This final project discusses the quadratic programming problem of linear con- straints and solves it using the Kuhn-Tucker condition method. This method starts by changing the inequality constraint into an equation using the additio- nal function of the Lagrange multiplier. The multiplier is used to convert the extreme point of a constraint function into a point. Each Lagrange multiplier must s…
This final project discusses the problem of mixed constraint linear programming and solves them using the Lagrange multiplier method. Linear programming is used to solve problems in everyday life. Problems that are often associated with linear programming are always related to various fields of economics such as problems that often occur in home industry businesses, namely the insta- bility o…
This final project discusses the dynamics of a predator-prey model involving interactions between predator and prey populations. This interaction is influ- enced by the fear effect on prey which causes prey to migrate to safer patches. Predator density decreases when the level of fear effect increases. Migration be- tween patches also has a large impact on predator density. The model is solved …
This final project discusses the development of Van Aubel’s theorem on nonconvex quadrilaterals with semicircles. The process of proving this theorem uses the cosine rule, and the congruence and congruence approaches. In a nonconvex quadrilateral, each side is constructed as a semicircle, with the diameter of each semicircle being a side of the non-convex quadrilateral. If the midpoints …
This final project presents fractional derivatives of polynomial functions with Caputo concept and related with gamma function and beta function. The fractional derivative is denoted by D(α)f (x) with α is fractional number greater than 0 and x is a variable. The result of the final project present that fractional derivatives provide more subtle and detailed changes from the original function…
This final project discusses general inverse on interval matrices and its applicationto climate change data. The topic of interval number arithmetic has attracted the attention of a number of researchers, especially in the context of multiplication operations. Some definitions of multiplication operations by researchers do not produce identities when interval numbers are multiplied by their i…
This final project presents increasingly rapid development of interval numbers. Many researchers have discussed algebraic operations on the number of intervals by presenting different formulas mainly on the multiplication formula and the division of two interval numbers. The formula given by many such researchers has a weakness that multiplication of an interval number with its inverse does not…
The Ministry of Education and Culture emphasizes that the five elements of mathematical ability are very important for students, one of which is mathematical reasoning ability. Current conditions show that students' mathematical reasoning skills are still low, this is influenced by the lack of independent learning habits, limited learning resources, and the lack of variations in learning approa…
This final project discusses the validity of Hamiltonian and Hypohamiltonian properties of the Petersen graph and the generalized Petersen graph (GPn,6) by constructing steps to find the existence of the Hamilton cycle. A graph that has a Hamilton cycle is called a Hamiltonian graph. Furthermore, a graph that is not Hamiltonian and if one of the vertices is removed then it will form a Hamilto…
This research aims to enhance the learning process and boost the Mathematical Problem Solving Ability (KPMM) among Class XII MIPA students at SMA Negeri 1 Langgam through the implementation of the Problem-Based Learning (PBL) model. Conducted as classroom action research, the study proceeded in two cycles and employed various learning tools and data collection instruments. These tools included …
This final project discusses the Moore-Penrose inverse of interval matrices. The development of interval numbers has been studied by many researchers. For example, the multiplication operation of interval numbers, but the operation used by most researchers still has a weakness, namely the result of multiplying an interval number with its inverse does not produce an identity. Therefore, a modi�…
The topic of interval numbers is growing quite fast. There are many researchers who have discussed the arithmetic of interval numbers. However, the multipli- cation operation defined by some researchers does not produce an identity when an interval number is multiplied by its inverse, so in this study a modification is needed for the arithmetic of interval numbers, especially in the multiplica-…