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# SEMP

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Course: Seminar on electromagnetic field

Department/Abbreviation: OPT/SEMP

Year: 2021

Guarantee: 'RNDr. Ivo Vyšín, CSc.'

Annotation: Matematické základy Teorie elektromagnetického pole a Elektromagnetické optiky

Course review:
- Vector algebra and vector analysis in the Cartesian coordinate system. Overview of the vectors used in electromagnetic field theory, operations with vectors and matrices. Operations with scalar and vector functions, curve and surface integrals. - Operators of the functions. Hamilton operator, gradient of the scalar function, divergence and curl of the vector function, Laplace operator. Combination of operators. Operators of products of scalar and vector functions, operators of the position vector. - Integral theorems. Gauss theorem, Stokes theorem, Green's theorem, its forms. - Non-Cartesian coordinates. Operators in non-Cartesian orthogonal coordinate systems. Spherical and cylindrical coordinate system. - Basic vectors for describing the electromagnetic field. Maxwell's equations, differential and integral forms. Material equations (constitutive relations), boundary conditions and their derivation. Definiton of the specific types of electromagnetic fields. - Electrostatic field. Scalar potential, Poisson equation and its solution. Solution of the multipole electrostatic fields. - Selected problems of quasistationary field. Linear current RLC circuits. Theory of skin effect. - Solutions of non-stationary electromagnetic field using the Hertz potentials. Solutions of the oscillating dipole field. - Solution of the basic problems of non-stationary electromagnetic fields propagation. Homogeneous and generalized wave equations, their derivation and solutions. Properties of the solutions, energy of the electromagnetic waves calculation. - Application of the program Mathematica 9.0 in the problems of electromagnetic fields solution. Mathematica built-in functions.