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13M081OPRA - Selected Topics in Real Analysis

Course specification
Course title Selected Topics in Real Analysis
Acronym 13M081OPRA
Study programme
Module
Type of study master academic studies
Lecturer (for classes)
Lecturer/Associate (for practice)
Lecturer/Associate (for OTC)
    ESPB 6.0 Status elective
    Condition Knowledge in classical mathematical analysis.
    The goal Introducing students with spaces with measure, Banach, Lp, Hilbert spaces and with theory of functions defined on these spaces, theory of Fourier series on Hilbert spaces.
    The outcome Students are prepared to apply mathematical theories of real analysis in various fields of Electrical Engineering.
    Contents
    Contents of lectures Definition of spaces with measure, Lebesgue measure and Lebesgue integral. Banach spaces, Hann-Banach theorem, dual spaces, Riesz representation theorem, Lp and Hilbert spaces, orthogonal systems, projections, Fourier series and conditions of convergence on Hilbert spaces.
    Contents of exercises Through examples, tasks and problems student learns how to apply theorems and basic concepts that are learnt through theoretical contents. Especially students are prepared how to solve problems that are occurring in Electrical Engineering, using mathematical tools.
    Literature
    1. A. Bruckner, J. Bruckner, B. Thomson; Real analysis; Prentice -Hall Int., London 1997.
    2. (Original title)
    Number of hours per week during the semester/trimester/year
    Lectures Exercises OTC Study and Research Other classes
    3 1
    Methods of teaching Combination of traditional presentation on blackboard, slides, communication of students through internet and individual work with students while working on home work and explanation of current topics. Discussion about home work during semester, colloquium at the end of semester.
    Knowledge score (maximum points 100)
    Pre obligations Points Final exam Points
    Activites during lectures 0 Test paper 50
    Practical lessons 0 Oral examination 20
    Projects
    Colloquia 30
    Seminars 0