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Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Published by Universitas Negeri Gorontalo
ISSN : 20879393     EISSN : 27763706     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi is a national journal intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in the research. Euler disseminates new research results in all areas of mathematics and their applications. Besides research articles, the journal also receives survey papers that stimulate research in mathematics and its applications. The scope of the articles published in this journal deal with a broad range of mathematics topics, including: Mathematics Applied Mathematics Statistics and Probability Applied Statistics Mathematics Education Mathematics Learning Computational Mathematics Science and Technology
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 18 Documents
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Search results for , issue "EULER: Volume 11 Issue 2 December 2023" : 18 Documents clear
Komparasi Skema Numerik Euler, Runge-Kutta dan Adam-Basforth-Moulton untuk Menyelesaikan Solusi Persamaan Osilator Harmonik Resmawan Resmawan; Binti Mualifatul Rosydah; Rizka Putri Handayani
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.22420

Abstract

This article discusses the comparison of different numerical schemes to visualize the solution of 2nd-order differential equations. One-step methods such as the Euler method and the 4th-order Runge-Kutta method are combined with the 3rd-order Adam-Bashforth-Moulton method to solve the solution of 2nd-order differential equations. This combination of methods solves the Harmonic Oscillator equation, an 2nd-order differential equation widely applied in various oscillation contexts. The order of accuracy and order of approximation error are determined analytically. Finally, simulations are given with different steps for the three methods to confirm the behavior of the solution to the Harmonic Oscillator equation. The results show that the Euler method with the lowest order of accuracy has good accuracy at the beginning of the oscillation but not when time t is increased. The Runge-Kutta method, with the highest order of accuracy, shows excellent and consistent accuracy and solution stability, while the Adam-Bashforth-Moulton method, although it has a lower accuracy than the Runge-Kutta method of order 4, can be improved by choosing a one-step method with a high order of accuracy to approximate some of the required initial solutions. All three methods can provide approximation values with excellent accuracy and stability if a small step, h, is chosen, but this step can increase the time duration to display the solution. Thus, it is necessary to choose the right h according to the context of the equation and the method used to obtain accurate solutions with optimal time duration.
Model Course Review Horay : Upaya Meningkatkan Hasil Belajar Matematika Bentuk Aljabar Sri Rahayu Dangkua; Resmawan Resmawan; Siti Zakiyah
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.22448

Abstract

This research aims to improve students' mathematics learning outcomes in the Algebraic Form material using the Course Review Horay learning model. This study is a classroom action research (CAR) conducted in two cycles, involving students from SMP Negeri 1 Kabila as the research subjects. Each student is considered successful if their mathematics learning outcome test meets the minimum completeness criteria, which is 75. The research results show that in the first cycle, the completeness rate was 67.86% out of 28 students, and it increased in the second cycle, with 24 students achieving a completeness rate of 85.71%. This indicates that implementing the Course Review Horay learning model is believed to improve students' mathematics learning outcomes in the Algebraic Form material.
Modifikasi Garis Singgung Untuk Mempercepat Iterasi Pada Metode Newton Raphson Maxrizal Maxrizal
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.23094

Abstract

The Newton-Raphson method is one of the methods to find solutions or roots of nonlinear equations. This method converges faster than other methods and is more effective in finding doubles. In this study, it will be shown that the Newton-Raphson modification uses modifications to the tangent equation. The results show that for every nth iteration, the speed difference of Newton Raphson modification is __. Furthermore, the convergence of Newton Raphson is __, and for Newton Raphson modification is __.
Modifikasi Metode Big-M dan Analisis Sensitivitasnya untuk Optimasi Produksi Usaha Kecil Menengah Nurul Fadhilah; Bayu Prihandono; Yudhi Yudhi
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.23007

Abstract

UKM (Small and Medium Enterprises) X is a business that produces various types of peanut brittle. Rempeyek is suitable as a snack and is popular with children and adults. The production process of UKM X is related to the quantity of demand and availability of raw materials. Therefore, optimal production planning is needed for UKM X to meet customer demand and obtain maximum profits. The problem of production is modeled into linear programming with the method used, namely, the method of Big M. The Big-M method is used because, on the function of the barrier on the production target, there is an equation , so artificial variables must be added to its solution. In this study, a modification of the Big-M method is made, and at the completion stage, it uses iteration with the determinant algorithm of the order of two matrices. The calculation results obtained the maximum profit of UKM X in a week of Rs5.455.775 by producing 56 kg of peanuts, 20 kg of seeds, 16 kg of spinach, 23 kg of tempe, and 60 kg of shrimp to meet customer requirements and utilize the availability of raw materials. Subsequently, sensitivity analysis is performed on the target function coefficient and the right street constants of the barrier to determine how the change affects the optimal solution. The results show that the solution remains optimal when profits are in the interval obtained, but the maximum profit value changes with constant production. Based on the calculation results, raw material supplies remain optimal when the change value is within the interval obtained.
Analisis Kesalahan Mahasiswa dalam Menyelesaikan Permasalahan Aljabar Boolean Berdasarkan Teori Kastolan Dian Kartika Sari
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.22478

