Further Mathematics, part 1

Major: Geodesy and Land Management
Code of subject: 6.193.00.O.002
Credits: 6.00
Department: Cartography and Geospatial Modelling
Lecturer: Ph.D., Associate Professor Brydun Andrii
Semester: 1 семестр
Mode of study: денна
Learning outcomes: • use knowledge of the theory of matrices and determinants for solving systems of linear algebraic equations and vector algebra tasks; • use of abilities and skills of analytic geometry in the plane and in space; • ability to use knowledge of the theory of functions of one and several variables; • understanding of the basic theory of differential calculus of functions of one variable and its application for the studying curves in plane and in space.
Required prior and related subjects: • Informatics and Programming of geodetic tasks.
Summary of the subject: Elements of linear algebra (Matrix. Rank of matrix. Determinant. Inverse matrix. System of linear equations. Vectors). Analytic geometry in the plane and in space (Straight line on a plane. The curves of the second order. Plane. Straight line in space. Straight line and plane. Surfaces of the second order). The functions of one variable (Numerical sets. Complex numbers. Function. Numerical sequence. Limit of function. Continuity functions). Derivative of the function of one variable and its differential (Derivative function. Rules of differentiation. Derivatives of higher orders. Differential of function. Differentials of higher orders. Taylor's formula). Using of derivatives of functions of one variable (Rolle's, Lagrange and Cauchy theorems. L'Hopital's rule. Monotony function. Extremum of functions. Maximum and minimum of the function on the segment. Convexity of functions graph. Full research function).
Assessment methods and criteria: • Work on practical exercises, verbal, combined and front polls, tests (30%). • Final control (exam): written and verbal forms (70%).
Recommended books: 1. Ефимов Н.В. Краткий курс аналитической геометрии, М.: Наука, 1969. – 272с. 2. Рудавський Ю.К., Костробій П.П., Луник Ф.П., Уханська Д.В. Лінійна алгебра та аналітична геометрія, Л.: Бескид Біт, 2002. – 262с. 3. Шкіль М.І., Колесник Т.В. Вища математика. – К. Вища школа, 1986.