| Course title | Mathematics III |
|---|---|
| Course code | KMF/IMA3E |
| Organizational form of instruction | Lecture + Tutorial |
| Level of course | Bachelor |
| Year of study | 2 |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Sequences and series of functions. Uniform convergence. Special tests for uniform convergence of sequences and series of functions. Power series. Differentiation and integration of power series. Expansion of functions in power series, Taylor series. Some important power series and their using to the approximative computations. 2. Fourier series Ortogonal functions, the proof for the set in the interval . Fourier expansion corresponding to a function, derivation of its coefficients. Sufficient conditions for convergence of Fourier series. 3. Systems of differentional equations The elimination method of solution of systems of differentional equaitons. Homogeneous and non-homogeneous systems of linear ordinary differentional equations. 4. Functions of a complex variable Basic properties of complex numbers. A single - valued and a multiple - valued function. Limits, continuity and derivatives of single - valued functions. Cauchy - Riemann conditions, analytic functions. Elementary functions, Euler relations. Logarithmic function. The integral of a function of a complex variable. Cauchy´s theorem and its conclusions. Cauchy´s integral formulas. Taylor series representation of a function.
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| Learning activities and teaching methods |
| Monologic (reading, lecture, briefing), Methods of individual activities, Skills training |
| Learning outcomes |
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The aim of the course is to acquaint the students with mathematical appliance so that they will be able to use acquired knowledge in solving concrete exercises within their study specialization.
A student acquires a satisfactory view of some topics of the mathematical analysis and numerical mathematics. The obtained knowledge enable students to use the mathematical appliance in various areas of mathematics and in special courses of their specialization. |
| Prerequisites |
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The course follows the courses Mathematics I and Mathematics II. The satisfactory knowledge of the differential and integral calculus of functions of one and more variables is required.
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| Assessment methods and criteria |
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Oral examination, Written examination, Student performance assessment, Work-related product analysis
Conditions for a credit: Successful passing of a kontrol test. Three reparations are possible. Informations about an exam: An exam consists of spoken part. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Process Control (2015) | Category: Special and interdisciplinary fields | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Communication and Microprocessor Technology (2014) | Category: Electrical engineering, telecommunication and IT | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Process Control (2013) | Category: Special and interdisciplinary fields | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Communication and Microprocessor Technology (2015) | Category: Electrical engineering, telecommunication and IT | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Process Control (2014) | Category: Special and interdisciplinary fields | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Communication and Microprocessor Technology (2016) | Category: Electrical engineering, telecommunication and IT | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Communication and Microprocessor Technology (2013) | Category: Electrical engineering, telecommunication and IT | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Electrical Engineering and Informatics | Study plan (Version): Process Control (2016) | Category: Special and interdisciplinary fields | 2 | Recommended year of study:2, Recommended semester: Winter |