Konformikuvauksista

Tarkastelen työssä konformikuvauksia, sekä niihin liittyviä tärkeitä tuloksia. Esitän Riemannin kuvauslauseen todistuksen sekä todistan Schwarzin ja Christoffelin kaavan, joka karakterisoi konformikuvaukset puolitasolta monikulmiolle. Lisäksi tarkastelen työssä konformikuvausten soveltamista muutami...

Täydet tiedot

Bibliografiset tiedot
Päätekijä: Jokiniemi, Lotta
Muut tekijät: Matemaattis-luonnontieteellinen tiedekunta, Faculty of Sciences, Matematiikan ja tilastotieteen laitos, Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylän yliopisto
Aineistotyyppi: Pro gradu
Kieli:fin
Julkaistu: 2016
Aiheet:
Linkit: https://jyx.jyu.fi/handle/123456789/51375
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author Jokiniemi, Lotta
author2 Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics University of Jyväskylä Jyväskylän yliopisto
author_facet Jokiniemi, Lotta Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics University of Jyväskylä Jyväskylän yliopisto Jokiniemi, Lotta Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics University of Jyväskylä Jyväskylän yliopisto
author_sort Jokiniemi, Lotta
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description Tarkastelen työssä konformikuvauksia, sekä niihin liittyviä tärkeitä tuloksia. Esitän Riemannin kuvauslauseen todistuksen sekä todistan Schwarzin ja Christoffelin kaavan, joka karakterisoi konformikuvaukset puolitasolta monikulmiolle. Lisäksi tarkastelen työssä konformikuvausten soveltamista muutamiin fysiikan ongelmiin virtausmekaniikan, termodynamiikan ja sähköstatiikan aloilla. In the thesis I study conformal mappings and some important results related to them. I introduce a proof for Riemann mapping theorem and prove the Schwarz-Christoffel formula, which characterizes the conformal mappings from the half plane to a polygon. In addition, I study applying the conformal mappings to some physical problems in the fields of fluid mechanics, thermodynamics, and electrostatics.
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spellingShingle Jokiniemi, Lotta Konformikuvauksista Konformikuvaus Riemannin kuvauslause Schwarzin ja Christoffelin kaava Matematiikka Mathematics 4041
title Konformikuvauksista
title_full Konformikuvauksista
title_fullStr Konformikuvauksista Konformikuvauksista
title_full_unstemmed Konformikuvauksista Konformikuvauksista
title_short Konformikuvauksista
title_sort konformikuvauksista
title_txtP Konformikuvauksista
topic Konformikuvaus Riemannin kuvauslause Schwarzin ja Christoffelin kaava Matematiikka Mathematics 4041
topic_facet 4041 Konformikuvaus Matematiikka Mathematics Riemannin kuvauslause Schwarzin ja Christoffelin kaava
url https://jyx.jyu.fi/handle/123456789/51375 http://www.urn.fi/URN:NBN:fi:jyu-201609154112
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