Real Analysis

The course covers the following topics: measure spaces, Borel and Lebesgue measure, abstract integration and differentiation, integration on product spaces, functions of bounded variations, and L ^p spaces. Prerequisite: Graduate Standing. existence and uniqueness theorems, linear systems with constant coefficients, matrix analysis and matrix exponential, sility, periodic coefficients, Two-Dimensional Autonomous linear and nonlinear systems, phase plane analysis, Liapunov stability, limit cycles and the Poincare’-Bendixson Theorem, and stability of linear non-autonomous systems. Prerequisite: Graduate Standing.