| Day |
Date |
Lecture |
Topic |
Guest
Lecturer |
Reading |
Homework |
Due Date |
| |
|
|
PART
I: Discrete Math and applications of difference equations |
|
|
|
|
| Thurs |
1/17/2008 |
1 |
Introduction to the class;
the Modeling Cycle; Example 1: the 1st-order difference equation
for modeling population dynamics |
|
Chapter
1.1 |
HW #1(corrected)
HW1 solutions |
1/24/2008 |
| Tues |
1/22/2008 |
2 |
PRIMER: Models and
common sense: dimensions, orders-of-magnitude estimation,
significant figures |
|
Ch. 1.2, 1.5 |
|
|
| Thurs |
1/24/2008 |
3 |
Second order difference
equations, the superposition principal. Example 2: plant
reproduction from a seedbank |
|
|
HW #2 (solutions) |
1/31/2008 |
| Tues |
1/29/2008 |
4 |
Coupled linear difference
equations; Bifurcations diagrams: Example 3: populations
with juvenile and adult stages |
|
Ch. 1.3,
1.6 |
|
|
| Thurs |
1/31/2008 |
5 |
General 2-D systems of
difference equations; Characteristic equations, eigenvalues and
stability analysis |
|
Ch. 1.4,
1.8 |
HW #3 (solutions) |
2/7/2008 |
| Tues |
2/5/2008 |
6 |
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 |
2/7/2008 |
7 |
Linearization of non-linear
diff. equations: the fundamental theorem of stability |
|
Ch. 2.2 |
Project #1(solutions) |
2/21/2008 (two weeks) |
| Tues |
2/12/2008 |
8 |
Parameterizing models with
data: maximum likelihood estimation |
|
(not in
book) |
|
|
| Thurs |
2/14/2008 |
9 |
Systems of non-linear
difference equations |
|
Ch. 2.7,
2.8 |
|
|
| Tues |
2/19/2008 |
10 |
Application:
Host-Parasite system: the Nicholson-Bailey model |
Cushing |
Ch. 3.2,
3.3, 3.4 |
|
|
| Thurs |
2/21/2008 |
11 |
Application: Population genetics &
Hardy-Weinberg equilibrium |
Cushing |
Ch. 3.6 |
Review for
exam 1 |
|
| Tues |
2/26/2008 |
|
EXAM 1 [SOLUTIONS] |
|
|
|
|
|
|
|
|
|
|
|
|
| |
|
|
PART
II: Continuous math models & differential equations |
|
|
|
|
| Thurs |
2/28/2008 |
12 |
Differences between discrete & continuous math, and
differential equations: 3 simple differential equations everyone
should know |
|
Ch. 4.1 - 4.6 |
HW #4 (solution) |
3/6/2008 |
| Tues |
3/4/2008 |
13 |
Phase-plane qualitative analysis: Lotka-Volterra
model of pop. Dynamics |
|
Ch 5.1 - 5.5, Ch. 6.1 - 6.2 |
|
|
| Thurs |
3/6/2008 |
14 |
Linearization & stability analysis with continuous math |
|
as above |
HW #5 (solution) |
3/13/2008 |
| Tues |
3/11/2008 |
15 |
Matrix approach to stability analysis: variations on
Lotka-Volterra |
|
Ch. 4.7-4.9, Ch. 5.6-5.8 |
|
|
| Thurs |
3/13/2008 |
16 |
Linking ecology to biogeochemistry (background for project
2) |
|
as above |
Project #2 (solution) |
3/27/2008 |
| Tues |
3/18/2008 |
|
SPRING BREAK |
|
|
|
|
| Thurs |
3/20/2008 |
|
SPRING BREAK |
|
|
|
|
| Tues |
3/25/2008 |
17 |
Models with more than two state variables; qualitative
stability analysis: Routh-Hurwitz criteria |
|
Ch. 6.4 - 6.5 |
|
|
| Thurs |
3/27/2008 |
18 |
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 |
HW #6: Ch.6, problems 19,24,30 (solution) |
4/3/2008 |
| Tues |
4/1/2008 |
19 |
Epidemiological models of Infectious disease: SIR models |
|
Ch. 6.6 |
|
|
| Thurs |
4/3/2008 |
20 |
Epidemiology, continued: unintended
outcomes; review for Exam 2 |
|
Ch. 6.7 |
Review for
exam 2 |
|
| Tues |
4/8/2008 |
|
EXAM 2 [SOLUTIONS] |
|
|
|
|
Thurs |
4/10/2008 |
21 |
|
|
Chapter 8 introduction (prior to 8.1), and 8.3-8.4 |
|
|
Tues |
4/15/2008 |
22 |
Application: neuron impulse conduction (Fitzhugh model) |
|
8.5 - 8.8 |
Project #3 (solution)
|
4/29/2008 |
Thurs |
4/17/2008 |
23 |
Oscillations and Limit cycles: the Hopf bifurcation; chaos in continuous models |
|
as above |
|
|
Tues |
4/22/2008 |
24 |
Application: evolution by natural & sexual selection |
|
(not in book) |
|
|
Thurs |
4/24/2008 |
25 |
Allometric scaling theory, part 1 (guest lecture) |
Enquist |
|
|
|
Tues |
4/29/2008 |
26 |
Allometric scaling theory, part 2 (guest lecture) |
Enquist |
|
HW #7; Proj 3 due |
|
Thurs |
5/1/2008 |
27 |
Coalescent theory in population genetics (guest lecture) (note: review genetics lecture by Prof. Cushing: Population Genetics)
|
Machado |
Hudson 1991 (pp 1-13 only)
|
|
|
| Tues |
5/6/2008 |
|
Last Day:
Course review and final exam discussion |
|
|
|
|