Abstract

Boolean algebra is a branch of mathematics that has many applications, especially in computer science, engineering, and information technology. Boolean algebra is one of the materials taught in discrete mathematics courses. However, students still feel that this material is quite difficult. Therefore, the solution to this problem is to analyze/describe the difficulties students feel. This research aims to describe students' mistakes in solving Boolean algebra problems based on Castolan theory. This study uses a qualitative method. The research subjects were 43 Informatics Engineering students at the Telkom Institute of Technology Purwokerto 2022/2023. The data collection technique uses a Boolean algebra ability test. Data were analyzed based on the Castolan error procedure. The results of this research showed that the percentage of conceptual errors was 33%, the percentage of procedural errors was 23%, and the percentage of technical errors was 44%. Several factors that cause students to make mistakes when solving problems include: 1) Students' lack of understanding of the problems they face, so they become confused when trying to solve them; 2) Lack of accuracy in the calculation process, which causes errors in their answers; 3) Students' inability to convert problems into mathematical models; 4) Lack of student knowledge about the stages needed to solve problems. Lecturers can utilize the results of this research to develop more effective teaching strategies and support students in overcoming difficulties they may encounter.
Sistem Kriptografi Klasik Dengan Memanfaatkan Orde Dari Grup Titik Pada Kurva Eliptik Bentuk Montgomery Yanuar Bhakti Wira Tama; Muhammad Firdhausi Fahmi
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.23009

Abstract

Elliptic curve cryptography is one of the application fields of algebra and number theory concepts. One form of elliptic curve cryptography is Montgomery elliptic curve cryptography. In this paper, a method for a classical cryptographic system be formulated, consisting of encryption and decryption involving twenty-six alphabetical letters which are mapped to points on an elliptic curve by utilizing the order of the point group on the Montgomery elliptic curve. Several examples of implementation in simple cases are given to verify the results.
Analysis of Students' Errors in Solving HOTS Problems on Algebraic Materials Based on the Complexity Level of the Problem Based on Bloom's Theory Yulia Muliana; Abdillah Abdillah; Mahsup Mahsup; Syaharuddin Syaharuddin; Abdul-Lateef Olamide Ahmodu; Mohammed Muniru Iddrisu
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.23053

Abstract

Mathematics discusses a lot about various kinds of problems that contain numbers that are classified as Higher Order Thinking Skills (HOTS). Math HOTS questions require a high level of thinking to solve the problem. Based on Bloom's theory, HOTS consists of analyzing (C4), evaluating (C5), and creating (C6). This study aims to determine the level of student errors in solving HOTS questions based on Bloom's theory. This research uses mixed method research, which is a combination of qualitative and quantitative methods, where the stages of this research include instrument development, instrument validation, data collection, data analysis and interpretation. The sample of this study used 25 students of class VIII junior high school in Mataram City. Researchers gave 10 essay questions that had been validated by material experts to students as research instruments. The results showed that students' understanding in solving HOTS problems was still lacking. For the error rate, it was found that there were no students who could solve the creating (C6) section with a percentage of 100% error, analyzing (C4) section with a percentage of 60%, evaluating (C5) 24%, applying (C3) 16%, understanding (C2) 12%, and in the remembering (C1) section there were no students who made mistakes with a percentage of 0% error. The biggest error was found in the creating part (C6), where the most mistakes were made by women with an average score of 50.55.
Analisis Dinamik Model SIRC pada Transmisi Hepatitis B dengan Sirosis Hati Ririn Febriyanti; Bayu Prihandono; Mariatul Kiftiah
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.22761

Abstract

Hepatitis B is an infection of the liver that can cause liver cirrhosis. Liver cirrhosis can occur due to the formation of scar tissue in individuals who have prolonged hepatitis B. Transmission of hepatitis B can occur in two ways, namely horizontal and vertical. In this research, this problem is modeled in a mathematical model using the SIRC model, where the population is grouped into four sub-populations, namely susceptible (S), infected (I), cured or immune due to vaccination (R) and cirrhosis. liver (C). From the analysis, two equilibrium points were obtained, namely the disease-free equilibrium point the endemic equilibrium point  The basic reproduction number   is obtained using the Next Generation Matrix. The analysis results show that if , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if  , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if , this means that hepatitis B transmission in liver cirrhosis is influenced by contact between susceptible and infectious individuals. To support the results of the analytical analysis, numerical simulations are provided to describe the behavior of the SIRC model.

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