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Mathematics for Electromagnetism
Rára, Michael ; Spousta, Jiří (referee) ; Doupovec, Miroslav (advisor)
The goal of this thesis is the description of elektromagnetism by means of selected parts of mathematics, in particular tensors, vector fields, integral calculus and integral theorems. Maxwell's equations will be derived by means of these notions in integral form, differential form and tensor form, we also show usefulness of tensor form of these equations.
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Vector fields on spheres
Strakoš, Filip ; Salač, Tomáš (advisor) ; Golovko, Roman (referee)
This thesis deals with partial results concerning the problem of existence of vector fields on spheres. The proof of the Hairy Ball Theorem is given using the tools of the the- ory of characteristic classes. Basic notions of algebraic topology are stated in order to define the Euler class. Its definition is followed by the computation of the Euler charac- teristic class for the tangent bundle of even-dimensional sphere. In the rest of the text, the method of construction of vector fields on spheres using the orthogonal multiplica- tion is explained and the Radon-Hurwitz-Eckmann Theorem is proved. A brief historical background of the existence of the finite-dimensional real division algebras is mentioned at the end.
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Flexible Moment Invariant Bases for 2D Scalar and Vector Fields
Bujack, R. ; Flusser, Jan
Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions. In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and\npresent superior bases that are optimal with respect to all three criteria for both scalar and vector fields.
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Mathematics for Electromagnetism
Rára, Michael ; Spousta, Jiří (referee) ; Doupovec, Miroslav (advisor)
The goal of this thesis is the description of elektromagnetism by means of selected parts of mathematics, in particular tensors, vector fields, integral calculus and integral theorems. Maxwell's equations will be derived by means of these notions in integral form, differential form and tensor form, we also show usefulness of tensor form of these equations.
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