| Course title | Selected Lessons in Mathematics |
|---|---|
| Course code | OPT/VPM |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Winter and summer |
| Number of ECTS credits | 7 |
| Language of instruction | Czech |
| Status of course | Compulsory-optional |
| 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 |
|
Algebra of complex numbers Progressions and series Function of the complex variable Limit and continuity of the complex function Complex function of the real variable Curves in the complex plane Differentiation of the complex function Holomorphic functions Progressions and series of complex functions Power series Elementary functions of the complex variable Contour integral of the complex function Cauchy theorem Cauchy formula and integral of Cauchy type Primitive functions Index of the point with respect to the contour Taylor series of the holomorphic function Total function Laurent series of the function holomorphic in the ring Isolated singular points of the holomorphic function and their classification Residuum of the function in the point Residuum theorem Use of the residuum theorem for the calculation of the integrals Jordan lemma </ul> <br> <br> Integral transforms <ul> Introduction, motivations: laws of thermomechanics, derivation of system of equations of nonlinear theory of bounded thermoelasticity, linearization, simplification, elasticity, heat conduction, idea of transformation of partial differential equation into ordinary differential equations by Fourier transform Formalization: abstract Hilber spaces, Fourier series, properties, examples, use Application: spaces of smooth integrable functions, distributions, functions with finite energy, Sobolev spaces, dual spaces, duality, interpretations in mechanics Fourier transform: definition, properties, examples, use of Fourier transform, definition of Sobolev spaces by means of Fourier transform, Fourier-Poisson integral, Green function, practical applications, heat conduction, examples Laplace transform: definition, properties, applications, examples </ul> </ul>
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| Learning activities and teaching methods |
| Monologic Lecture(Interpretation, Training) |
| Learning outcomes |
|
Algebra of complex numbers Progressions and series
Knowledge Define the main ideas and conceptions of the subject, describe the main approaches of the studied topics, recall the theoretical knowledge for solution of model problems. |
| Prerequisites |
|
No prior requirements.
|
| Assessment methods and criteria |
|
Oral exam
<ul> <li> Knowledge within the scope of the course topics (examination) </ul> |
| 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 Science | Study plan (Version): Biophysics - Specialization in General Biophysics (2024) | Category: Physics courses | 2 | Recommended year of study:2, Recommended semester: Summer |