Romberg Integration: A Symbolic Approach with Mathematica

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2003

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.
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Software Engineering
(2005)
Department of Software Engineering was founded in 2005 as the first department in Ankara in Software Engineering. The recent developments in current technologies such as Artificial Intelligence, Machine Learning, Big Data, and Blockchains, have placed Software Engineering among the top professions of today, and the future. The academic and research activities in the department are pursued with qualified faculty at Undergraduate, Graduate and Doctorate Degree levels. Our University is one of the two universities offering a Doctorate-level program in this field. In addition to focusing on the basic phases of software (analysis, design, development, testing) and relevant methodologies in detail, our department offers education in various areas of expertise, such as Object-oriented Analysis and Design, Human-Computer Interaction, Software Quality Assurance, Software Requirement Engineering, Software Design and Architecture, Software Project Management, Software Testing and Model-Driven Software Development. The curriculum of our Department is catered to graduate individuals who are prepared to take part in any phase of software development of large-scale software in line with the requirements of the software sector. Department of Software Engineering is accredited by MÜDEK (Association for Evaluation and Accreditation of Engineering Programs) until September 30th, 2021, and has been granted the EUR-ACE label that is valid in Europe. This label provides our graduates with a vital head-start to be admitted to graduate-level programs, and into working environments in European Union countries. The Big Data and Cloud Computing Laboratory, as well as MobiLab where mobile applications are developed, SimLAB, the simulation laboratory for Medical Computing, and software education laboratories of the department are equipped with various software tools and hardware to enable our students to use state-of-the-art software technologies. Our graduates are employed in software and R&D companies (Technoparks), national/international institutions developing or utilizing software technologies (such as banks, healthcare institutions, the Information Technologies departments of private and public institutions, telecommunication companies, TÜİK, SPK, BDDK, EPDK, RK, or universities), and research institutions such TÜBİTAK.

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Higher order approximations of an integral can be obtained from lower order ones in a systematic way. For 1-D integrals Romberg Integration is an example which is based upon the composite trapezoidal rule and the well-known Euler-Maclaurin expansion of the error. In this work, Mathematica is utilized to illustrate the method and the under lying theory in a symbolic fashion. This approach seems plausible for discussing integration in a numerical computing laboratory environment.

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computer engineering

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https://hdl.handle.net/20.500.14411/6366

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