This final project discusses the identities of finite sum of the reciprocal and reciprocal square Fibonacci numbers with two, three or four functions of sums of the Fibonacci numbers. The sum solution is found by using floor function with mn Fibonacci numbers for any value of m and n which are even and odd integers. The sum is proven by using the combination of some propositions of recipro…
This final project discusses Newton type method for solving nonlinear equation systems introduced by Wang and Li [Algorithms, 10 (2017), 1-9]. Through convergence analysis it is shown that this Newton type method has a six-order convergence. By computational cost this method requires one LU decomposition in each iteration, so this method can be said to be efficient in computing. Therefore,…
This final project discusses the average total opportunity cost method to solve transportation problem, with the proposed method is easy since computation works. North west corner method, least cost method and Vogels approximation method used to determine the initial basic feasible solution and to compare of the new method. Then simplex transportation method is used to verifying optimality…
This final project discusses the New Jersey method for adjusted reserve of term life insurance using Makeham’s distribution. In this project, life annuity due and premium for term life insurance are obtained based on Makeham’s law of mortality. By using the value of annuity due and premium insurance it can be determined the adjusted reserve calculation with New Jersey method based on M…
The nal project discusses the modied method of Vogel approximation for solving the balanced transportation problem. This method is used to determine the feasible solution and simplex method to verify the optimal solution. The modied method Vogel's approximaton is more advantageous compared to the method of Vogel approximation. Illustration by example is given to comprehend the advantage…
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'…