Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Conference Object Measure on Time Scales With Mathematica(Springer Verlag, 2006) Ufuktepe, Ünal; Yantır, AhmetIn this paper we study the Lebesgue Delta-measure on time scales. We refer to [3, 4] for the main notions and facts from the general measure and Lebesgue Delta integral theory. The objective of this paper is to show how the main concepts of Mathematica can be applied to fundamentals of Lebesgue Delta- and Lebesgue Delta- measure on an arbitrary time scale and also on a discrete time scale whose rule is given by the reader. As the time scale theory is investigated in two parts, by means of alpha and rho operators, we named the measures on time scales by the set function DMeasure and NMeasure respectively for arbitrary time scales.Article An Application With Webmathematica(Springer Verlag, 2003) Ufuktepe, ÜnalThere have been many technological dawns in the last 30 years, during which the desktop computer and the Internet have been developed. The importance of Internet in education, particularly using its Web is a well-recognized fact. A wealth of resources and techniques now exist which serve as a source both for exciting examples of new teaching practices, as well as easily accessible methods for adoption into various formats of teaching and learning. Internet technology allow teachers and students keep up with their minds. It let them try their ideas as soon as they come up with them. Generally, students appreciate the convenience, choice, and flexibility that an online courses offers. Instructional designers value the standardized framework and flexibility. WebMathematica is a web-based technology developed by Wolfram Research that allows the generation of dynamic web content with Mathematica. With this technology, the distance education students should be able to explore and experiment with the mathematical concepts. In this paper we will elucidate the pedagogical issues in the application of Hamiltonian systems in the webMathematica for the distance learning environment and the shape of the future "classroom" as well as relevant educational strategies towards improving mathematics education.Article Citation - WoS: 2Citation - Scopus: 1Basic Calculus on Time Scale With Mathematica(Springer Verlag, 2003) Yantır, Ahmet; Ufuktepe, ÜnalMathematical modeling of time dependent systems are always interesting for applied mathematicians. First continuous and then discrete mathematical modeling are built during the mathematical development from ancient to the modern times. By the discovery of the time scales, the problem of irregular controlling of time dependent systems is solved in 1990's. In this paper, we explain the derivative of functions on time scales and the solutions of some basic calculus problems by using Mathematica. © Springer-Verlag Berlin Heidelberg 2003.Article Citation - WoS: 17Citation - Scopus: 19Lebesgue-Stieltjes Measure on Time Scales(TUBITAK, 2009) Deniz, Aslı; Ufuktepe, ÜnalThe theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes Δ and ▶-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes Δ-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes Δ-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes Δ-integral.Conference Object E-Calculus at Iztech(Springer Verlag, 2006) Ufuktepe, Ünal; Ufuktepe, Günnur; Deniz, Aslı; Dündar, VeliIn today's new economy, characterized by industrial revolutions, globalization and information technology changes traditional classroom and teaching methods. Calculus is the basic course for the fresher at university. Mathematics has a negative development at universities and colleges. The number of students taking mathematics courses and those successfully passing the exams are rapidly decreasing. To overturn this negative development, it may be necessary to teach in a different way. This is where new technology could play an important role. We create a web browser environment by using the webMathematica, which is a new technology based on Java Server Page, Tomcat and Mathematica, in learning calculus. The modules consist of topic modules linked with case study modules, to help learn calculus and see it in context. The aim of our project is to use new technology to present mathematics on the web, and create a pilot course for students and teachers available free on the web. The heart of our approach is the development of mathematical power: understanding, using, and appreciating mathematics. Students can reach any documents for calculus and solve their problems with webMathematica to check whether their results are correct or not. It is possible to reach our page at the following URL address: http://galois.iyte.edu.tr/calculus.Article Citation - WoS: 2Citation - Scopus: 2Applying Mathematica and Webmathematica To Graph Coloring(Elsevier Ltd., 2007) Ufuktepe, Ünal; Bacak, GökşenThis paper analyzes some graph issues by using the symbolic program Mathematica and its version for the Web, webMathematica. In particular, we consider the problem of graph coloring: the assignment of colors to the vertices/edges of the graph such that adjacent vertices/edges are colored differently. In addition, we address the problem of obtaining the tenacity of binomial trees with Mathematica. Finally, we describe briefly an example of the application of our software to a scheduling problem.Conference Object Citation - WoS: 3Citation - Scopus: 3Mathematica Applications on Time Scales(Springer Verlag, 2005) Yantır, Ahmet; Ufuktepe, ÜnalStefan Hilger introduced the calculus on time scales in order to unify continuous and discrete analysis in 1988. The study of dynamic equations is an active area of research since time scales unifies both discrete and continuous processes, besides many others. In this paper we give many examples on derivative and integration on time scales calculus with Mathematica. We conclude with solving the first order linear dynamic equation N Δ(t) = N(t), and show that the solution is a generalized exponential function with Mathematica.Conference Object Citation - WoS: 1Citation - Scopus: 2Applications of Graph Coloring(Springer Verlag, 2005) Ufuktepe, Ünal; Bacak, GökşenA graph G is a mathematical structure consisting of two sets V(G) (vertices of G) and E(G) (edges of G). Proper coloring of a graph is an assignment of colors either to the vertices of the graphs, or to the edges, in such a way that adjacent vertices / edges are colored differently. This paper discusses coloring and operations on graphs with Mathematica and webMathematica. We consider many classes of graphs to color with applications. We draw any graph and also try to show whether it has an Eulerian and Hamiltonian cycles by using our package ColorGArticle Citation - WoS: 1Graph Coloring With Webmathematica(Springer Verlag, 2004) Ufuktepe, Ünal; Bacak, Gökşen; Beşeri Sevim, TinaColoring of a graph is an assignment of colors either to the edges of the graph G, or to vertices, or to maps in such a way that adjacent edges/vertices/maps are colored differently. We consider the problem of coloring graphs by using webMathematica which is the new web-based technology. In this paper, we describe some web-based interactive examples on graph coloring with webMathematica.Article Citation - Scopus: 1Inequalities for Buckling of a Clamped Plate(Taylor and Francis Ltd., 2002) Ufuktepe, Ünal; Mchale, K. P.We study the eigenvalue problems for the buckling of a clamped plate. The previous upper bound on low eigenvalues due to Payne, Pólya, and Weinberger, and Rile and Yeh are reviewed. Using methods similar to those used in bounding ratios of eigenvalues of the membrance problem, bounds for ratios of eigenvalues are found for the buckling of a clamped piate