Control and Optimization
Mohammad Darvisahzadeh; Ahmad Shahvarani Semnani; Hassan Alamolhodaei,; Hassan Behzadi
Abstract
Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics. On ...
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Experiences of teaching Integral have indicated that the vast majorities of Iranian university students commit numerous errors while solving integral problems and have weak skills in this field; we might even say that they hide away from integral and consider it the nightmare of mathematics. On the other hand, Integral is the base of pure and applied mathematics for all students of science, especially engineering, which some of their lessons are dependent on it directly or indirectly, so it is important to pay attention to it. Through descriptive method-exposed factor, an exam has been conducted in the form of three questions, the first of which is consisted of 4 sections on fifty students from different fields, and then interviews were conducted with a few of those students about their answers in order to study the students' behaviors when solving integral problems and to determine the type of their errors. By analyzing the performance of students in this test, we can see that students often struggle with integral and mostly have a feeble performance in solving trigonometric integrals. They want to learn computational integral instead of how to conceptualize integral in their minds correctly. The error most committed by university students was procedural errors, which arise from using derivative instead of integral. Besides most of the mistakes happen in solving definite integrals, and calculating finite areas between two curves. This is due to a lack of understanding of integrals and a lack of information in other areas of mathematics.
Control and Optimization
Mostafa Nouri Jouybari; Yahya Talebi Rostami; Siyamak Firouzian
Abstract
In this study, $R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module, respectively. Scalar Product Graph of $M$, denoted by $G_R(M)$, is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in ...
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In this study, $R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module, respectively. Scalar Product Graph of $M$, denoted by $G_R(M)$, is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in $M$ are connected if and only if there exists $r$ belong to $R$ such that $a=rb$ or $b=ra$. This paper studies some properties of such weakly perfect graphs.
Control and Optimization
Mehdi Ahmadi; Hamid Esmaeili; R Erfanifar
Volume 1, Issue 2 , October 2016, , Pages 53-62
Abstract
In this paper, we suggest a fifth order convergence three-step method for solving system of nonlinear equations. Each iteration of the method requires two function evaluations, two first Fr\'{e}chet derivative evaluations and two matrix inversions. Hence, ...
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In this paper, we suggest a fifth order convergence three-step method for solving system of nonlinear equations. Each iteration of the method requires two function evaluations, two first Fr\'{e}chet derivative evaluations and two matrix inversions. Hence, the efficiency index is $5^{1/({2n+4n^{2}+\frac{4}{3}n^{3}})}$, which is better than that of other three-step methods. The advantages of the method lie in the feature that this technique not only achieves an approximate solution with high accuracy, but also improves the calculation speed. Also, under several mild conditions the convergence analysis of the proposed method is provided. An efficient error estimation is presented for the approximate solution. Numerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with the existing results.
