Diferenciālformu elementi
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Latvijas Universitāte
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Abstract
Darbs veidots kā metodiskais materiāls bakalaura līmeņa studentiem par diferenciāformām. Tajā tiek aplūkots formas un diferenciālformas jēdziens, izmantojot uzdevumus, piemērus un ģeometriskas interpretācijas. Izvērstas būtiskākās diferenciālformu operācijas – ārējais reizinājums, diferenciālis un integrālis. Darbā aprakstīta arī formu saistība ar tenzoriem. Darba beigās tiek definēta un pierādīta vispārīgā Stoksa teorēma, kā arī norādīti tās pielietojumi.
Darba apjoms – 104 lpp., 1 tabula, 23 attēli un 2 pielikumi.
Atslēgvārdi: forma, diferenciālforma, tenzors, Stoksa teorēma
The paper is developed as a methodological material for bachelor's students about differential forms. The concept of a form and a differential form is introduced through excersises, examples and geometrical interpretations. The most important operators – wedge product, differential and integral – are expanded. Additionally, the connection between the forms and the tensors is explained. The final part of the paper explores general Stokes theorem: its definition, proof and aplications. The paper contains 104 pages, 1 table, 23 figures and 2 appendixes. Key phrases: form, differential form, tensor, Stokes theorem
The paper is developed as a methodological material for bachelor's students about differential forms. The concept of a form and a differential form is introduced through excersises, examples and geometrical interpretations. The most important operators – wedge product, differential and integral – are expanded. Additionally, the connection between the forms and the tensors is explained. The final part of the paper explores general Stokes theorem: its definition, proof and aplications. The paper contains 104 pages, 1 table, 23 figures and 2 appendixes. Key phrases: form, differential form, tensor, Stokes theorem