Integral Transforms

Lectures:
Introduction to Fourier series. Orthogonal systems of functions. Generalized Fourier series. Applications.
Introduction to integral transforms. Convolution.

Laplace transform, fundamental properties. Inverse Laplace Transform. Applications.
Fourier transform, fundamental properties. Inverse Fourier transform. Applications.
Z-transform, fundamental properties. Inverse Z-transform. Applications.
Distribution. Dirac impuls.


Exercises:
Examples of orthogonal systems of functions, Fourier series and applications.
Practising of Laplace transform. Solution of differential equation.
Practising of Fourier transform and examples.
Practising of Z-transform. Solution of difference equation.


Projects:
Two individual works and their presentation on the theme:
Fourier series.

Laplace transform.