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Lecturer(s)
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Course content
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Lectures: 1. Introduction. Overview about possible kinds of mathematical description of the real-world problems. Steady state. Temporal evolution of quantities. 2. Solving algebraic equations, transcendent equations and systems of equations over a real domain. 3. Ordinary Differential Equations (ODEs) and their systems - Natural mechanical or electrical oscillations. Coupled natural processes (chemical reactions). Forced oscillations (mechanical, electrical). 4. Symbolic vector manipulation - Validity checking of equations/formulas in vector algebra, divergence, gradient. Physics examples. 5. Symbolic matrix computation - Properties of matricies. Matrix operators. Introduction to tensor calculus. Examples of mechanics. 6. Processing of measured data 1 - Interpolation. Extrapolation. Method of least squares. Linear dependence between variables. Indirect measurement of an electrical resistance. 7. Processing of measured data 2 - Values of Interpolated/Extrapolated functions. Horner's Method. Tutorials: Tutorials will be focused on solving equations similar to illustrative examples from lectures.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
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Learning outcomes
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The course goal is to make students familiar with the use of selected software tools for symbolic computations. These software tools make it easier to perform usually time demanding analytical computations which appear in Physics, Chemistry, Technical practice, etc. During the lectures, illustrative examples from previous courses (Math, Physics, Chemistry, Linear algebra, etc.) will be solved.
The course brings basic knowledge about advanced use of analytical computations for a description of real-world processes.
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Prerequisites
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Unspecified
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Assessment methods and criteria
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Oral presentation of self-study
Podmínkou získání zápočtu je aktivní účast studenta na cvičeních a průběžné plnění zadávaných úkolů.
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Recommended literature
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