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MAM091 Funktionalanalys 4.0 poäng | |
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ÄMNE (enl SCB) Matematik/Tillämpad matematik NIVÅ/DJUP D M PROGRAM/TIDSPERIOD F4, D4 / Lp IV SPRÅK: Engelska/Svenska EXAMINATOR L Maligranda Prof FASTSTÄLLD Kursplanen är fastställd av institutionen för matematik 1997-02-17 att gälla från H97. FÖRKUNSKAPSKRAV SYFTE/MÅL This course is intended to familiarize the students with the basic concepts, principles and methods of functional analysis and its applications. INNEHÅLL Metric spaces, examples, open and closed sets, convergence, completeness; Normed and Banach spaces, examples, properties, finite dimensional spaces, compactness; Bounded linear operators and functionals, dual space; Inner product and Hilbert spaces, examples, properties, orthogonal projection, orthonormal sequences, Fourier series in Hilbert spaces, orthonormal polynomials, linear functionals on Hilbert space; The Hahn-Banach theorem, functionals on C[a,b], adjoint operators, reflexive spaces; Uniform boundedness theorem and some applications, strong and weak convergence, numerical integration; Open mapping theorem, closed graph theorem; Banach fixed point theorem, applications to linear, differential and integral equations; Approximation in normed spaces, uniquess and strict convexity, uniform approximation; Compact operators UNDERVISNING EXAMINATION The examination consists of a written exam at the end of the course. KURSENS BETYGSKALA: U, 3, 4, 5 MOMENT/PROV | |
| Tentamen | 4.0poäng |
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LITTERATUR Kreyszig E.: Introductory Functional Analysis with Applications. John Wiley 1978.
Senast reviderad litteratur:
2001-02-16
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Ytterligare kursinformation: http://www.sm.luth.se/math/education/ |
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