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Lecturer(s)
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Černohlávek Vít, Ing. Ph.D.
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Pitrová Veronika, RNDr. PhD., Ph.D.
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Course content
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Vector spaces Linear dependence and independence, basis and dimension, subspaces of a vector space. Scalar, vector and mixed product of vectors. Orthogonal coordinate system. Matrices and Determinants Matrices, determinants, linear matrix display. Eigenvalues and eigenvectors, quadratic form. Systems of linear equations and their solutions. Analytic geometry in the plane and space General and parametric equations of lines and planes, their relative positions, distances and deviations. Conic, technical curve (cycloides, spirals). Quadrics. Ordinary Differential Equations First-order equations and their solutions. Integral curves uniqueness problem. Bernoulli equation, with separable variables, homogeneous and exact equations. Equations of higher order. Fundamental system of solutions, reduction of order, method of variation of constants. Linear differential equations with constant coefficients and a special right side, Euler's differential equation. Systems of linear differential equations of first Regulations. Differential calculus of real functions of several real variables Limit and continuity. Directional derivative, partial and total derivatives. Differentiability of functions, differential. Increment function theorems, higher order derivatives, Taylor's theorem. Local, global and constrained extrema. Functions defined implicitly. Basic concepts of vector analysis (vector, scalar and potential-field rotation). Integral calculus of real functions of several real variables The concept of Riemann integral in two-and three-dimensional space, basic properties. Methods of integration, Fubini theorem. Geometric and physical applications of multidimensional integrals. Line and surface integrals I and II. species. Green, Gauss and Stokes theorem. The use of curvilinear and surface integrals in physics and engineering.
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Learning activities and teaching methods
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unspecified, unspecified
- unspecified
- 50 hours per semester
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Learning outcomes
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Mathematics from the university point of view continues on the secondary school mathematics and contains above all the differential and integral calculus, analytic geometry and linear algebra. The knowledge gained here are prerequisite for vocational subjects studied at the Faculty of Mechanical Engineering, J. E. Purkyně University, therefore not to mere knowledge of mathematical substance, but also skills in the field of applications especially on technical issues. In Mathematics II, it is primarily a problem for functions on two and three variables.
Competence in the fundamentals of mathematics, students will be able to solve tasks and problems differential and integral calculus of functions on two and three variables and finally realizes connections with physical and technological applications.
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Prerequisites
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Successfully completed course Mathematics I.
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Assessment methods and criteria
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unspecified
A necessary condition for obtaining credit is at least 70% attendance at seminars. In addition, credit will be given only if the student succeeds in at least 70% of tests and assignments.
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Recommended literature
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Budinský, B., Charvát, J. Matematika II, SNTL Praha. 1990.
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Černý, I. Úvod do inteligentního kalkulu 2. Academia, Praha, 2005.
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Dontová E. Matematika IV. ČVUT Praha, 1996.
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Pytlíček J. Lineární algebra a geometrie. ČVUT Praha, 2007.
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