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Lecturer(s)
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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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Methods of Written Work
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Learning outcomes
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Course in mathematics for physics - basic knowledge in vector calculus, differencial and integral calculus.
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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Student performance
<ul> <li> Active attendance in the exercise lessons and solving the examples </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. (2004). 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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