Textbook: Mathematical Models in Biology, Leah Edelstein-Keshet (SIAM 2005 edition)
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Week |
Topics |
Read |
Homework |
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#1 (1/11-13) |
Single population models - Exponential (Malthusian) model - Logistic model |
Sections 4.1 and 6.1 |
Due Friday, 1/20 (by |
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#2 (1/16-20) |
Separable equations Intro to Matlab (dsolve, ezplot, dfield) Autonomous equations: qualitative analysis |
Lecture notes Section 5.1 (and review 4.1, 6.1) Handout on population models |
Due Friday, 1/27 (by |
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#3-#4 (1/23-2/3) |
Autonomous equations: qualitative analysis Linear equations - - mixing problems The spruce budworm model: parameter analysis and bifurcations |
Lecture notes on linear equations Sections 5.1, 6.1 Handout and article on the spruce budworm model |
Due Friday, 2/03 (by |
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#5 (2/6-2/10) |
Intro to systems of differential equations Bacterial growth in a chemostat Delivery of drugs by continuous infusion |
Sections 4.2, 4.3, 4.4, 4.5, 4.6, 4.11 |
HW #4: Ch.4 6,
9, 12, 14(a,b,c), 25(a,b) Due Monday, 2/13 (by 1pm) |
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#6 (2/13-2/17) |
Brief intro to matrix algebra; Leslie population model Linear systems of differential equations Eigenvalue-eigenvector method |
Class notes Section 4.8 (pp. 134-140) |
Due Friday, 2/24 (by 1pm) |
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#7 (2/20-2/24) |
Linear systems of differential equations Phase-plane portraits Stability of the steady state |
Class notes Sections 5.7, 5.8 |
Due Friday, 2/24 (by 1pm) |
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#8-#9 (2/28-3/10) |
Qualitative analysis of planar systems Nullclines Linearization and stability of steady states Interacting species: competing models, predator-prey models |
Class notes Sections 5.2, 5.3, 5.4, 5.5, 5.6, 5.9, 6.2, 6.3 |
Due Wednesday, 3/29 (by |
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#10-#12 (3/20-4/05) |
Chemostat analysis Infectious diseases models Models for molecular events |
Class notes Sections 5.10, 6.6, 7.1, 7.2, 7.3, 7.5, 7.6 |
Due Wednesday, 4/19 (by |
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#13-#14 (4/10-4/21) |
Intro to discrete models (difference equations) Linear difference equations (second order); Fibonacci rabbits Linear discrete systems Red blood cell model, Leslie population model Intro to nonlinear discrete models Logistic equation |
Class notes; Overview of linear
equations/systems Sections 1.1, 1.3, 1.4, 1.6, 1.7, 1.8, 1.9 Sections 2.1, 2.2, 2.3, 2.4, 2.5 |
Due Thursday, 4/27 (by |