AMATH 503
http://www.amath.washington.edu/courses/503-autumn-2003/
SLN 8531, TTh 9:00-10:20, Loew Hall 101

Mathematical Biology


Instructor:

 Professor Hong Qian
Guggenheim 408K
tel: 543-2584
fax: 685-1440
qian@amath.washington.edu
office hours: M, Th: 3:30-4:30PM

Homework Grades Message Board 2002 Web Page
Course description Textbook Syllabus Objectives Schedule

Course Description

Formulating mathematical models for biomedical problems is an increasingly important aspect of quantitative biological and medical sciences. This course focuses on various models for biomedical processes based on differential equations. The biological area ranges over molecular and cell biology, physiology and neural science, population genetics, ecology, and epidemiology. Topics might be covered include Mendelian dynamics, Michaelis-Menton theory for enzyme kinetics, Hodgkin-Huxley model for cellular electrical activity, neural network, continuous and discrete population interactions, biological oscillators, the dynamics of infectious diseases, and diffusion driven pattern formation.

Textbook

Murray, J.D. Mathematical Biology I: An Introduction (3rd Ed.) Springer-Verlag, New York, (2002). Available at the University Bookstore and also on reserve at Mathematic Research Library.

Reference Books

Edelstein-Keshet, L.N. Mathematical Models in Biology. Random House, New York, 1988. [QH323.5 .E34 1988]

Gillespie, J.H. Population Genetics: A Concise Guide. The Johns Hopkins Univ. Press, Baltimore, MD, 1998. [QH455 .G565 1998]

Hertz, J., Krogh, A., and Palmer, R.G. Introduction to the Theory of Neural Computation. Addision-Eesley Publish Co., Redwood, CA, 1991. [QA76.5 .H475 1991]

Hoppensteadt, F.C. An Introduction to the Mathematics of Neurons. 2nd Edition, Cambridge University Press, London, 1997. [QP363.3 .H67 1997]

Keener, J. and Sneyd, J. Mathematical Physiology. Springer-Verlag, New York, 1998. [QT 35 K26m 1998]

Murray, J.D. Mathematical Biology II: Spatial Models. 3rd Edition, Springer, New York 2002. [QH323.5 .M88 2002 v.2]

Segel, I.H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. John Wiley & Sons, New York, 1975. [QU 135 S454e 1975]

Syllabus

(1) Review of Ordinary Differential Equations: Mechanics, population dynamics, chemical kinetics, theory of rate equation.

(2) Continuous Population Dynamics: Single species, bifurcation, and stability (Ch.1).

(3) Continuous Interacting Population Models. (Ch.3)

(4) Mendelian Population Dynamics: Allel frequency and relation to simple population dynamics

(4.1) Additional Reading.

(5) Delay Models.(Ch.1)

(6) Discrete Population Models: Logistic model, bifurcation to chaos (Ch.2).

(7) Discrete Population Genetic Models:

(8) Marital Interaction and Dynamics. (Ch.5)

(9) Application of Reaction Kinetics. Protein polymerization reaction (See Lecture Notes).

(10) Enzyme Kinetics: Michaelis-Menten Theory, rapid pre-equilibrium and pseudo-steady state (Ch.6).

(11) Michaelis-Menten Theory: Detailed Mathematical Analysis and Singular Perturbation.

(12) Simple Oscillatory Reactions. (Ch.6)

(13) Hodgkin-Huxley Theory and Neural Networks.

(13.1) On Stochastic Resonance

(14) Discrete, Continuous, and Delay Neural Networks.

(15) Belousov-Zhabotinskii Reaction. (Ch. 7)

(15.1) Additional Reading.

(16) Coupled Oscillators. (Ch. 8)

(17) ODEs and Boundary Value Problems. Poisson-Boltzmann equation, elastic bending of DNA.

Learning Objectives and Instructor Expectations

Although the subject matter of Mathematical Biology can be made rather difficult, I will attempt to present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will not be presented. Applications will be emphasized.

I will let you know clearly what you need to learn and what can be skipped. Homeworks are used to reinforce class lectures, but not as a way to introduce material not covered in class. Exams will emphasize basic techniques as applied to simple, fundamental problems. There will be no deliberately obscure questions in exams to test your mental dexterity.

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Homework and Exams Homework Due Date Homework Problem Sets Homework Solutions
First day of classes Monday, Sept. 29
Homework#1 due Tuesday, Oct. 14 Homework #1 (.ps, .pdf, reading)
Homework#2 due Thursday, Oct. 23 Homework #2 (.ps, .pdf)
Homework#3 due Tuesday, Nov. 4 Homework #3 (.ps, .pdf)
Homework#4 due Thursday, Nov. 13 Homework #4 (.ps, .pdf)
Veteran's Day Tuesday, November 11 No class
Homework#5 due Thuesday, Nov. 20 Homework #5 (.ps, .pdf)
Homework#6 due Tuesday, Dec. 2 Homework #6 (.ps, .pdf)
Thanksgiving Day Thursday, November 27 No class
Thanksgiving Friday, November 28 No class
Homework#7 Last Homework! due Tuesday, Dec 9 Homework #7 (.ps, .pdf)
Last day of classes Thursday, December 11

Grading

You may view your homework and exam grades on-line. Before doing so for the first time, you must request a password. Please note this change to our system: Your student ID number should be entered including any leading zeros (e.g. 0012345).

Tutorials

No on-line tutorials have been assigned for AMATH 503.

<qian@amath.washington.edu> Mon Sep 22 14:56:07 PDT 2003