CTU FEE Moodle
Complex Analysis
B241 - Winter 24/25
This is a grouped Moodle course. It consists of several separate courses that share learning materials, assignments, tests etc. Below you can see information about the individual courses that make up this Moodle course.
Complex Analysis - B0B01KAN
Main course
| Credits | 5 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 2P+2S |
Annotation
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.
Study targets
None
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
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 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 tutorial
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.
[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
None
Complex Analysis - B0B01KANA
| Credits | 4 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 2P+2S |
Annotation
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.
Study targets
None
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
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 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 tutorial
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.
[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
None