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…
One of the objectives of learning mathematics in the independent curriculum is to equip students with mathematical creative thinking skills. However, the facts indicate that the level of students' creative thinking skills is still low. The reason is because students are not accustomed to facing contextual problems that demand creativity, argumentation and reasoning, and the use of LKPDs that ar…
The purpose of this development research is to produce discovery learning-based LKPD that can facilitate the mathematical critical thinking skills of phase D students by fulfilling valid and practical requirements. The background of the research begins with the importance of students' critical thinking skills. This research method is a development research (R&D) with the 4- D model (define…
This thesis discusses a derivative free three-step iterative method to solve a nonlinear equation using Steffensen's method, after approximating the derivati- ve in the method proposed by Abro and Shaikh [Appl. Math. Comput.,55(2019),516- 536] by a divided difference method. This study shows analytically that the method is of order sixth under a condition and for each iteration it requires …
Mathematical representation skills are one of the skills that students must have in learning mathematics. Learning that facilitates mathematical representation skills can build students' knowledge and understanding of mathematical concepts. Mathematical representation skills are the foundation for how students understand mathematical ideas and use them so that mathematical representations have …
Algebra for interval numbers has been developed by various authors. For the operations of addition, subtraction, and scalar multiplication, there aren't many differences among the numerous algebras for interval numbers. However, other algebraic alternatives are offered by various authors for division/inverse operations and multiplikation. All of the provided algebras, however, are irrelevant to…