ABSTRACT This paper discusses discusses the preconditioner for solving the linear system Ax = b, where A is of the form M-matrix, which is a review of the Zhuan-De Wang and Ting-Zhu Huang paper [Applied Mathematics Letters, 19 : 1029 − 1036 (2006)]. Numerical experiments using some sizes of A show that the convergence rate of Jacobi and Gauss-Seidel type methods can be increased using t…
ABSTRACT This final project discusses how to obtain a polynomial solution of linear Fredhlom integro-differential equation with constant coefficients using a matrix method. The linear Fredhlom integro-differential equation with constant coefficients and its initial-boundary conditions are tranformed into a matrix, resulting a system of linear equations. Polynomial solutions of linear Fredh…
ABSTRACT We discuss the application of the least square and weighted least square methods to determine the amount of fuel consumption at a given distance, in the use of vehicles in and out of town, at the same time mathematical models is also used. Computational examples using real data show that the solution given by the weighted least squares method to a mathematical model of gasoline c…
ABSTRACT This final project discusses a goal programming technique for security rostering. The goal programming used is the weighted. This technique is implemented to solve a case study in a real life problem of security rostering in a construction company. The results of computation with Lingo show that security rostering by goal programming is better than the manual rostering. Keywords:…
ABSTRACT This article discusses the extension of Newton’s method derived from the Taylor expansion, where the curve is approached by a tangent line of the parabola is called the parabolic method. Analytically shown that the iterative methods have the order of convergence cubic and for each iteration, so it is more effective than the Newton’s method. Furthermore, computational results s…
In this thesis we discuss the diagram forms of semigroup presentations and . The discussion starts with the word-word outlines of semigroup presentations and . Then it is proceeded to make a diagram of word-word description obtained. All of characteristics are expressed in the form of a semigroup diagram theorem. The discussion in this article refers to Guba, V. & M. Sapir. 1996. Diag…
This research purposed to produced the mathematics learning devices based on problem based learning on social arithmetic material for VII grade students of SMP/MTs. Learning devices in this research are syllabus, Lesson Plans, and Student’s Worksheet. The research method used is the 4D models which consists of the stage define, design, development dan disseminate, but in this research only ca…
This research is motivated by the limited mathematics learning tools that are in accordance with the 2013 Curriculum. The purpose of this study is to produce products in the form of learning tools that are Syllabus, RPP, and Student Activity Sheet (LAS) by using discovery learning models in the material of Quadrilateral and Triangle VII class of SMP/MTs . The development model used in this stud…
The background of this research is the difference between the expected achievement and the achieved by students of class VIII4 SMP Negeri 8 Pekanbaru. The proposes of this research are to improve the learning process, to increase mathematics achievement from the students, and to increase student percentage that reaches Minimum Mastery Criteria (MMC) with applied problem based learning model. Th…
This final project discusses the predator-prey model with three-order interactions using the Routh-Hurwitz criteria. This model uses a nonlinear differential equation system from the classical predator-prey model. The observed model consists of four equilibrium points. Analysis for the model is carried out at the non-negative equilibrium point using the Routh-Hurwitz criteria. Then simulat…
This final project studies the global asymptotic stability of a Holling-Tanner predator-prey model using Holling type II. The global asymptotic stability is investigated using the Lyapunov method based on the equilibrium point that has been obtained. This final project is a review of articles of Lisena [Mathematical Methods in the Applied Sciences, 41 (2017), 1-12]. Keywords: Predator-prey…
This research is a class action research that aims to improve the learning process and mathematics learning outcomes through the implementation of the Problem Based Learning (PBL) model. The subjects of this research were VIII.7 grade students of SMP Negeri 5 Pekanbaru in the academic year 2019/2020, which total of participants are 38 students, consists of 20 male students and 18 female student…
This research was conducted due to limited mathematics learning devices that corresponds to The 2013 Curriculum. This research aims to produce learning devices by Problem Based Learning (PBL) model on Linear Program material of class XI. The development model used is 4-D that consist of define, design, develop, and disseminate. The research instrument used is validity device and practicality de…
Penelitian ini dilatarbelakangi oleh rendahnya kemampuan pemecahan masalah matematis (KPMM) siswa SMA Negeri 8 Pekanbaru. Tujuan penelitian ini adalah: (1) mendeskripsikan perbedaan KPMM siswa yang mengikuti pembelajaran melalui model Problem Based Learning (PBL) dengan siswa yang mengikuti pembelajaran biasa dengan pendekatan saintifik; (2) mengetahui peningkatan KPMM siswa yang mengikuti pemb…
The background of this research is the low ability of mathematical problem solving skill of students class X SMA Negeri 8 Pekanbaru. The purposes of this research are 1) to describe the difference of mathematical problem solving skill of students who study through PBL model with student who study through conventional learning with scientific approaching; 2) to examine the improvment of mathemat…
This final project discusses the epidemic model of chickenpox disease with vaccination (SVEIR) which has two equilibrium points, namely disease-free and endemic equilibrium points. Analysis of the global stability of the equilibrium points is carried out using the Lyapunov function which shows that the spread is determined by basic reproduction numbers. Then the simulation is performed usi…
Analysis of predator-prey acarine models in trophic level is discussed in this final project. The system of differential equation of the predator-prey acarine model is used in each population. The model consists of three observed equilibrium points. The stability of the system around the equilibrium point is determined by the linearization method in order to obtain the characteristic equati…
The background of this research is the difference between the expected achievement and the achieved by students of class XI MIA 1 MA Muhammadiyah Pekanbaru. The proposes of this research are to improve the learning process and to increase mathematics achievement from the students with applied discovery learning model. The form of this research is a class action research which is carried out in …
This research is a classroom action research (CAR) that aims to find out the improvement of mathematics learning outcomes through the application of Think Pair Square (TPS) Type Cooperative learning. The subjects of this study were Class VII-A students of SMP Negeri 1 Bangkinang Kota in the odd semester of the academic year 2019/2020, with a total of 30 students, consisting of 13 men and 17 wom…
The learning process is seen as one of the main factors that influence learning outcomes so that this research aims to improve learning process and students’ mathematics learning achievement by applying Discovery Learning model. This research is a classroom action research with two cycles. The research instruments used are mathematical learning instruments (Syllabus, Lesson Plans, and Activit…