Integral and Discrete Transform
Code  Completion  Credits  Range 

W01T001  ZK  45B 
 Garant předmětu:
 Lecturer:
 Tutor:
 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 Ztransform  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, CauchyRiemann 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, HilbertHuang transform.
 Syllabus of tutorials:

1.  3. weekComplex function of complex variable: basic functions exp(z), sin(z), cos(z), ... , function derivative, analytic function, CauchyRiemann 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, HilbertHuang transform.
 Study Objective:
 Study materials:

E.Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 1993
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: