MS1OPR - Selected Topics in Real Analysis
Course specification | ||||
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Course title | Selected Topics in Real Analysis | |||
Acronym | MS1OPR | |||
Study programme | Electrical Engineering and Computing | |||
Module | Applied Mathematics | |||
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 vocational electrotechnical subjects | |||
Literature | ||||
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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 | 0 | |||
Colloquia | 30 | |||
Seminars | 0 |