Math 6190 Analysis I. Three credits. Prerequisite: MATH 4250 or equivalent.Rigorous treatment of limits, continuity, differentiation, andintegration in n-dimensional Euclidean space; infinite series;introduction to metric spaces.
Math 6200 Analysis II. Three credits. Prerequisite: MATH 6190 or equivalent.A continuation of MATH 6190. Lebesgue measure, Lebesgueintegral, functions of bounded variation.
Math 6210 Complex Variables. Three credits. Prerequisite: MATH 6190.Theory of functions of complex variables and their application inmathematics and physics.
Math 6250 Real Analysis. Three credits. Prerequisite: MATH 6200. A continuationof MATH 6200. Advanced topics in real analysis. Abstractmeasure and integration theory. Introduction to functional analysis.
Math 6260 Advanced Differential Equations I. Three credits. Prerequisites:MATH 3120 and 4250. Qualitative and quantitative analysis ofsystems of differential equations. Gradient systems, Sturm-Liouvilleproblems. Elementary techniques for boundary value problemsof partial differential equations.
Math 6270 Advanced Differential Equations II. Three credits. Prerequisite:MATH 6260. Solution techniques for boundary value problems.Problems involve heat, wave, and potential equations. Topicsinclude the method of characteristics, series solutions, integral transforms, and Green's functions.