Requirements/prerequisites:

Duration: 21 weeks

Number of lectures per week: 3

Assessment: Homework: 20%, Presentation: 30%, Paper: 50%

End-of-year Examination: One 3-hour examination in May/June.

Description:

Fourier Series:

Basic properties, Convergence, Applications

Fourier Transform on \mathbbR:

Basic properties, Applications to heat equations, Heat and Poisson kernels

Fourier Transform on \mathbbR^d:

Basic properties, Applications to wave equations, Radon transform

ODE models in Biology:

Linear stability, Population dynamics, Molecular events, Limit cycles, Oscillations, Excitable systems

PDE and Diffusion in Biology:

Convection, Diffusion, Attraction

PDE models in Biology:

Population model, Steady states, Travelling waves, Transport model, Do-It-Yourself model

Pattern formation in Biology:

Aggregation, Diffusive instability, Morphogenesis

Survey paper & Presentation:

Article survey project (perhaps in collaboration with another student) which arises during the second semester. At the end of the course each team will be expected to give a short presentation on their research and write a survey paper on it. Submission of a survey paper is due on May, 1, 2006, Monday.

Textbooks:

1. Fourier Analysis. An introduction. By Elias M. Stein & Rami Shakarchi. Princeton Lectures in Analysis I.

2. Mathematical models in Biology. By Leah Edelstein-Keshet. SIAM Classics in Applied mathematics.

References:

1. Introduction to Fourier Analysis on Euclidean spaces. By Elias M. Stein & Guido Weiss. Princeton University Press.

2. Mathematical Biology. By James D. Murray. Springer-Verlag.

Oct 11, 2005