Subject description - B0B01KANA
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Explanatory Notes
Instructions
| B0B01KANA | Complex Analysis | ||
|---|---|---|---|
| Roles: | P | Extent of teaching: | 2P+2S |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Mihula Z. | Completion: | Z,ZK |
| Lecturers: | Mihula Z. | Credits: | 4 |
| Tutors: | Drážný L., Mihula Z., Turčinová H. | Semester: | Z |
Web page:
https://moodle.fel.cvut.cz/courses/B0B01KANAAnotation:
The course is an introduction to the fundamentals of complex analysis and its applications. The basic principles of Fourier, Laplace, and Z-transform are explained, including their applications, particularly to solving differential and difference equations.Course outlines:
| 1. | Complex numbers. Limits and derivatives of complex functions. | |
| 2. | Cauchy-Riemann conditions, holomorphic functions. Harmonic functions. | |
| 3. | Elementary complex functions. Line integral. | |
| 4. | Cauchy's theorem and Cauchy's integral formula. | |
| 5. | Power series representation of holomorphic functions. | |
| 6. | Laurent series. Isolated singularities. | |
| 7. | Residues. Residue theorem. | |
| 8. | Fourier series and basic properties of Fourier transform. | |
| 9. | Inverse Fourier transform. Applications of Fourier transform. | |
| 10. | Basic properties of Laplace transform. | |
| 11. | Inverse Laplace transform. Applications of Laplace transform. | |
| 12. | Basic properties of Z-transform. | |
| 13. | Inverse Z-transform. Applications of Z-transform. | |
| 14. | Spare lecture |
Exercises outline:
| 1. | Complex numbers. Limits and derivatives of complex functions. | |
| 2. | Cauchy-Riemann conditions, holomorphic functions. Harmonic functions. | |
| 3. | Elementary complex functions. Line integral. | |
| 4. | Cauchy's theorem and Cauchy's integral formula. | |
| 5. | Power series representation of holomorphic functions. | |
| 6. | Laurent series. Isolated singularities. | |
| 7. | Residues. Residue theorem. | |
| 8. | Fourier series and basic properties of Fourier transform. | |
| 9. | Inverse Fourier transform. Applications of Fourier transform. | |
| 10. | Basic properties of Laplace transform. | |
| 11. | Inverse Laplace transform. Applications of Laplace transform. | |
| 12. | Basic properties of Z-transform. | |
| 13. | Inverse Z-transform. Applications of Z-transform. | |
| 14. | Spare tutorial |
Literature:
| [1] | H. A. Priestley: Introduction to Complex Analysis, Oxford University Press, Oxford, 2003. | |
| [2] | E. Kreyszig: Advanced Engineering Mathematics, Wiley, Hoboken, 2011. | |
| [3] | L. Debnath, D. Bhatta: Integral Transforms and Their Applications, CRC Press, Boca Raton, 2015. |
Requirements:
Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| BPEK_2018 | Common courses | P | 3 |
| BPEEM2_2018 | Electrical Engineering and Management | P | 3 |
| BPEEM1_2018 | Applied Electrical Engineering | P | 3 |
| BPEEM_BO_2018 | Common courses | P | 3 |
| Page updated 9.7.2025 17:53:42, semester: Z/2025-6, Z/2026-7, L/2025-6, L/2026-7, L/2024-5, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |