The references in parentheses are to these books , using notations from that list.

Lecture 1 (08/25): introduction (what is mathematical biology); discrete vs. continuous models; SIR model (dV 1.2)

Lecture 2 (08/27): Matlab training, working on homework 1.

Lecture 3 (09/01): Solving general linear homogeneous difference equations (case of distinct real eigenvalues) (EK 1.1,1.3,1.6)

Lecture 4 (09/03): Applications: red blood cells, aphid population, segmental organism (EK 1.9, exercises of chapter 1)

Lecture 5 (09/08): Non-linear first order difference equations, fixed points and stability (analytically and graphically with cobwebbing) (EK 2.1,2.2, 2.5; dV 2.2.2)

Lecture 6 (09/10): Logistic difference equation: building it from data, fixed points and stability (dV 2.2.1, 2.2.2)

Lecture 7 (09/15): Logistic difference equation: bifurcation diagram, periodic solutions, period doubling and chaos (EK 2.4, 2.5; dV 2.2.2-2.2.4)

Lecture 8 (09/17): Systems of non-linear equations. Linearization, fixed points and stability. Review of linear algebra: eigenvalues and eigenvectors of matrices (EK 2.7-2.9,1.4; dV 2.3.2)

Lecture 9 (09/22): Nicholson-Bailey model, Poisson process. (EK 3.2, 3.3; dV 2.3.4)

Lecture 10 (09/24): Application to population genetics. Hardy-Weinberg law (EK 3.6, dV 2.2.5)

End of Midterm 1 material Lecture 11,12 (09/29, 10/01): One-dimensional non-linear continuous systems (EK 5.1, dV 3.1,3.2, extra: St ch2)) Introduction to phase plane analysis, nullclines (EK 5.2-5.5, extra: St ch6))

Lecture 13, 14 (10/20,22) Classification of fixed points in 2-dimensional systems (dV 3.4.1, 3.4.2, EK 5.6-5.9). Examples of SIR model and two-population ineractions model (dV 3.3.2, 3.3.3, 3.4.3, 3.4.4; Ek 6.2, 6.3, 6.6). Discrete models from continuous models (dV 3.6.1)

Lecture 15, 16 (10/27, 29) Bifurcations (dV 3.7, St ch.3, 8.2)

Lecture 17 (11/03) Applications. Cell cycle. Regulation of G1-checkpoint. Based on 13.2.1 of Keener and Sneyd " Mathematical Physiology" chapter .

Lecture 18 (11/05) Michaelis-Menten kinetics (EK 7.1, 7.2; extra: St ch7)

Lecture 19 (11/10) Fitzhugh-Nagumo model. Relaxation oscillators. Fast-slow systems (EK 8.3 - 8.5)

End of Midterm 2 material Lecture 20 (11/12) Examples from neuroscience. Lecture material and section 5 of a book chapter from: Methods and Models in Neurophysics, Les Houches Summer School, Session LXXX, C. Chow, B. Gutkin, D. Hansel and C. Meunier (eds). Elsevier, 2004