MATH 3F03, Fall 2018
ADVANCED DIFFERENTIAL EQUATIONS
Mathematical models involving linear and nonlinear differential equations are used in all branches of the natural and social sciences and in engineering. Predictions based on models help us better understand the phenomena under investigation and how to control them and create better designs. The emphasis of the course will be to develop skills in analyzing systems of linear and nonlinear differential equations using analytical and geometrical approaches widely applicable in science and engineering. For linear systems of differential equations, explicit solutions can be obtained. However, for nonlinear systems this is not usually possible and so the aim is to determine the qualitative behaviour of the solutions, e.g. the existence, uniqueness, and long term behaviour. The course will focus on studying systems of ordinary differential equations including linear systems, nonlinear autonomous systems in the plane, phase portraits, local and global stability of invariant sets such as equilibria and periodic solutions, the Poincare-Bendixson Theorem, the Dulac criterion, and Lyapunov's method for higher order nonlinear systems. Students will be expected to learn precise statements of Definitions and Theorems and to use them appropriately (i.e., to verify the hypotheses to determine when they apply and when they do not, and make appropriate conclusions). Students will be introduced to software for time-series simulations, phase portraits, and bifurcation diagrams.
INSTRUCTOR: G. Wolkowicz
3 unit(s) Systems of ordinary differential equations, autonomous systems in the plane, phase portraits, linear systems, stability, Lyapunov’s method, Poincare-Bendixson theorem, applications.
Three lectures, one tutorial; one term
Prerequisite(s): MATH 2C03; and MATH 2X03 (or 2A03 or ISCI 2A18 A/B); and credit or registration in MATH 2R03
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS