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Öğe MAPLE AS A TOOL FOR THE TEACHING OF CYCLOTOMIC POLYNOMIALS ELEMENTARILY(Drustvo Matematicara Srbije, 2023) Zahedi, Zahedi; Kamil, Anton Abdulbasah; Fajriana, Fajriana; Siswadi, Siswadi; Almir, Almira; Suparni, SarminCyclotomic polynomials are an interesting topic and play an important role for other topics in Number Theory. For special values of n, computing a cyclotomic polynomial is not difficult; this can be done by using properties of the polynomial. For a prime value of n, the polynomial can be written quickly. However, for values which are multiples of odd prime numbers, say 85 = 17 . 5, the task can be quite difficult if it must be done manually. The polynomial has 41 terms and the degree of 64. Software for cyclotomic polynomials is available; Maple for example, can solve the problem of cyclotomic polynomials very easily. However, understanding of how to compute polynomials is very important for a student in applying various properties of the cyclotomic polynomial. Here, we will use Maple to help students understand cyclotomic polynomials from the basic. Answer is not obtained directly but step-by-step using properties of the polynomial. So, Maple is used to simulate the process of obtaining the polynomial. Once the students grasp the skill, they will be able to use the software for advanced applications.Öğe Some Applications of Cubic Equations in Engineering(International Information and Engineering Technology Association, 2022) Zahedi; Kamil, Anton Abdulbasah; Irvan; Jelita; Amin, Harahap; Marwan, Affandi; Suparni, SarminCubic equations have many applications in engineering, three of them are discussed in this paper. There are many equations of states for real gases but the cubic equations are the simplest ones and are sufficiently accurate for a limited range of temperatures and pressures. Degree of dissociation of chemical equilibrium for carbon dioxide and water can be written as cubic equations. Slope of a simply supported beam loaded by a continuous load is also represented as a cubic equation. Cubic equations can be solved exactly using Cardano’s formula. They can also solve numerically; Newton-Raphson method is a popular choice. Although a cubic equation has three roots, only real roots are valid in real applications discussed in this paper. Even there may be only one root that can be used; two other roots will be discarded. There are many ways a cubic equation solved but the simplest one is to solve it manually using a scientific calculator. Software and programming languages are better if there are many equations to be solved repeatedly © 2022, Mathematical Modelling of Engineering Problems. All Rights Reserved.