Browsing by Author "Ergenç, Tanıl"

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Citation - Scopus: 0
Romberg integration: A symbolic approach with mathematica
(Springer Verlag, 2003) Yazici,A.; Ergenç,T.; Altas,I.; Mathematics; Software Engineering
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 underlying theory in a symbolic fashion. This approach seems plausible for discussing integration in a numerical computing laboratory environment. © Springer-Verlag Berlin Heidelberg 2003.
Romberg Integration: a Symbolic Approach With Mathematica
(2003) Yazıcı, Ali; Ergenç, Tanıl; Altaş, İrfan; Mathematics; Software Engineering
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.
Citation - Scopus: 2
Symbolic polynomial interpolation using mathematica
(Springer Verlag, 2004) Yazici,A.; Altas,I.; Ergenc,T.; Mathematics; Software Engineering
This paper discusses teaching polynomial interpolation with the help of Mathematica. The symbolic power of Mathematica is utilized to prove a theorem for the error term in Lagrange interpolating formula. Derivation of the Lagrange formula is provided symbolically and numerically. Runge phenomenon is also illustrated. A simple and efficient symbolic derivation of cubic splines is also provided. © Springer-Verlag Berlin Heidelberg 2004.