Mathematics Commons^™

Integration Bar, Erik Talvila

Journal of Humanistic Mathematics

In this humourous story, the narrator is dragged by their friend to a crazy bar for a late night of wild drinking and dancing. Except, the drinking is replaced with computing integrals.

The Art Of Analysis, Christopher Hammond

Open Educational Resources

Christopher Hammond, Professor of Mathematics at Connecticut College, has written an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply …

Numerical Integration Through Concavity Analysis, Daniel J. Pietz

Rose-Hulman Undergraduate Mathematics Journal

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

Area Of Irregular Shaped Roof, Omar Alkhawaldeh

Undergraduate Journal of Mathematical Modeling: One + Two

This project makes use of calculus, specifically integration, to find the exact area of a roof garden to minimize the cost of material used in flooring it. Since the roof is of irregular shape, it is divided into four sections, the integral of each section is taken, and a relationship between the integrals is generated. Positive results are found, and the data reveal that the area of the grass floor is 175.3 m² while the area of the wooden floor is 23.4 m² with the total price being 2472 US dollars.

Launch-Explore-Summarize In High School Calculus, Nate Mattis

Honors Theses

Current research on high school calculus instruction indicates that students often possess a procedural knowledge of differentiation and integration as opposed to a conceptual knowledge (Orton, 1983; Ferrini-Mundy & Graham, 1994). Given the prominence of traditional lecture and textbook-based calculus classes in the United States, students are not always given the opportunity to expand their conceptual knowledge of essential calculus concepts. This project introduces calculus students to a more active and communal method of teaching: Launch-Explore-Summarize (LES) (CMP, n.d.). This methodology places students at the center of their learning and emphasizes inquiry-based thinking during a class. Specifically, two LES lessons …

Measure And Integration, Jose L. Menaldi

Mathematics Faculty Research Publications

Abstract measure and integration, with theory and (solved) exercises is developed. Parts of this book can be used in a graduate course on real analysis.

Distributions And Function Spaces, Jose L. Menaldi

Mathematics Faculty Research Publications

Beginning with a quick recall on measure and integration theory, basic concepts on (a) Function Spaces, (b) Schwartz Theory of Distributions, and (c) Sobolev and Besov Spaces are developed. Moreover, only a few number of (solved) exercises are given. Parts of this book can be used in a graduate course on real analysis.

Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett

Analysis

No abstract provided.

The Study Of Middle School Mathematics And Science Teachers' Practices, Perceptions, And Attitudes Related To Mathematics And Science Integration, Eliza Leszczynski

Theses, Dissertations and Culminating Projects

The purpose of this qualitative study was to investigate the nature of mathematics and science connections made by sixth and seventh grade mathematics and science teachers in their classrooms. This study also examined the extent to which these connections represented mathematics and science integration and described the teachers’ perceptions of and attitudes about mathematics and science integration. The primary data sources included classroom observations and teacher interviews.

Findings suggested that teacher practices in making mathematics and science connections in the classroom incorporated many of the characteristics of integrated instruction presented in the literature. Teacher attitudes toward integration were found to …

The Fifth Function Of University: “Neutrosophic E-Function” Of Communication-Collaboration-Integration Of University In The Information Age, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The study is based on the following hypothesis with practical foundation: - Premise 1 - if two members of university on two continents meet on the Internet and initiate interdisciplinary scientific communication; - Premise 2 - subsequently, if within the curricular interests they develop an academic scientific collaboration; - Premise 3 - if the so-called collaboration integrates the interests of other members of the university; - Premise 4 - finally, if the university allows, accepts, validates and promotes such an approach; - Conclusion: then it means the university as a system (the global academic system) has, and it is, exerting …

Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec

Mathematics and Statistics Faculty Research & Creative Works

We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality. © ELEMENT, Zagreb.

