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The Riemann-Stieltjes integral: and some applications in complex analysis and probability theory
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-5130-1941
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The purpose of this essay is to prove the existence of the Riemann-Stieltjes integral. After doing so, we present some applications in complex analysis, where we define the complex curve integral as a special case of the Riemann- Stieltjes integral, and then focus on Cauchy’s celebrated integral theorem. To show the versatility of the Riemann-Stieltjes integral, we also present some applications in probability theory, where the integral generates a general formula for the expectation, regardless of its underlying distribution. 

Place, publisher, year, edition, pages
2014. , p. 41
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-89199OAI: oai:DiVA.org:umu-89199DiVA, id: diva2:719488
Educational program
Bachelor of Science in Physics and Applied Mathematics
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Examiners
Available from: 2014-06-18 Created: 2014-05-26 Last updated: 2024-02-06Bibliographically approved

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The Riemann-Stieltjes integral(857 kB)23671 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf