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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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Tensors and their applications in mechanics
Adejumobi, Mudathir ; Doupovec, Miroslav (referee) ; Tomáš, Jiří (advisor)
The tensor theory is a branch of Multilinear Algebra that describes the relationship between sets of algebraic objects related to a vector space. Tensor theory together with tensor analysis is usually known to be tensor calculus. This thesis presents a formal category treatment on tensor notation, tensor calculus, and differential manifold. The focus lies mainly on acquiring and understanding the basic concepts of tensors and the operations over them. It looks at how tensor is adapted to differential geometry and continuum mechanics. In particular, it focuses more attention on the application parts of mechanics such as; configuration and deformation, tensor deformation, continuum kinematics, Gauss, and Stokes' theorem with their applications. Finally, it discusses the concept of surface forces and stress vector.
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Tensors and their geometrical and mechanical applications
Kunz, Daniel ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
In this thesis I describe construction of tensor algebra and its following usage of this magnificent structure for description of curved surfaces. This structure can be used in geometry or for example in mechanic. The thesis is focused on clear construction and if it is possible than to sustain visual aspect of current problem. Main task of this thesis was got the feel of tensor algebra and its construction and then use it on tasks in physic and mechanic.
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Tensors and their applications in mechanics
Adejumobi, Mudathir ; Doupovec, Miroslav (referee) ; Tomáš, Jiří (advisor)
The tensor theory is a branch of Multilinear Algebra that describes the relationship between sets of algebraic objects related to a vector space. Tensor theory together with tensor analysis is usually known to be tensor calculus. This thesis presents a formal category treatment on tensor notation, tensor calculus, and differential manifold. The focus lies mainly on acquiring and understanding the basic concepts of tensors and the operations over them. It looks at how tensor is adapted to differential geometry and continuum mechanics. In particular, it focuses more attention on the application parts of mechanics such as; configuration and deformation, tensor deformation, continuum kinematics, Gauss, and Stokes' theorem with their applications. Finally, it discusses the concept of surface forces and stress vector.
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Tensors and their geometrical and mechanical applications
Kunz, Daniel ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
In this thesis I describe construction of tensor algebra and its following usage of this magnificent structure for description of curved surfaces. This structure can be used in geometry or for example in mechanic. The thesis is focused on clear construction and if it is possible than to sustain visual aspect of current problem. Main task of this thesis was got the feel of tensor algebra and its construction and then use it on tasks in physic and mechanic.
|
|
|
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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