Mathematical Fundamentals of Cartography

Major: Earth Sciences
Code of subject: 6.103.00.O.065
Credits: 5.00
Department: Cartography and Geospatial Modelling
Lecturer: Full prorfesor, Doctor of Physical and Mathematical Sciences Zazulyak Petro Mykhailovych
Semester: 6 семестр
Mode of study: денна
Learning outcomes: • Understand the mathematical laws of mapping the earth's surface on a plane, to wit food mapping projections and mathematical foundations of cards; • Know the methods of cartographic grids and their purpose; • To be able to choose for a particular map projection map according to its purpose, size and location on the earth's surface, etc.; • Explore projection to determine the nature of distortion.
Required prior and related subjects: •Higher Mathematics. •Mathematical Processing of Geodetic Measurements.
Summary of the subject: Basic information about the card. A brief historical overview of the development of cartography. The mathematical basis of maps (scale, projection). Systems of coordinates on the ellipsoid (ball) and the plane. Map projections, its essence, mapping grid. Key designations used in mathematical cartography. The scale lengths of lines in any direction and along the meridians and parallels. The relationship between the azimuth of the ellipsoid and its image in the plane. The convergence of meridians, the azimuth angle. The angle between the meridian and parallel projected. Conditions and equal conformal mapping. Classification of map projections on the properties of the image (in character distortion) and by type of normal grid. Cylindrical projection. Conformal, equal and cylindrical projection. Loksodromiya and the great circle route in Mercator. The concept of perspective-cylindrical projections. Conical projections and their application. Conformal, equal and rivnopromizhni conical projection. Methods for determining the parameters of conical projections. Azimuthal projection and perspective projection. Hnomonichni Stereographic and orthographic projections. External projections and their use for satellite images. Gauss-Kruger. The concept of projection Lomberta.
Assessment methods and criteria: •Reports on laboratory work, oral examination, reference work (30%); •Final control (70% credit): written, oral form (70%).
Recommended books: 1.Вахрамеева Л.А., Бугаєвський Л.М., Козакова З.Л. Математическая картография. –М.. Недра.–1986.–286 с. 2.Бугаєвський Л.М. Математическая картография. – М.Златоуст.–1998. –400 с. 3.Соловьев М.Д. Математическая картография. – М. Недра.–1969. –208 с.