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The chapter and section numbers labeled EK are those in Mathematical Models in Biology by L. EdelsteinKeshet. Reading assignments are also given for the online notes by Professor Sontag. Additional material may also be assigned and links are given.
Date  Topics  Text  Assignments  
1  9/2  Dynamical models, introduction Single species population models Logistic model. 
EK, 4.2 and 6.1 Review of elementary ode Sontag, 1.11.5 
Assignments due 9/4 and 9/9 Solutions 
2  9/4  Qualitative analysis of scalar ode; Logistic equation, continued; Spruce budworm 
EK, 4.2 and 6.1 Supplementary notes, qualititative ode analysis 

3  9/9  Spruce budworm model analysis The chemostat model 
EK, 4.34.5 Sontag, 1.61.10 
Spruce budworm project, due 9/18
Solutions 
4  9/11  The chemostat model, scaling, equilibria and stability 
EK, 4.34.10 Sontag, 1.61.10, Chapter 2 
Problems due on 9/18
Solutions 
5  9/16 
Stability of the origin for nonlinear systems; Linearization and stability for equilibria of nonlinear systems 
EK, 4.34.10 Sontag, Chapter 2 Class notes 

6  9/18  Stability of the chemostat Solving linear systems in dimension 2 Notes Drug infusion model 
EK, 4.11 Sontag, 1.61.10, Chapter 2 
Problems due on 9/25 Solutions 
7  9/23  Phase plane analysis: null clines and phase portraits 
EK, Chapter 5 Sontag, Chapter 4 

8  9/25  Phase portraits near equilibria for linear and nonlinear systems 
EK, Chapter 5 Sontag, Chapter 4 
Problems due on 10/2 Solutions, part I Solutions, part II 
9  9/30  Multispecies models  EK, 6.3, 6.4  
10  10/2  Phase plane analysis of a model with competition Lecture 10 Notes  EK, 6.3, 6.4  Problems due on 10/9 Solutions 
11  10/7  Chemical kinetics and quasisteady state approximation  EK, 7.17.2, Sontag, Chapter 6.  
12  10/9  MichaelisMenten kinetics via quasisteady states  EK, 7.2, Sontag, Chapter 6  
13  10/14  First midterm  Open book; open notes.  
14  10/16  Chemical kinetics equations: general approach Quasisteady state analysis of a model with inhibition  EK, 7.4, Sontag, Chapter 6  Problems due on October 23 Solutions 
15  10/21  Quasisteady state approximations, continued; Limit cycles  EK, 8.1, Sontag, Chapter 8  
16  10/23  Limit cycles, PoincareBendixon theorem  EK, 8.3, Sontag, Chapter 8  Problems due on October 30 Solutions Solutions, part II Van der Pol Applet JODE manual 
17  10/28  Applyling PoincareBendixon and the Bendixson negative criterion; The Van der Pol oscillator  EK, 8.4, Sontag Chapter 8  
18  10/30  The Van der Pol oscillator 
EK, 8.4, Sontag Chapter 8 Class Notes 
Problems due on November 6. Solutions 
19  11/4  The Van der Pol oscillator, continued  
20  11/6  Relaxation Oscillations, FitzhughNagumo 
EK, 8.5; Sontag, 8.7 Class Notes on FitzhughNagumo 
Problems due November 13
Problem A;
Solution Problem B Solution to B 
21  11/11  Kolmogorov theory of predator prey 
EK, 8.7 Class Notes on predator prey. 
Problems due November 13
Problem A Problem B 
22  11/13  Introduction to pde modeling 
EK, 9.19.5 
Problems due November 18 Solutions 
23  11/18  Introduction to pde modeling 
EK, 9.19.5 
Problems For Dec. 4 Solutions 
24  11/20  Midterm Exam  
25  11/25  Diffusion equations; boundary conditions, separation of variables 
EK, Appendix to Chapter 9 

26  12/2 
Diffusion equations; steady states transit times, diffusive motion 
EK, 9.5, 9.6 

27  12/4 
Transport equations and traveling wave solutions Equations with attraction/repulsion, chemotaxis 
Sontag, Chapter 9 
Problems For Dec. 9
Solutions 
28  1/29  Review  
29  12/15  FINAL EXAM, DEC. 15; SEC211, 8AM11AM  PDE material on final will be selected from: from EK, sections 9.2, 9.3, 9.4, 9.5 and appendices, (to extent covered in homework problems); stationary solutions; Sontag, 9.49.6, and homework problems/class discussion. 
Please note: New version to solutions to
problem set 11 (was due Dec 4.) with typographical corrections to flux equalities in solution of problem 9, chapter 9. 