This nal project discusses how to nd the eigenvalues and eigenvectors of matrix trapezoidal fuzzy numbers. Trapezoidal fuzzy numbers are expressed as negative-positive denition. The goal is to determine the algebraic operations that are constructed on the result of multiplying the trapezoidal fuzzy numbers, and are used to determine the eigenvalues and eigenvectors of trapezoidal fuzzy …
This nal project discusses the solution to a systems linear equations in complex fuzzy numbers. In solving complex fuzzy number, arithmetic is used in numbers fuzzy and arithmetic is also usesd in complex fuzzy number. This system of equation is converted into 2n 2n matrix form. Then the solution of the equation are obtained using Gauss-Jordan elimination. Keywords: Fuzzy numbers, compl…
This final project discusses the stability of the predator-prey model using the Holling-II and threshold harvesting functions against predator. Three of five equilibrium points obtained are stable as seen from the eigenvalues of the system linearity matrix. At the end of the discussion, the model behavior for the two equilibrium points generated with threshold harvesting shows that the solu…
This final project discusses how to apply sensitivity analysis to the triangular fuzzy number linear programming. Sensitivity analysis is used to determine the changes in the triangular fuzzy number on the coefficient of the objective function, the changes in the value of the right side of the constraint function and the addition of new constraints so that the optimal solution can be mainta…
The ratio estimators studied here are ratio estimators for population mean of simple random sampling by using information of correlation coefficient, second quartile, quartile deviation and decile mean. Each estimator is biased estimator. Furthermore, to obtain an efficient estimator is carried out comparing the MSE of each estimator with the simple ratio estimator used by Cochran. Then it …
This final project discusses a decreasing sequence (an) of nonnegative terms, the- re exist subsequences (nk) of (n) such thatP1k=1(nk+1−nk)ank andP1n=1 an ha- ve the same convergence. Then for P1n=1 an converges if and only if P1k=1 qkaqk converges for 1 < q ∈ N. Using these results, an extension of the ratio test is formed. Keywords: Sequence, series, convergency, divergency
This final project discusses the sensitivity analysis of transportation problems in triangular fuzzy numbers. The optimal solution of the transportation problem is obtained after converting the triangular fuzzy number in the transportation problem into a crisp number. When the optimal solution obtained remains the same for a long time, a sensitivity analysis is carried out to determine chan…
This nal project discusses the determinant of interval matrix with the calculation used is a combination of some interval arithmetic which has a shorter interval value than others. Assuming that a shorter interval value is an optimal value. The method used in determining the determinant of interval matrix is the modied Crout's method in the article of Nirmala and Ganesan [Journal of Phys…
This nal project discusses the modication of the fourth order multistep Adam- Bashforth and Adam-Moulton method by changing the integral boundaries of [xn; xn+1] to [xn−2; xn+1] to solve initial value problems. In generally, the com- parison results show that the numerical solution obtained with the modication of the fourth order multistep Adam-Bashforth and Adam-Moulton method has an…
This research is a development purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheet by using discovery learning on curved face three dimensional (cylinder, cone, and ball) material for the 9th grade of junior high school. This research is motivated by the incompatibility instruments which arranged by teacher based on 2013 Curriculum. The…
This final project discusses the premium of contingent endowment life insurance using Gompertz’s law. In this project, the number of insurance participants is limited to two people aged x and y years. The premium of contingent endowment life insurance are divided into two parts, namely the premium of contingent endowment joint life and last survivor status life insurance. In contingent e…
The background of this research is the existence of curriculum change that claiming teacher to can develop the learning devices and also still the limited learning devices that matching with 2013 curriculum.This research aims to produce products in the form of mathematics learning devices such as syllabus, lesson plan and student worksheet.The development model in this research is 4-D mode whic…
This research is motivated by the lack of mathematics teaching materials that introduce Malay Culture, namely traditional Malay games for students in accordance with the demands of the 2013 curriculum. The purpose of this research is to produce mathematics teaching materials in the form of books using the tradisional Malay Riau games. This research is a research and development (R&D) using the …
This research is motivated by the limited mathematics learning devices that are in accordance with the 2013 Curriculum. This research purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheets by using problem based learning on sets material for the seventh grade of junior high school. The development model used in this research is the 4-D model w…
This study is aimed to produce mathematic learning tools consisting of a Syllabus, Lesson Plan (LP), and Students' Worksheet (SW) in the material Linear Equation System of Three Variables in class X which applies valid and practical Problem Based Learning models. This developmental model used is the 4-D model which consists of 4 stages of development, namely define stage (definition), design st…
The research was based on the limited innovative mathematics learning device as a means of supporting learning in the 2013 Curriculum. The purpose of this research is to produce mathematics learning device in the form of syllabus, Lesson Plan (LP), and Student Activity Sheet (SAS) based on cooperative learning models type think pair square material of the sine and cosine rules of class X SMK/MA…
This research was conducted due the limited learning instruments in accordance with the 2013 Curriculum, especially the application of learning models and learning approaches. The purpose of this research is to develop the mathematics learning instruments: syllabus, lesson plans, and student worksheets using Problem Based Learning model with Melayu cultural context on circle’s topic for 8th g…
This research aims to produce the mathematics learning instruments which includes syllabus, learning implementation plans (RPP) and student activity sheets (LAS) model discovery learning on the material of quadrilateral and triangles to facilitate the mathematical representation students abilities of SMP/MTs that are valid and qualified of the practicality. The development research model used i…
This research aims to produce mathematics learning instrument which includes syllabus, learning implementation plans (RPP) and student activity sheets (LAS) based on the Discovery Learning on the sine and cosine rules topic of students of Vocational high school that are valid and practical. This research development model is a 4-D model which consists of the stages of define, design, developmen…
Most students have difficulty for learning mathematics because of mathematical abstract objects. Teachers can link everyday life with math material to make it easier for students to learn mathematics. One of the learning concepts that can connect learning material with everyday life is Contextual Teaching and Learning approach. Mathematical communication skills are needed to make it easier for …