M.Garbey

Spring 2004.

List of Topics:

• Solving a linear system of equations: direct and iterative method
• Interpolation theory: piece wise polynomial approximation
• Numerical quadrature:
• Least square approximation: growth rate of population bacteria
• Fourier Analysis: (medical) image filtering
• Singular Value Decomposition: image compression
• ODEs and time series: population model
• Solving a non linear set of equations: equilibrium of population model
• Two points boundary value problems: avascular tumor
• Reaction-Diffusion equation: growth of bacteria on plates
• Reaction-Convection-Diffusion equation: chemotaxis
• Variational Formulation: extraction of image contour.
• Cellular automata: game of life
• Random walk and diffusion: epidemic spread
• Brownian motion: microscope image
• Stochastic ODEs: growth of aquatic plants in river
• Game theory: animal strategy.

Complex applications:

• Blood flow circulation.
• Gas Exchange in the lungs etc….

References:

For the life sciences:
Mathematics in Medicine and the Life Sciences, F.C.Hoppensteadt and C.S. Peskin, Springer Verlag, TAM 10,
Essential Mathematical Biology, N.F.Britton, Springer Undergraduate Mathematics series, ISBN 1-85233-536-X
Mathematical Biology, J.D.Murray, Springer Verlag

For the numeric:

Numerical Recipies: http://www.nr.com/
Numerical Methods and Software, D.Kahaner, C.Moler and S.Nash, Prentice hall Series in Computational Mathematics.
Introduction to Scientific Computing, C.F.Van Loan, Matlab Curriculum Series.