The Generalized Riemann Integral in R<sup>2</sup>
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Youngstown State University / OhioLINK
2018
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-ysu15278538270191422021-08-03T07:07:09Z The Generalized Riemann Integral in R<sup>2</sup> Conway, Mark Mathematics Generalized Riemann Analysis Gauge integral Henstock integration In their undergraduate studies, new calculus students learn how to integrate a function using the Riemann integral. The Riemann integral is used in Mathematics and Engineering and is a fairly simple concept to understand. However, the Riemann integral has some drawbacks and limitations. These limitations include improper integrals, application of the Fundamental theorem of Calculus, and others that will be discussed. By using the generalized Riemann integral, we can eliminate these limitations by only slightly changing our definition of the Riemann integral. However, what has been written on it isn’t particularly easy to understand. Because of this, the theory is only taught at the higher undergraduate or graduate level. This paper will take a look at the generalized Riemann integral. Being a more general version of the standard Riemann integral, it is not subject to these restrictions. The focus of this paper will be in one and two dimensions, but the theory from there can be easily generalized into higher dimensions. In this paper we will look at the generalized Riemann integral and will show all the ways all in which it is more powerful than the standard Riemann integral taught in calculus courses. While showing that the generalized Riemann is superior, we will also break the theory down for both the one and two-dimensional cases in a more understandable way. 2018-06-04 English text Youngstown State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142 http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics Generalized Riemann Analysis Gauge integral Henstock integration |
| spellingShingle |
Mathematics Generalized Riemann Analysis Gauge integral Henstock integration Conway, Mark The Generalized Riemann Integral in R<sup>2</sup> |
| author |
Conway, Mark |
| author_facet |
Conway, Mark |
| author_sort |
Conway, Mark |
| title |
The Generalized Riemann Integral in R<sup>2</sup> |
| title_short |
The Generalized Riemann Integral in R<sup>2</sup> |
| title_full |
The Generalized Riemann Integral in R<sup>2</sup> |
| title_fullStr |
The Generalized Riemann Integral in R<sup>2</sup> |
| title_full_unstemmed |
The Generalized Riemann Integral in R<sup>2</sup> |
| title_sort |
generalized riemann integral in r<sup>2</sup> |
| publisher |
Youngstown State University / OhioLINK |
| publishDate |
2018 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142 |
| work_keys_str_mv |
AT conwaymark thegeneralizedriemannintegralinrsup2sup AT conwaymark generalizedriemannintegralinrsup2sup |
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1719454188657704960 |