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Lecturer(s)
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Fürst Tomáš, RNDr. Ph.D.
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Vodák Rostislav, doc. RNDr. Ph.D.
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Ženčák Pavel, RNDr. Ph.D.
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Course content
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1. Fourier methods and their application in digital music, sound processing 2. Fourier methods and their application in PDE 3. Boundary value problems -- an overview. Application to linear elasticity 4. Introduction to image processing 5. Introduction to analysis of biological signals. Application to ECG data
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
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Learning outcomes
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The aim of the course is to discuss with students several larger and more complex practical problems from the real world that require the use of mathematical tools from various subjects. The aim is the synthesis and application of mathematical tools.
Ability to solve complex practical tasks.
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Prerequisites
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Linear algebra, calculus, basic numericals, basic programming, English
KMA/MA1 and KMA/MA2 and KMA/MA3 and KAG/LA1A and KMA/DR
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Assessment methods and criteria
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Oral exam, Seminar Work
Colloquiu: active participation. presentation of a solution to a selected more complex problem
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Recommended literature
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Benson, D. (2006). Music: A Mathematical Offering.
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Brockwell, P. J., Davis, R. A. (2009). Time Series: Theory and Methods.
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Brunton, S. L., Kutz, J. N. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control.
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Gonzalez, R. C., Woods, R. E. (2017). Digital Image Processing.
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Körner T. W. (1988). Fourier Analysis.
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Kutz, N. (2013). Data Driven Modeling & Scientific Computation.
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Morton, K. W., Mayers, D. F. (2005). Numerical solution of partial differential equations: an introduction. Cambridge.
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Vitásek, E. (1994). Základy teorie numerických metod pro řešení diferenciálních rovnic. Praha.
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