| Day |
Date |
Lecture |
Topic |
Guest
Lecturer |
Reading |
Homework |
Due Date |
| |
|
|
PART
I: Discrete Math and applications of difference equations |
|
|
|
|
| Tues |
8/25/2009 |
1 |
Introduction to the class;
the Modeling Cycle; Example 1: the 1st-order difference equation
for modeling population dynamics |
|
Chapter
1.1 |
HW #0 (solution) |
8/27/2009 |
| Thurs |
8/27/2009 |
2 |
Example 1, Cont. + PRIMER: Models and
common sense: dimensions, orders-of-magnitude estimation,
significant figures |
|
Ch. 1.2, 1.5 |
HW #1 (solution) |
9/3/2009 |
| Tues |
9/1/2009 |
3 |
Second order difference
equations, the superposition principal. Example 2: plant
reproduction from a seedbank |
|
|
|
|
| Thurs |
9/3/2009 |
4 |
Coupled linear difference
equations; Bifurcations diagrams: Example 3: populations
with juvenile and adult stages |
|
Ch. 1.3,
1.6 |
HW #2 (solution) |
9/10/2009 |
| Tues |
9/8/2009 |
5 |
General 2-D systems of
difference equations; Example 4: Characteristic equations giving complex eigenvalues, and
stability analysis |
|
Ch. 1.4,
1.8 |
|
|
| Thurs |
9/10/2009 |
6 |
Parameterizing models with data: maximum likelihood estimation |
|
(not in book) |
Project #1 (solution) |
9/24/2009 |
| Tues |
9/15/2009 |
7 |
Non-linear difference equations: the discrete logistic equation; Cobweb diagrams (free downloadable software for cobwebbing: E&F Chaos) |
|
Ch. 2.1, 2.3, 2.5 |
|
|
| Thurs |
9/17/2009 |
8 |
Linearization of non-linear diff. equations: the fundamental theorem of stability |
|
Ch. 2.2 |
|
|
| Tues |
9/22/2009 |
9 |
Systems of non-linear
difference equations |
|
Ch. 2.7,
2.8 |
|
|
| Thurs |
9/24/2009 |
10 |
Application: Host-parasite system, Nicolson-Baily model |
|
Ch. 3.2,
3.3, 3.4 |
Review for exam 1 |
|
| Tues |
9/29/2009 |
11 |
PART
II: Continuous math models & differential equations
Differences between discrete & continuous math: 3 DEQ's everyone should know |
|
Ch. 4.1 - 4.6 |
|
|
| Thurs |
10/1/2009 |
|
MIDTERM 1 (lectures 1-10, and homeworks 1-2; Project 1) |
|
|
HW #3 (solution) |
10/8/2008 |
| Tues |
10/6/2009 |
12 |
Phase-plane qualitative analysis: Lotka-Volterra model of pop. Dynamics |
|
Ch 5.1 - 5.5, Ch. 6.1 - 6.2 |
|
|
| Thurs |
10/8/2009 |
13 |
Linearization & stability analysis with continuous math |
|
as above |
HW #4 (solution) |
10/15/2009 |
| Tues |
10/13/2009 |
14 |
Matrix approach to stability analysis: variations on Lotka-Volterra |
|
Ch. 4.7-4.9; 5.6-5.8 |
|
|
| Thurs |
10/15/2009 |
15 |
L-V competition/mutualism summary; linking ecology to biogeochemistry (background for project
2) |
|
as above |
Project #2
(Solution)
|
10/29/2009 |
| Tues |
10/20/2009 |
16 |
Models with more than two state variables; qualitative
stability analysis: Routh-Hurwitz criteria |
|
Ch. 6.4 - 6.5 |
|
|
| Thurs |
10/2/2009 |
17 |
Application: Does biological complexity influence
stability? (for those interested, see Robert May's classic 1972 paper, "Will a large complex system be stable?" |
|
as above |
|
|
| Tues |
10/27/2009 |
18 |
Epidemiological models of Infectious disease: SIR models |
|
Ch. 6.6 |
|
|
| Thurs |
10/29/2009 |
19 |
Epidemiology, continued: unintended
outcomes; review for Exam 2 |
|
Ch. 6.7 |
Review for
exam 2
HW 4.5 pre-exam
(solution) |
|
| Tues |
11/3/2009 |
20 |
Oscillations and Limit cycles; Poincare-Bendixson theorem |
|
Ch. 8 (intro); 8.3-8.4 |
|
|
Thurs |
11/5/2009 |
|
MIDTERM 2 (Lectures 11-19; homeworks 3-4; Project 2) |
|
|
|
Tues |
11/10/2009 |
21 |
Application: neuron impulse conduction (Fitzhugh model) |
|
8.5 - 8.8 |
HW #5 (solution) |
11/17/2009 |
Thurs |
11/12/2009 |
22 |
Oscillations and Limit cycles: the Hopf bifurcation; chaos in continuous models |
Cushing |
as above |
|
11/19/2009 |
| |
|
|
PART
III: Miscellaneous: Genetics, Evolution, and Allometry |
|
|
|
|
Tues |
11/17/2009 |
23 |
Population Genetics: Hardy-Weinberg equilibria (pdf posted: Cushing page) |
Cushing |
Ch. 3.6 |
|
|
Thurs |
11/19/2009 |
24 |
Natural selection in structured populations: evolution of cooperation 1 |
Michod |
Michod, 1999, Darwinian Dynamics, Ch1. |
Project #3- AProject #3 - B (solution)
|
12/3/2009 |
Tue |
11/24/2009 |
25 |
Natural selection in structured populations: evolution of cooperation 2 |
Michod |
Ch 4 from above |
|
|
Thurs |
11/26/2009 |
|
THANKSGIVING |
|
|
|
|
| Tues |
12/1/2009 |
26 |
Allometric scaling theory |
|
|
|
|
| Thurs |
12/3/2009 |
27 |
Allometric scaling theory, 2 |
|
|
|
|
| Tues |
12/8/2009 |
28 |
Last Day:
Course review and final exam discussion |
|
|
|
|
