This nal project aims to popularize the Perron's theorem, which contains the power of matrices with integers. The discussion begins by looking at integer powers of the stochastic matrix. Then using the properties of the eigenvalues and eigenvectors of the positive matrix it is shown that the Perron's theorem holds. Keywords: Positive matrices, stochastic matrix, eigen vector, eigen value,…
This final project discusses the technique of solving ordinary differential equations of second order nonhomogen with right exponential functions in the form of complex exponentials. The solution is obtained through two new formulas obtained through the modification of the exponential shift theorem and using differentiation techniques and the properties of linearity. Next, two examples are…
This article discusses the predator-prey model with infection and harvesting in predator populations. The model used is in the form of a system of differential equations. This model has five equilibrium points. Furthermore, the theoretical stability analysis of the discussed model was carried out using the Routh-Hurwitz criteria with regard to two cases, namely the system without disease a…
This nal project discusses a new iteration algorithm for solving a system of the absolute value equation. Before proving convergence, rst an analysis is carried out on how to obtain solutions from the application of the iteration algorithm. The convergence analysis of the algorithm is done by showing the spectral radius of the iteration matrix of the new iteration algorithm is smaller th…
This final project discusses fractional derivatives from the definition of Khalil et al. Based on this definition it is investigated that the rules that exist in the derivative in classical calculus are also fulfilled. These rules are multiplication, division and rules of some special functions. After that it is also investigated for Rolle’s theorem and average value theorem, next to find…
Hepatitis B is an infection of the liver caused by the hepatitis B virus (HBV). Hepatitis B can be interpreted by mathematical model. In this research, we present a fractional mathematical model of HBV infection with cure of infected cells use the fractional derivative order ∈ (0, 1). Based on the model analysis, there are two equilibrium points, namely the disease-free equilibrium poi…
This final project discusses chaos in mathematical models of predator-prey interactions for the consumption of illegal drugs. This model uses a differential equation system from the NERA model that describes the consumption of illegal drugs in a proportion of the population consisting of users and non-users. In this model there are five equilibrium points where they are unstable, then bifu…
This nal project discusses the solutions of the Diophantine equations px+qy = z2 and p3+q2 = z2. To solve the equations px+qy = z2, two cases are introduced. When p = 2 and q = 3 the Diophantine equations px + qy = z2 have innitely many solution. To solve the equations p3 + q2 = z2, three cases are introduced, (i) no solution when p = 2, (ii) exactly two solutions when p = 3 with q primes…
This final project discusses a method for solving a quadratic programming problems with constraint coefficient fuzzy numbers in triangular form. Quadratic programming is solved by triangular fuzzy numbers by transforming it first in crisp constraint. Then, simplex method is used through the formation process of linear programming by Wolfe’s method. The simplex method is used for solving …
This final project discusses Balducci assumptions on contingent term life insurance premiums for two persons at the age x and y years old. Contingent life insurance is an insurance whose payment are based on the sequence of the deceased insured. In determining the order in which death is delayed, the compound contingent function is used. In this project, net single premium contingent term …
This final project discusses the premium of life insurance of the last survivor status with life appourtunity using Gompertz distribution. In this project, insurance clients are limited to only two persons who are x and y years old with the premium paid until the last death of the insurance clients. In life insurance of the last survivor the premium is determined by associated with individu…
This final project discusses the dynamics of a predator-prey model incorporating prey refuge, predator infection and harvesting. This model are used the system of differential equations of the model predator-prey predator-prey with prey refuge, predator infection and harvesting. The model consists of five observed equilibrium points. Stability analysis is performed using Routh-Hurwitz crit…
This thesis discusses determining the side length of Napoleon's textit outer development of a triangle using an isosceles right triangle as the outer triangle. Then each side of the triangle is divided into 2, 3 and 4 parts. By using a special case in the Miquel's theorem, the Miquel's point on each of the isosceles right triangles can be applied, so that a triangle is formed whose the same…
This tesis discusses the Economic Order Quantity (EOQ) for multi-item deterministic inventory. Deterioration happens to each item when the constraints of shortage capacity are active. Then, Lagrange method is used to determine the EOQ of this case. The main purpose of this model is to determine the time cycle with and without backorder, as well as the amount of optimal shortage so as to mi…
This research is motivated by the low ability of students to think creatively and the limited learning tools that implement 21st century skills, especially creative thinking. Based on the results of interviews and preliminary studies conducted by researchers, it was found that the learning tools owned by the teacher had not yet referred to the 2013 curriculum process standards so that students'…
This study was motivated by the low thinking ability of high-level learners. The low level of thinking ability of learners is due to the learning process in class that does not accommodate the development of high-level thinking skills. Mathematics learning tends to be devoted to low-level thinking skills that solve problems with procedural formulas, memorization instead of understanding co…
The results of the achievements of Indonesian students 'ability in mathematics literacy in the 2018 PISA survey showed that they were ranked 7th from the bottom with a score of 379. This achievement still showed that Indonesian students' abilities were towards a lower level when compared to 489 which is the OECD average score. The fact found in the results of research conducted by Ruspiani (in …
This research was motivated by the students' weak mathematical understanding. Based on the results of the documentation study and analysis conducted by researchers, information was obtained that the teaching materials used by students were textbooks obtained from publishers that were not in accordance with the learning needs of students. The book only contains a summary of the material, a colle…
This research is motivated by the low mathematical critical thinking ability of learners and the lack of learning tools that are seen to facilitate the critical thinking ability of learners. Based on interviews, observations, documentation studies, analysis of test students' test of critical thinking ability, the researchers obtained the fact that the learning tools owned by teachers have not c…
This research is motivated by the inadequacy of teachers in developing learning tools that have an impact on students' mathematical problem-solving abilities. The results of the document review that the researcher conducted on the learning tools used by the teacher obtained information that the learning tools used by the teacher had not met the rules contained in the 2013 Curriculum so that it …