Integral and Discrete Transform
| Code | Completion | Credits | Range |
|---|---|---|---|
| W01T001 | ZK | 45 |
- Lecturer:
- Jan Halama (gar.)
- Tutor:
- Jan Halama (gar.)
- Supervisor:
- Department of Technical Mathematics
- Synopsis:
-
Introduction to complex analysis. Laplace transform - basic properties, application to solution of problems for ordinary and partial differential equations. Discrete Laplace transform and Z-transform - basic properties, aplication to solution of diference equations. Fourier series, Fourier integral, Fourier integral transform, Fourier spectra of nonperiodic signal. Solution of exercises is demonstrated using MAPLE software.
- Requirements:
- Syllabus of lectures:
-
1. - 3. weekComplex function of complex variable: basic functions exp(z), sin(z), cos(z), ... , function derivative, analytic function, Cauchy-Riemann conditions, line integral, Cauchy integral theorem, Cauchy integral formula, Taylor serie of analytic function, Laurent serie, singular points, residual of function in singular point.
3. - 6. weekLaplace transform: basic properties, inverse Laplace transform, Laplace transform of Dirac a Heaviside function, application of Laplace transform to solution of ODE and PDE.
6. - 8. week1Discrete Laplace a Z transform: basic properties, inverse transform, application of Z transform to solution of difference equations.
8. - 10. weekFourier series: Fourier serie of periodic function, amplitude spectra, application to solutions of ODE with periodical forcing term, solution of PDE by Fourier method, extension to nonperiodic functions, Fourier integral.
10. - 12. weekFourier transform: basic properties, amplitude spectra of nonperiodic function, application to solution of PDE, discrete Fourier transform (DFT), fast Fourier transform (FFT).
12. - 13. weekTodays techniques used for real time transfer of signal: windowed Fourier transform, wavelet transform, Hilbert-Huang transform.
- Syllabus of tutorials:
-
1. - 3. weekComplex function of complex variable: basic functions exp(z), sin(z), cos(z), ... , function derivative, analytic function, Cauchy-Riemann conditions, line integral, Cauchy integral theorem, Cauchy integral formula, Taylor serie of analytic function, Laurent serie, singular points, residual of function in singular point.
3. - 6. weekLaplace transform: basic properties, inverse Laplace transform, Laplace transform of Dirac a Heaviside function, application of Laplace transform to solution of ODE and PDE.
6. - 8. week1Discrete Laplace a Z transform: basic properties, inverse transform, application of Z transform to solution of difference equations.
8. - 10. weekFourier series: Fourier serie of periodic function, amplitude spectra, application to solutions of ODE with periodical forcing term, solution of PDE by Fourier method, extension to nonperiodic functions, Fourier integral.
10. - 12. weekFourier transform: basic properties, amplitude spectra of nonperiodic function, application to solution of PDE, discrete Fourier transform (DFT), fast Fourier transform (FFT).
12. - 13. weekTodays techniques used for real time transfer of signal: windowed Fourier transform, wavelet transform, Hilbert-Huang transform.
- Study Objective:
- Study materials:
-
E.Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 1993
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri - The course is a part of the following study plans: