Browsing by Author "Ergenç, Tanıl"
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Article Romberg Integration: A Symbolic Approach with Mathematica(2003) Ergenç, Tanıl; Ergenç, Tanıl; Yazıcı, Ali; Mathematics; Software EngineeringHigher 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.Article Citation Count: 0Romberg integration: A symbolic approach with mathematica(Springer Verlag, 2003) Yazıcı, Ali; Ergenç, Tanıl; Altas,I.; Mathematics; Software EngineeringHigher 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.Article Citation Count: 2Symbolic polynomial interpolation using mathematica(Springer Verlag, 2004) Yazıcı, Ali; Ergenç, Tanıl; Ergenc,T.; Mathematics; Software EngineeringThis 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.