Course: Selected Lessons in Mathematical Analysis

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Course title Selected Lessons in Mathematical Analysis
Course code OPT/VKMN
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study 2
Semester Summer
Number of ECTS credits 7
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Mišta Ladislav, doc. Mgr. Ph.D.
  • Leskovjanová Olga, Mgr.
Course content
1. Algebra of complex numbers. 2. Sequences and series. Power series. Convergence in the Gauss plane. 3. Functions of a complex variable. 4. Limit, continuity, derivative, Cauchy-Riemann condition. 5. Analytical functions. 6. Line integrals. 7. Cauchy integral theorem, consequences. 8. Residual theorem and applications. 9. Integral transforms. 10. Laplace transform. Inverse Laplace transform, rational functions. Application of the Laplace transform to the differential equation solution. 11. Fourier series. Fourier integral. Fourier transform and application. 12. Further similar integral transforms.

Learning activities and teaching methods
Lecture
Learning outcomes
Prerequisites
unspecified

Assessment methods and criteria
Oral exam, Written exam

Credit: two written tests during the semester, the student has to obtain at least 50% of possible points. Exam (combined): written test - examples, oral exam.
Recommended literature
  • Černý, I. (1983). Analýza v komplexním oboru. Praha.
  • Fuks, B. A.; Šabat, B. V. Funkce komplexní proměnné. Praha. 1961.
  • Kopáček, J. a kol. Příklady z matematiky pro fyziky IV. Praha. 1996.
  • Kopáček, J. Matematická analýza pro fyziky IV. Praha. 2003.
  • Veit, J. (1983). Integrální transformace. Praha.


Study plans that include the course
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Faculty: Faculty of Science Study plan (Version): Optics and Optoelectronics (2019) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Summer
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Faculty: Faculty of Science Study plan (Version): General Physics and Mathematical Physics (2019) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Summer
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