Goal: To learn the physical laws and mathematical and
computational methods necessary to build, test and analyze models of
fundamental biological
phenomena.
Jan. 8 Sections 1.1 and 1.2, 1st and 2nd order difference equations.
Jan. 10 Sections 1.3 and 1.4, Linear systems of difference equations.
A geometric look at eigenvalues via eigshow.
Jan. 15 Sections 1.3 and 1.4, computation of eigenvalues and
eigenvectors by hand at via eig.
Jan. 17 Section 1.8, complex eigenvalues.
Assignment 1: Due Tuesday Jan. 22,
Chapter 1, exercises 1,2,4,6,7,11,18.
For number 2 sketch with MATLAB. For example, for part (a), try
commands
n = 1:10;
x = power(2,n)+power(3,n);
semilogy(n,x,'*-')
then use xlabel, ylabel and title. You might wish to put all
6 solutions on one plot. You could then use legend to distinguish them.
For number 7 confirm your hand calculations in MATLAB via commands like
[V,D]=eig(A). Submit a MATLAB diary.
Jan. 22 Sections 2.1 and 2.2
on 1st order nonlinear difference equations.
Section 2.5: Graphical methods. cob-webber.
Jan. 24 Finish cob-webing. Sections 2.7-8
on 2nd order nonlinear difference equations.
Assignment 2: Due Thursday Jan. 31,
Chapter 2, exercises 1,2,3,4,11,17. Use MATLAB on problem 4(d).
Jan. 29 Stability of 2nd order nonlinear difference equations.
Chapter 3. Nicholson-Bailey system with modifications.
Graphical Phase-Plane methods.
Feb. 5 Chapter 3.
Graphical Phase-Plane methods.
Population Genetics.
Feb. 7 Chapter 3.
Exam Review.
Feb. 12 Chapter 3.
Graphical Phase-Plane methods.
Population Genetics.
Feb. 14 Chapter 4.
Section 1.
Feb. 19 Chapter 4. Chemostat.
Feb. 21 NO CLASS.
Assignment 3: Due Thursday Feb 28.,
Chapter 4, exercises 1,2,3,4,7,8,14,17,18.
Feb. 26 Chapters 4.
Chemostat.
Feb. 28 Chapter 4.
Chemostat.
March 4 Spring Break
Section 1.
March 6 Spring Break
Sections 2-10.
March 11 Chapter 4.
Chemostat.
March 13 Chapter 6.
Section 6.2. Predator Prey.
Assignment 4: Due Tuesday March 25.,
Chapter 4, exercises 21 and 22; Chapter 5, exercises 5, 6, 12, 23;
Chapter 6; 9, 13, 17.
March 18 Chapter 6.
Section 6.3. Populations in Competition.
March 20 Chapter 7.
Section 7.1 Michaelis-Menten Kinetics.
March 25 Chapter 7.
Section 7.2-3. The Quasi-Steady-State Assumption and Cooperative Reactions
March 27 Chapter 7.
Section 7.4-7. The Biomolecular Switch.
Synthetic Biology
Notes on Numerical Methods
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