COURSE AIMS AND OBJECTIVES: The goal of the course is to introduce students with basic methods of nonlinear analysis: function spaces, fixed-point methods and convex analysis and to present the applications of the developed theory to the analysis of integral equations and ordinary differential equations.
COURSE DESCRIPTION AND SYLLABUS:
- Normed spaces and examples (3 weeks)
- Operators on normed spaces (linear operators, compact operators, Banach fixed point theorem, integral equations, 4 weeks)
- Differential and integral calculus (integration of vector functions, Frechet and Gateaux derivative, Newton method, 4 weeks)
- Convex analysis, Brower and Schauder fixed point theorem, applications to ordinary differential equations and integral equations (4 weeks).
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