Fall Quarter I am teaching Math 244, Linear Analysis I,and Math 4i6, Differential Equations II.

Math 244 is a first course in differential equations and linear algebra for students in engineering and science. The emphasis is on linear systems. After discussing first order separable and linear differential equations, a system of two first order differential equations is used to motivate the introduction of vector notation and matrix multiplication. The linear algebra portion of the course begins with Gaussian elimination and ends with an introduction to R^n as a vector space. Vector space ideas are applied to second order linear differential equations and then to the analysis of linear systems of constant coefficient differential equations. Click here to go the page of assigned exercises in Math 244.

Math 416 is an intermediate level course in differential equations with special attention given to their interpretation as a dynamical system. Beginning with first order equations emphasis will be on the geometry of the solution space and simple bifurcations. We will then consider linear and non-linear planar systems, linearization at a fixed point, stability, limit points, limit cycles, and the Poincare-Bendixon Theory. The second half of the course will explore non-planar phase spaces, attracting sets, and Poincare maps. Applications will be made to mechanical and electrical systems, competing species, heartbeat and nerve impulses, and higher dimensional bifurcation theory, culminating in an introduction to chaotic dynamics. Click here to go the page of assigned exercises in Math 416.