This course surveys weekly topics in physiology and mathematics for those interested in building intuition surrounding quantifying biological phenomenon. While each week's physiological topic will be different, the mathematical topics will build across weeks, culminating in a final problem set which will bring together the entire quarter's math into a single application in neuroengineering. Weekly problem sets aim to cover the week's physiological concept from both an analytical approach and numerical simulation in Python. Specific emphasis is placed on understanding the approach to using tools and techniques for solving problems and justifying answers.

 

Biological Topic	Mathematical Technique
Epidemiological spread of infectious disease	Linear algebra & Dynamical systems (stability & fixed-point analysis)
Cardiovascular system flow	Passive circuits (2nd order ODEs) LTI systems
Endocrine system: insulin/glucagon feedback	State space control Laplace transforms
Auditory system Middle ear impedance matching	Signal processing & filtering Fourier transforms Impedance & Power transfer
Membrane diffusion Action potentials	Monte Carlo Methods Bootstrapping
Cortical activity of movement	Deminsionality reduction (PCA) Estimation & Classification