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Differential and Fractal Geometry
Major: Earth sciences
Code of Subject: 8.103.00.O.7
Credits: 3
Department: Cartography and Geospatial Modelling
Lecturer: Ph.D., Associate Professor Brydun Andrii
Semester: 2 семестр
Mode of Study: денна
Learning outcomes:
• Find the length of the curve,
• Perform natural parameterization,
• Find curvature and torsion, special points of the curve,
• Calculate evolution and evolution,
• Find the first and second quadratic forms,
• Find curvature lines and asymptotic lines,
• Find geodetic lines,
• Use and equate for the construction of fractals.
• Perform natural parameterization,
• Find curvature and torsion, special points of the curve,
• Calculate evolution and evolution,
• Find the first and second quadratic forms,
• Find curvature lines and asymptotic lines,
• Find geodetic lines,
• Use and equate for the construction of fractals.
Required prior and related subjects:
• Higher Mathematics.
• Statistical Analysis of Geospatial.
• Web mapping.
• Statistical Analysis of Geospatial.
• Web mapping.
Summary of the subject:
Differential geometry is a section of mathematics that studies the general properties of curves and surfaces by methods of analysis of infinitesimally small, that is, properties of arbitrarily small pieces of curves and surfaces.
Fractal geometry is also widely used in computer graphics to construct images of natural objects such as trees, shrubs, mountain landscapes, seas.
Recommended Books:
1. Борисенко О.А. Диференціальна геометрія і топологія / Борисенко О.А. – Х., 1995.
2. Куратовский К. Топология Т. 1. / Куратовский К. – M., 1966.
3. Мищенко А.С. Курс дифференциальной геометрии и топологи / Мищенко А.С., Фоменко А.Т. – M., 1980.
4. James Gleick, Chaos – Making a New Science, Viking, New York, 1987.
5. Б. Мандельброт (Не)послушные рынки. Фрактальная революция в финансах / Б. Мандельброт и Ричард Л. Хадсон – Вильямс, 2006. ISBN 5-8459-0922-8.
2. Куратовский К. Топология Т. 1. / Куратовский К. – M., 1966.
3. Мищенко А.С. Курс дифференциальной геометрии и топологи / Мищенко А.С., Фоменко А.Т. – M., 1980.
4. James Gleick, Chaos – Making a New Science, Viking, New York, 1987.
5. Б. Мандельброт (Не)послушные рынки. Фрактальная революция в финансах / Б. Мандельброт и Ричард Л. Хадсон – Вильямс, 2006. ISBN 5-8459-0922-8.
Assessment methods and criteria:
• written reports on practical work, oral examination (40%)
• final control (exam): written, verbal form (60%)
• final control (exam): written, verbal form (60%)