MATH 4FT3/6FT3, Fall 2018
TOPICS IN DIFFERENTIAL EQUATIONS
Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many of the laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. The course Math 4FT3 addresses the principal partial differential equations that arise in physical contexts; the course material will present methods (both specific and abstract) for solving them. In the course of this analysis we will deduce many of the main features of their solutions, including finite propagation speed and conservation of energy for wave equations, maximum principles for heat flow, shock formation for nonlinear conservation laws, and other mathematical aspects of familiar and less familiar laws of physics. No knowledge of physics is assumed.
INSTRUCTOR: W. Craig
Topics to be selected from the theory of ordinary differential equations, bifurcation and stability, and partial differential equations.
Three lectures; one term
Prerequisite(s): Permission of the instructor
MATH 4FT3 may be repeated, if on a different topic.