Fields, Forces and Flows in Biological Systems, Spring 2007

Abstract:: This course introduces the basic driving forces for electric current, fluid flow, and mass transport, plus their application to a variety of biological systems. Basic mathematical and engineering tools will be introduced, in the context of biology and physiology. Various electrokinetic phenomena are also considered as an example of coupled nature of chemical-electro-mechanical driving forces. Applications include transport in biological tissues and across membranes, manipulation of cells and biomolecules, and microfluidics.

Principles of Applied Mathematics, Spring 2006

Abstract:: Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.

Abstract:: Principles of mass transport and electrical signal generation for biological membranes, cells, and tissues. Mass transport through membranes: diffusion, osmosis, chemically mediated, and active transport. Electric properties of cells: ion transport; equilibrium, resting, and action potentials. Kinetic and molecular properties of single voltage-gated ion channels. Laboratory and computer exercises illustrate the concepts. For juniors and seniors. Students engage in extensive written and oral communication exercises.