Calculus of Transforms 390-FM2-1RTR
A short introduction to the complex analysis: holomorphic functions, residues. Residue theorem.
Laplace transform and Z-transform. Fourier series, Fourier transform, Cosine transform.
Uncertainty principle. Discrete Fourier transform (DFT), fast Fourier transform (FFT).
Hilbert space. Bases. Operators. Scalar products. Dirac Delta. Wavelet transform. Low-pass and high-pass filters and their role in signal analysis. Radon transforms.
Applications in tomography and image analysis.
Type of course
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
The student knows and understands:
1. in depth the mathematical issues necessary in physics and astronomy within the scope of the educational program,
2. in depth contemporary physical theory and, within the scope of the educational program, its relevance to health care,
3. specialized research tools used in the selected field of physics.
The student is able to:
4. properly select mathematical models for solving and analyzing physical issues,
5. select and apply in practice research tools appropriate to a given field of physics,
6. present the results of conducted research in an elaborate written form and in the form of a public speech, preserving the context of the research conducted, and draw conclusions,
7. obtain information and assess its reliability, interpret it, draw conclusions and form opinions based on it,
8. develop students' creativity and ability to think independently and critically.
The student is ready to:
9. continuously improve their own competence, bearing in mind the rapid progress in the field of physics,
10. to critically evaluate their knowledge by measuring themselves against real research and applied problems,
11. to think and act creatively in research, development and service institutions using the tools and achievements of physics.
Codes
KP7_: WG1, WG2, WG4, UW1, UW2, UW4, UK2, UO1, KK1, KK2, KO1.
Assessment criteria
After completing the training, a written and oral exam takes place, which verifies the acquired knowledge.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: