Developing a systems-level Mathematical approach to the single neuron as a
prototype of complex Biological systems. Two main Mathematical persectives, will
be emphasized: Nonlinear dyanmical systems and random processes in continuous time.
Main topics: Introduction to the biophysics of neurons, axons and dendrites and
their analyais as input-output systems in the engineering sense.
The neuron: basic properties of the membrane and its Chemical and Electrical
properties - electrodiffusion and the resting potential.
The propagation of signals along passive cables and cell to cell communication
through Chemical synapses. The Hodgkin-Huxley model for cell excitbability, and
simplified mathematical models allowing a detailed analysis of excitability.
Stochastic elements in neurons and synapses.