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Lecturer(s)
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Kubínek Roman, doc. RNDr. CSc.
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Horváth Pavel, RNDr. Ph.D.
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Richterek Lukáš, Mgr. Ph.D.
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Vyšín Ivo, RNDr. CSc.
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Říha Jan, Mgr. Ph.D.
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Vůjtek Milan, Mgr. Ph.D.
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Course content
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<ul> <li> Introduction to vector algebra <ul> <li> Scalar and vector physical quantities, their properties <li> Definition of a vector, vector space <li> Arithmetical and geometrical definition of a vector <li> Linear combinations of vectors, linearly-dependent and independent system vectors, bases and dimensions of vector space <li> Operation with vectors - scalar, vector and mixed product of vectors <li> Transformations of vector coordinates in curvilinear systems of coordinates used in physics <li> Use of vector calculus in physics </ul> <br> <br> <li> Introduction to tensor calculus <ul> <li> Anisotropic media, tensor physical quantities, their properties <li> Definition of a tensor <li> Algebraic operations with tensors <li> Transformations of tensor components <li> Tensors in physics </ul> <br> <br> <li> Differential calculus of a function with one variable <ul> <li> Real function of one real variable, basic types of functions, their properties <li> Limit of a function, basic rules for calculation of function limits <li> Differentiation of a function, its physical and geometrical interpretation <li> Differential of a function, its physical and geometrical interpretation <li> Differentiations of higher orders, physical interpretation of the second differentiation </ul> <br> <br> <li> Differential calculus of a function with two and more variables <ul> <li> Real function of more real variables <li> Partial differentiation of the first order and higher orders <li> Total differential of the first order and higher orders </ul> <br> <br> <li> Integral calculus of a function with one variable <ul> <li> Primitive function, indefinite integral <li> Basic methods and rules of integration <li> Definite integral and its calculation <li> Use of definite integral in geometry and physics </ul> <br> <br> <li> Introduction to solving of differential equations <ul> <li> Definition of differential equation <li> Solving of basic types of the first-order differential equations - equations with separable variables, homogeneous equations, linear equations <li> Solving of the second-order differential equations with constant coefficients </ul> <br> <br> <li> Integral calculus of a function with two and more variables <ul> <li> Double integral and its calculation <li> Triple integral and its calculation </ul> </ul>
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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<ul> <li> Introduction to vector algebra <ul> <li> Scalar and vector physical quantities, their properties <li> Definition of a vector, vector space <li> Arithmetical and geometrical definition of a vector <li> Linear combinations of vectors, linearly-dependent and independent system vectors, bases and dimensions of vector space <li> Operation with vectors - scalar, vector and mixed product of vectors <li> Transformations of vector coordinates in curvilinear systems of coordinates used in physics <li> Use of vector calculus in physics </ul> <br> <br> <li> Introduction to tensor calculus <ul> <li> Anisotropic media, tensor physical quantities, their properties <li> Definition of a tensor <li> Algebraic operations with tensors <li> Transformations of tensor components <li> Tensors in physics </ul> <br> <br> <li> Differential calculus of a function with one variable <ul> <li> Real function of one real variable, basic types of functions, their properties <li> Limit of a function, basic rules for calculation of function limits <li> Differentiation of a function, its physical and geometrical interpretation <li> Differential of a function, its physical and geometrical interpretation <li> Differentiations of higher orders, physical interpretation of the second differentiation </ul> <br> <br> <li> Differential calculus of a function with two and more variables <ul> <li> Real function of more real variables <li> Partial differentiation of the first order and higher orders <li> Total differential of the first order and higher orders </ul> <br> <br> <li> Integral calculus of a function with one variable <ul> <li> Primitive function, indefinite integral <li> Basic methods and rules of integration <li> Definite integral and its calculation <li> Use of definite integral in geometry and physics </ul> <br> <br> <li> Introduction to solving of differential equations <ul> <li> Definition of differential equation <li> Solving of basic types of the first-order differential equations - equations with separable variables, homogeneous equations, linear equations <li> Solving of the second-order differential equations with constant coefficients </ul> <br> <br> <li> Integral calculus of a function with two and more variables <ul> <li> Double integral and its calculation <li> Triple integral and its calculation </ul> </ul>
Knowledge Define the main ideas and conceptions of the subject, describe the main approaches of the studied topics, recall the theoretical knowledge for solution of model problems.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
<ul> <li> Active attendance in the exercise lessons and solving the examples <li> Passing the written and oral examination </ul>
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Recommended literature
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Baumann G. (1993). Mathematica for Theoretical Physics.. Springer-Verlag, Heidelberg.
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Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
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Brabec J., Martan F., Rozenský Z. (1989). Matematická analýza I. SNTL, Praha.
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Čechová M., Marková L. (1990). Proseminář z matematiky A, B. UP Olomouc.
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Dick S., Riddle A., Stein D. (1997). Mathematica in the Laboratory. Cambridge University Press.
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Jirásek F., Čipera S., Vacek M. (1989). Sbírka řešených příkladů z matematiky I., II. a III.. SNTL, Praha.
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Kolesárová A., Kováčová M., Záhonová V. (2004). Matematika I - Návody na cvičenia s programovým systémom Mathematica. Slovenská technická univerzita v Bratislave.
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Kolesárová A., Kováčová M., Záhonová V. (2002). Matematika II - Návody na cvičenia s programovým systémom Mathematica. Slovenská technická univerzita v Bratislave, 2002.. Slovenská technická univerzita v Bratislave.
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Kučera J., Horák Z. (1963). Tenzory v elektrotechnice a ve fyzice. Nakladatelství ČSAV, Praha.
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Kvasnica J. (1989). Matematický aparát fyziky. Academia, Praha.
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LEA S. M. (2004). Mathematics for Physicists. Brooks/Cole.
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Wolfram S. (2003). The Mathematica Book. Wolfram Media.
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Zimmerman, R. L., Olnes, F. I. (2002). Mathematica for Physics. Addison-Wesley.
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