Physics 548—Mathematical Methods in Biology
Instructors:
James A. Glazier
Swain West 159
Tel. 855-3735
e-mail: glazier@indiana.edu
Santiago Schnell
Eigenmann Hall 906
Tel. 856-1833
e-mail: schnell@indiana.edu
Classes: Tu. Thu. 8:00AM-10:00AM Swain West 219
Office Hours: By appointment.
Texts:
1) Britton, Essential Mathematical Biology [Main Text].
2) Murray, Mathematical Biology volume 1 [More detailed than Britton and more
mathematical in approach, useful as a reference and source of ideas and proofs].
3) Fall, Marland, Wagner and Tyson, Computational Cell Biology [An excellent
book in range of coverage and level of detail. Unfortunately it is out of stock in
the bookstore here till February—you can buy it on-line now if you want it].
Supplemental Reading/Reference Suggestions:
1) Keener and Sneyd, Mathematical Physiology [An excellent and comprehensive
reference with a rather different focus from the texts we are using].
2) Murray, Mathematical Biology volume 2.
3) Rubinow, Introduction to Mathematical Biology [An older text, very clear and
simple explanations. Covers Population Dynamics, Reaction Kinetics, Diffusion
and Hydrodynamics].
4) Perceval and Richards, Introduction to Dynamics [A good, simple introduction to
mathematical methods, with exercises].
5) Guckenheimer and Holmes, Nonlinear Oscillations, Dynamical Systems and
Bifurcations of Vector Fields [A more technical treatment of mathematical
methods].
6) Strogatz, Nonlinear Dynamical Systems and Chaos with Applications to Physics,
Biology, Chemistry, and Engineering.
7) Allen, An Introduction to Stochastic Processes with Applications to Biology.
8) Renshaw, Modeling Biological Populations in Space and Time.
Requirements:
1) Homeworks every other week (40% of Grade)
2) Written Project (40% of Grade)
3) Oral Presentation (20% of Grade)
There will be no final exam in this course. Late assignments will be marked down.
Tentative Syllabus:
1/11/05 Introduction, Course Structure.
1/13/05 Non-credit Quiz, Introduction Concluded, Introduction to Population Dynamics,
Iterated Maps, Cobweb Diagrams.
1/18/05 Population Dynamics of Single Species, Continuum Models, Verhulst Model,
Fisheries (First homework assigned)
1/20/05 Population Dynamics of Single Species, Bifurcations, Chaos
1/25/05 Population Dynamics of Two Species, Lotke-Volterra Model
1/27/05 Population Dynamics of Two Species, Improved Predator-Prey Models,
Competitive Exclusion, Ecology
2/1/05 Infectious Diseases, Epidemics (First homework due, second homework assigned)
2/3/05 Infectious Diseases, Complications
2/8/05 Population Genetics and Evolution, Mendelian Evolution
2/10/05 Population Genetics and Evolution, Selection and Mutation
2/15/05 Population Genetics and Evolution, Game Theory (Second homework due, third
homework assigned)
2/17/05 Biological Motion, Advection and Diffusion (Schnell)
2/22/05 Biological Motion, Chemotaxis, Muskrat Model
2/24/05 Biological Motion, Traveling Wave Solutions
3/1/05 Network Structure and Properties, Fractals (Third homework due, fourth
homework assigned)
3/3/05 Network Structure and Properties
3/8/05 Reaction Kinetics, Michaelis-Menten Kinetics
3/10/05 Reaction Kinetics, Activation and Inhibition
3/22/05 Reaction Kinetics Cooperativity (Project titles and abstracts due. Fourth
homework due, fifth homework assigned)
3/24/05 Pattern Formation, Turing Patterns (Schnell)
3/29/05 Pattern Formation, Chemotactic Patterning
3/31/05 Excitable Media and Traveling Waves
4/5/05 Tumor Modeling (Fifth homework due, sixth homework assigned)
4/7/05 Angiogenesis Modeling
4/12/05 Stochastic Differential Equations—Ion Channels (Schnell)
4/14/05 Stochastic Differential Equations—Molecular Motors (Schnell)
4/19/05 Neurons and the Hodgkin-Huxley Equation (Sixth homework due)
4/21/05 Neurons and the Hodgkin-Huxley Equation
4/26/05 (Oral Presentations, Project papers due)
4/28/05 (Oral Presentations)