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Lecturer(s)
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Peška Patrik, RNDr. Ph.D.
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Course content
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unspecified
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Learning activities and teaching methods
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Training in job and motor Skils, Activating (Simulations, Games, Dramatization), Group work, Analyzing and producing audiovisual content
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Learning outcomes
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The aim of the course is to introduce the basics of Differential Geometry of curves and surfaces with emphasis on computation and visualization using software tools. Students will: - learn to use Maxima for analytical and graphical computations, - understand the geometric meaning of vector-valued functions, - analyze tangent properties of curves and surfaces, - understand curvature and torsion of curves, - work with the Frenet-Serret frame, - use the first and second fundamental forms of surfaces, - gain introductory knowledge of tensor-based descriptions, - connect analytical results with graphical visualization.
After completing the course, the student: Knowledge: - understands the basics of Differential Geometry of curves and surfaces, - understands curvature, torsion, and fundamental forms, - has introductory knowledge of tensor-based geometry, - knows the role of computational tools in geometry. Skills: - uses Maxima for computation and visualization, - works with vector-valued functions and surfaces, - computes tangent properties of curves and surfaces, - determines curvatures and interprets their meaning, - connects analytical computations with graphical outputs. Competences: - connects mathematical theory with practical computation, - uses software tools to solve mathematical problems, - develops geometric intuition through visualization, - is prepared to apply knowledge in teaching and practice.
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Prerequisites
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Knowledge of Mathematical Analysis (derivatives of functions of one and several variables) and Linear Algebra is assumed. Basic computer skills are required.
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Assessment methods and criteria
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Student performance, Systematic Observation of Student, Seminar Work
To successfully complete the course, the student must: - demonstrate basic proficiency in using Maxima for symbolic and graphical computations, - understand the fundamentals of Vector Algebra, - work with scalar and vector-valued functions of one and two variables and their visualization, - determine tangent properties of curves (tangent, normal, binormal vectors), - compute curvature and torsion of curves and use the Frenet-Serret frame, - determine tangent planes and normal vectors of surfaces, - work with the first and second fundamental forms of surfaces, - compute basic surface characteristics (curvatures), - understand introductory concepts of tensor calculus, - solve practical and computational problems using software tools, - complete continuous assessment tasks (assignments, visualizations, projects), - pass the final assessment (course credit or exam).
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Recommended literature
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Doupovec, M. (1999). Diferenciální geometrie a tenzorový počet. Brno.
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Gray, A. (1994). Differential geometry.
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Kreyszig E. (2013). Differential geometry.. Dover publ.
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Podolský J. (1994). Modern Differential Geometry of Curves and Surfaces. Spectrum Akad. Verl.
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Struik J. D. (1961). Lectures on classical differential geometry. Courier corp.
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