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Course specification
Course title Selected Topics in Real and Complex Analysis
Acronym OE2OPA
Study programme Electrical Engineering and Computing
Module Electronics
Type of study bachelor academic studies
Lecturer (for classes) prof. dr Siniša Ješić
Lecturer/Associate (for practice) doc. dr Nataša Ćirović
Lecturer/Associate (for OTC) doc. dr Nataša Ćirović
ESPB 3 Status elective
Condition Prerequisite: Mathematics 1 (OO1MM1), Mathematics 2 (OO1MM2), Mathematics 3 (OE2M3)
The goal Introducing students with more advances topics in real and complex analysis with applications in vocational subjects of electrical engineering.
The outcome Student is capable to apply Fourier and Z transformations on functions in various fields of vocational courses in electrical engineering. Student is able to determine points of branching, Riemann surface, form branch cut, allocate branch of multiform function, perform integration of multiform function with different choices of model of Riemann surfaces and application on solving real integrals.
Contents
Contents of lectures Systems of orthogonal functions, representation of functions with generalized Fourier series. Discrete and fast Fourier transformation with applications. Z transformation, properties, applications, connection to Laurant series. Complex multiform function. Notion. change of argument. Branches, Riemann surfaces and integration of multiform functions, application to solving real integrals.
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
1Siniša N. Ješić: Matematika 3. Kompleksne funkcije, Furijeovi redovi i integrali, Laplasova transformacija. Gerundijum, Beograd 2011., Sinisa N. Jesic: Mathematics 3. Complex functions, Fourier series and integrals, Laplace Transformation. Gerundijum, Belgrade, 2011.
Number of hours per week during the semester / trimester / year
Lectures Exercises OTC Study and Research Other classes
1 1 0.5
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
Activities during lectures 0 Test paper 50
Practical lessons 30 Oral examination 20
Projects 0
Colloquia 0
Seminars 0