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Lecturer(s)
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Polášek Vladimír, Mgr. Ph.D.
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Fiľo Jaroslav, Mgr.
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Course content
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- Complex numbers - Coordinate systems - Analytic geometry in the space - Conic sections - Quadrics - Plane and spatial curves - Field theory - Function approximation - Applications of the definite integral - Numerical derivative and integration - Applications of double integral - Triple integrals
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Demonstration, Projection (static, dynamic), Practice exercises
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| prerequisite |
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| Knowledge |
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| Standard knowledge and computational skills of Mathematics I in a level which allow direct consecution to linear algebra, analytic geometry and integral calculus. |
| Standard knowledge and computational skills of Mathematics I in a level which allow direct consecution to linear algebra, analytic geometry and integral calculus. |
| learning outcomes |
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| Define a complex number, its trigonometric and exponential form. |
| Define a complex number, its trigonometric and exponential form. |
| Name the relative positions of geometric figures such as points, vectors, linear and quadratic figures. |
| Name the relative positions of geometric figures such as points, vectors, linear and quadratic figures. |
| Define metric concepts such as a deviation, a distance of geometric shapes, an area content. |
| Define metric concepts such as a deviation, a distance of geometric shapes, an area content. |
| Identify a conic section based on the equation and using sections of quadratic surfaces. |
| Identify a conic section based on the equation and using sections of quadratic surfaces. |
| Define the concepts: a curve in a plane and a curve in space. |
| Define the concepts: a curve in a plane and a curve in space. |
| Skills |
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| Convert complex numbers from algebraic to trigonometric form. |
| Convert complex numbers from algebraic to trigonometric form. |
| Calculate powers and square roots of a complex number in trigonometric form. |
| Calculate powers and square roots of a complex number in trigonometric form. |
| Convert Cartesian coordinates of the points in the plane to polar coordinates. |
| Convert Cartesian coordinates of the points in the plane to polar coordinates. |
| Convert the coordinates of the points in the space between Cartesian, cylindrical and spherical coordinate systems. |
| Convert the coordinates of the points in the space between Cartesian, cylindrical and spherical coordinate systems. |
| Transform the equations of conics and curves into polar coordinates. |
| Transform the equations of conics and curves into polar coordinates. |
| Adjust the equation of the conic section to axial form. |
| Adjust the equation of the conic section to axial form. |
| Determine the parameters of the given conic section, such as the coordinates of the center, the vertices of the focus, or the equation of the directrix or the asymptote. |
| Determine the parameters of the given conic section, such as the coordinates of the center, the vertices of the focus, or the equation of the directrix or the asymptote. |
| Eliminate a parameter from parametric equations of curves in a plane. |
| Eliminate a parameter from parametric equations of curves in a plane. |
| Find the equation of the tangent to the curve given in the parametric equations. |
| Find the equation of the tangent to the curve given in the parametric equations. |
| Compute geometric applications of a definite integral for functions specified parametrically or in polar coordinates. |
| Compute geometric applications of a definite integral for functions specified parametrically or in polar coordinates. |
| teaching methods |
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| Knowledge |
|---|
| Monologic (Exposition, lecture, briefing) |
| Practice exercises |
| Demonstration |
| Monologic (Exposition, lecture, briefing) |
| Practice exercises |
| Demonstration |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| assessment methods |
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| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Written examination |
| Written examination |
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Recommended literature
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Matejdes, M. Aplikovaná matematika. Matcentrum-Zvolen, 2005.
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Olšák P. Úvod do algebry, zejména lineární. FEL ČVUT Praha, 2007.
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Ostravský J., Polášek V. Diferenciální a integrální počet funkce jedné proměnné: vybrané statě. Zlín, 2011. ISBN 978-80-7454-124-7.
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POLÁŠEK, V., SEDLÁČEK, L. & KOZÁKOVÁ, L. Matematický seminář. Zlín, 2021. ISBN 978-80-7454-987-8.
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TOMICA, R. Cvičení z matematiky II. Brno : VUT, 1974.
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