| Course title | Selected Lessons in Mathematical Analysis |
|---|---|
| Course code | OPT/VKMN |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| 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) |
|---|
|
| 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 |
| Monologic Lecture(Interpretation, Training) |
| Learning outcomes |
|
Algebra of complex numbers.
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 |
|
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 |
|
| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Optics and Optoelectronics (2019) | Category: Physics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| 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 |
| 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 |
| Faculty: Faculty of Science | Study plan (Version): Biophysics - Specialization in Molecular Biophysics (2024) | Category: Physics courses | 2 | Recommended year of study:2, Recommended semester: Summer |