comparison of the expected value of the stochastic model with predictions from the analogous deterministic model.
15
Tue, Dec 8 Selected topics. Selected topics.
FINAL EXAM:
TBA in Hutchison 138.
(Covers TBA.)
(No calculator.)


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