MATH 213, Basic Mathematical Biology, Spring 2008

TR 10:50-12:05, HZ 117

Steve Cox, DH 2007, x-5192, cox@rice.edu, 1-2:30pm TR.

Required Text: Mathematical Models in Biology by Leah Edelstein-Keshet

Material: Chapters 1 through 8

Prerequisites: MATH 101

Grade: 40% homework, 60% exam

Homework: weekly assignments, 60% modeling/analysis, 40% computational

Exams: 1 take home exam every 5 weeks, No final

Read the instructions for Exam 1 and, when ready, open the exam itself
Read the instructions for Exam 2 and, when ready, open the exam itself
Exam 3 may now be opened.

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
Code: mycub
Code: mycub_fe
Code: cub_err