Romberg integration: A symbolic approach with mathematica

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

2d polynomial interpolation: A symbolic approach with mathematica

This paper extends a previous work done by the same authors on teaching 1d polynomial interpolation using Mathematica [1] to higher dimensions. In this work, it is intended to simplify the the theoretical discussions in presenting multidimensional interpolation in a classroom environment by employing Mathematica's symbolic properties. In addition to symbolic derivations, some numerical tests are provided to show the interesting properties of the higher dimensional interpolation problem. Runge's phenomenon was displayed for 2d polynomial interpolation

Symbolic polynomial interpolation using Mathematica

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

Selection of steady states in planar Darcy convection

The planar natural convection of an incompressible fluid in a porous medium is considered. We study the selection of steady states under temperature perturbations on the boundary. A selection map is introduced in order to analyze the selection of a steady state from a continuous family of equilibria which exists under zero boundary conditions. The results of finite-difference modeling for a rectangular enclosure are presented

An impulsive ratio-dependent predator-prey system with diffusion

We investigate the predator-prey system with diffusion, when biological and environmental parameters are assumed to change in periodical manner over time. The system is affected by impulses which can be considered as a control. Conditions for the permanence of the predator-prey system and for the existence of a unique globally stable periodic solutions are obtained

The effect of thrombosis-related laboratory values on mortality in COVID-19 infection

OBJECTIVE: COVID-19 may cause thrombosis in both venous and arterial systems. Familiarity with the signs and symptoms of thrombosis and its treatment is essential in treating COVID-19 infection and its complications. D-Dimer and mean platelet volume (MPV) are measurements related to the development of thrombosis. This study investigates whether MPV and D-Dimer values could be used to determine the risk of thrombosis and mortality in the COVID-19 early stages. PATIENTS AND METHODS: 424 patients who were COVID-19 positive, according to the World Health Organization (WHO) guidelines, were randomly and retrospectively included in the study. Demographic and clinical characteristics such as age, gender, and length of hospitalization were obtained from the digital records of participants. Participants were divided into living and deceased groups. The patients’ biochemical, hormonal, and hematological parameters were analyzed retrospectively. RESULTS: White blood cells (WBC), neutrophils, and monocytes were significantly different in the two groups (p-value <0.001), and their values were lower in the living group than in the deceased group. MPV median values did not differ according to prognosis (p-value = 0.994). While the median value was 9.9 in the survivors, it was 10 in the deceased. Creatinine, procalcitonin, ferritin, and the number of hospitalization days in living patients were significantly lower than in patients who died (p-value <0.001). Median values of D-dimer (mg/L) differ according to prognosis (p-value <0.001). While the median value was 0.63 in the survivors, it was found as 438 in the deceased. CONCLUSIONS: Our results did not show any significant relationship between the mortality of COVID-19 patients and their MPV levels. However, a significant association between D-Dimer and mortality in COVID-19 patients was observed