Abstract: This research was motivated by the low mathematical understanding ability of student in class X SMA IT Al-Fityah Pekanbaru is caused by the learning process being still teacher-centered, students does not constructing their own knowledge, and teachers are teaching using conventional methods. One way that can be used to overcome this is by applying the Discovery Learning model. This ty…
This final project presents fractional derivatives of trigonometric functions with Riemann-Liouville fractional derivative and related with gamma functions. The fractional derivative is denoted by Dα f (x) with α is a fractional number greater than 0 and x is a variable. The fractional derivative of a trigonometric function is obtained by using some properties of the gamma functio…
This final project discusses the mathematical modeling of linear programming problems production using the fuzzy multi objective linear programming method. The goal to be achieved is to optimize production by fulfilling constraints de- termined to achieve the goal of maximum profit and more efficient use of ti- me. Mathematical models in this problem is designed using the LINGO 19.0 application…
This final project discusses the interaction between two populations namely prey and predators, which is then investigated using the Leslie type with an increased functional response. In the observed model, it is shown that the model has a predator-free equilibrium point and a positive equilibrium point. It indicated that the model has saddle-type stability at the predator-free equilibrium poin…
This final project discusses the application of the weighted goal programming method to financial statements. The goal programming method is used because it can solve problems with multi-objectives. The objectives in this study are to maximize revenue, minimize expenses, maximize assets, and maximize emplo- yee salaries. The four objectives will be formed into a mathematical model that will b…
Health insurance is one type products that specifically guarantees the cost of he- alth insurance or care when participants experience health problems that caused hospitalized. This final project discusses the premium of healthy insurance of the Erlang Truncated Exponential distribution. The parameters in the Erlang Truncated Exponential distribution are estimated using maximum likelihood estim…
This final project discusses a new iterative method that is derivative-free and is obtained by converting a single nonlinear equation to a system consisting of two equations. By using the splitting method, a sufficient conditions will be obtained that must be met for the convergence of this method. The convergence analysis shows that the proposed method has a third order convergence for certai…
In any polygon, especially a triangle, several special lines can be given. One of them is the angle trisector. An angle trisector is two lines that divide an angle into three equal parts. One theorem that uses angle trisectors is Morley’s Theorem. Basically, Morley’s Theorem applies angle trisectors to the inner angles of any triangle. From these angle trisector lines, several intersection …
This final project presents fractional derivatives of polynomial functions with Riemann-Liouville fractional derivative and the concept of limit. Riemann- Liouville derivative is denoted by Dα f (x) with α is a fractional number greater than 0 and x is variable. Riemann-Liouville fractional derivative of a polynomial function is obtained by determining the fractional integral of …
Every insurance policyholder is required to pay premiums to the insurance com- pany during the payment period. To fulfill the payment of the insured amount to policyholders, the insurance company must prepare reserve funds. These re- serves are used to fulfill the operational needs of the insurance company and to pay claims in the case of the policyholder’s death. This study aims to determine…
Life insurance companies provide protection to address the risks that may af- fect the lives of policyholders due to unpredictable events. The company needs to prepare reserve funds to mitigate these risks. These reserves are obtained from the premiums paid by policyholders and are used to cover the needs of both the insurance company and the policyholders. The full preliminary term reserve and…
This final project discusses two new iterative methods based on quantum calcu- lus for solving nonlinear equations. First of all, a nonlinear equation is expressed into the q-Taylor’s formula and then converted into a coupled system. After that the decomposition technique is used to obtain a sequence of high order iterative methods. The convergence analysis shows that the two proposed methods…
This final project discusses two-step and three-step iteration methods for solving nonlinear equations. This method is obtained by adding Newton’s method as an additional step of Javidi’s method. Convergence analysis using Taylor expansion and geometric series shows that this iteration method has convergence order four and six with efficiency index 1.587 and 1.565. Numerical computation sho…
This final project discusses properties of T *-Semiring, the structure of T *- Semiring, and the structure of totally ordered T *-Semiring. The properties and structure of semiring are used in showing the properties and structure of T *-Semiring. Then by taking some basic properties of semiring, algebraic properties of semiring can be constructed and form relationships with other semiring struc…
This final project discusses the existence of Hamiltonian cycle in the wheel graph by constructing steps to find the existence of the Hamiltonian cycle. A graph that has a Hamiltonian cycle is called a Hamiltonian graph. A cycle graph is a graph in which each vertex is of degree two, which has n vertices denoted by Cn. A graph containing n-cycles and one additional central vertex vc that is a…
This final project discusses the generalization of the Sylvester matrix of order (n+1) (n+1) with main diagonal alternating x and x, its upper subdiagonal n, (n 1), . . . , 1 while its lower subdiagonal 1, 2, . . . , n. The proof is carried out by partitioning the matrix into 2 2 block matrices, which are divided into two cases namely when n is odd and when n is even. This matrix partition aims…
This final project discusses a new sixth-order iterative method free from second derivative to solve a nonlinear equation. The method is obtained by Taylor’s expansion, then the second derivative that appears in the formula is appro- ximated using a cubic polynomial with Hermite orthogonal polynomial basis. Analytically using the Taylor’s expansion and geometric series that iterative method…
This final project discusses the analysis of mathematical models in territorial waters with two different treatments. In this model the system of differential equation for the mathematical model uses two regions, namely free and protected territory. The observed model consists of two equilibrium points. Stability analysis is performed using the Routh-Hurwitz Criteria. Finally a simulation …
Life insurance is a protection program for individuals or families from death that can cause financial loss. Insurance companies need to calculate reserves to prepare funds when participants request a claim. This final project discusses the prospective reserve of joint life endowment life insurance for two insurance participants who are x and y years old by using Joe copula model. The solution …
This final project discusses the control of raw material inventory to determine the optimal order quantity per order, in order to be able to minimize the total inventory cost. The method used in this final project is the EOQ multi-item model and min-max stock method based on data on seven types of raw materials for making electrical panels consisting of the amount of inventory of each item, t…