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The Generalized Riemann Integral in R2

Conway, Mark
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142

Abstract Details

2018, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
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.
Eric Wingler, PhD (Advisor)
Jozsi Jalics, PhD (Committee Member)
Thomas Smotzer, PhD (Committee Member)
42 p.
Mathematics
Generalized Riemann; Analysis; Gauge integral; Henstock integration

Recommended Citations

Citations

  • Conway, M. (2018). The Generalized Riemann Integral in R2 [Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142

    APA Style (7th edition)

  • Conway, Mark. The Generalized Riemann Integral in R2. 2018. Youngstown State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142.

    MLA Style (8th edition)

  • Conway, Mark. "The Generalized Riemann Integral in R2." Master's thesis, Youngstown State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527853827019142

    Chicago Manual of Style (17th edition)

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This open access ETD is published by Youngstown State University and OhioLINK.