The Torsion Angle Of Random Walks, Mu He

Masters Theses & Specialist Projects

In this thesis, we study the expected mean of the torsion angle of an n-step
equilateral random walk in 3D. We consider the random walk is generated within a confining sphere or without a confining sphere: given three consecutive vectors ^→e₁ , ^→e₂ , and ^→e₃ of the random walk then the vectors ^→e₁ and ^→e₂ define a plane and the vectors ^→e₂ and ^→e₃ define a second plane. The angle between the two planes is called the torsion angle of the three vectors. Algorithms are …

Orthogonal Systems In L^2 Spaces Of A Vector Measure, Eduardo Jiménez Fernández

Turkish Journal of Mathematics

Let m:\Sigma \to X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m-orthogonal system in the space L^2(m) of square integrable functions with respect to m. If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to this vector measure. On the other hand, if the vector measure is fixed, then we can obtain sequences of orthogonal functions using the Kadec-Pelczynski disjointification method.

"Toward Integration: From Quantitative Biology To Mathbio-Biomath?", Pat Marsteller, Lisette G. De Pillis, Ann Findley, Karl Joplin, John Pelesko, Karen Nelson, Katerina Thompson, David Usher, Joseph Watkins

All HMC Faculty Publications and Research

In response to the call of BIO2010 for integrating quantitative skills into undergraduate biology education, 30 Howard Hughes Medical Institute (HHMI) Program Directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI-funded mini-grant, led by Karl Joplin of East Tennessee State University, and support in institutional HHMI grants at Emory and University of Delaware, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative …

Finding The Area Of An Irregularly Shaped Room, Justin Walls

Undergraduate Journal of Mathematical Modeling: One + Two

This experiment utilized integration in a practical sense by determining the floor area of an irregularly shaped room. By taking the integral summation of three sections formed from semi-circles, the desired areas as well as positive results were found. The final data determined that the floor area of the irregularly shaped room was around 580 square feet.

Convergence And The Lebesgue Integral, Ryan Vail Thomas

Graduate Theses/Dissertations

In this paper, we examine the theory of integration of functions of real variables. Background information in measure theory and convergence is provided and several examples are considered. We compare Riemann and Lebesgue integration and develop several important theorems. In particular, the Monotone Convergence Theorem and Dominated Convergence Theorem are considered under both pointwise convergence and convergence in measure.

Sur Les Logarithmes Des Nombres Négatifs Et Imaginaires, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Considérations Sur Quelques Formules Intégrales Dont Les Valeurs Peuvent Être Exprimeés, En Certains Cas, Par La Quadrature Du Cercle, Leonhard Euler

All Works by Eneström Number

No abstract provided.

De Integralibus Quibusdam Inventu Difficillimis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

De Integrationibus Difficillimis, Quarum Integralia Tamen Aliunde Exhiberi Possunt, Leonhard Euler

All Works by Eneström Number

No abstract provided.

De Insigni Usu Calculi Imaginariorum In Calculo Integrali, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Formae Generales Differentialium, Quae, Etsi Nulla Substitutione Rationales Reddi Possunt. Tamen Integrationem Per Logarithmos Et Arcus Circulares Admittunt, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Ulterior Disquitio De Formulis Integralibus Imaginariis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Integratio Succincta Formulae Integralis Maxime Memorabilis ∫∂Z/((3±Zz)∙(1±3Zz)1/3), Leonhard Euler

All Works by Eneström Number

No abstract provided.

Integratio Formulae Differentialis Maxime Irrationalis, Quam Tamen Per Logarithmos Et Arcus Circulares Expedire Licet, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Evolutio Formulae Integralis ∫∂Z(3+Zz)/((1+Zz)∙(1+6Zz+Z4)1/4) Per Logarithmos Et Arcus Circulares, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Specimen Integrationis Abstrusissimae Hac Formula ∫∂X/((1+X)∙(2Xx–1)1/4) Contentae, Leonhard Euler

All Works by Eneström Number

No abstract provided.

De Formulis Differentialibus Angularibus Maxime Irrationalibus, Quas Tamen Per Logarithmos Et Arcus Circulares Integrare Licet, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Demonstratio Theorematis Insignis Per Coniecturam Eruti Circa Intagrationem Formulae ∫ ∂&Straightphi; Cos(I&Straightphi;)/(1+Aa–2ACos(&Straightphi;))N+1, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Memorabile Genus Formularum Differentialium Maxime Irrationalium Quas Tamen Ad Rationalitatem Perducere Licet, Leonhard Euler

All Works by Eneström Number

No abstract provided.