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All Journal Pentagon: Jurnal Matematika dan Ilmu Pengetahuan Alam
Lauren Teresia Tamba
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Mathematics

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Penerapan Metode Trapesium , Metode Simpson 1/3, dan Metode Simpson 3/8 Dalam Integrasi Numerik Menggunakan Software Matlab Bes Hendi Rio Pardede; Bunga Diviya Kusfa; Lauren Teresia Tamba
Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam Vol. 2 No. 4 (2024): Desember: Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/pentagon.v2i4.268

Abstract

Numerical integration is a method used to calculate the integral of functions that cannot be integrated analytically. Several methods that are often used in numerical integration include that Simpson 1/3 method, Simpson 3/8 method, and the Trapezoidal method. This research aims to apply and compare the accuracy and efficiency of the third method in solving various types of integral functions using computing software. With the help of software such as MATLAB and Python, the precision of the results obtained from each method is analyzed and compared with analytical solutions (if available) or approximate integral value estimates. The results show that the Simpson 3/8 method tends to be more accurate for more complex functions than the Simpson 1/3 and Trapezoid method. However, the Trapezoidal method has advantages in computational speed and algorithm simplicity. This study provides important insights for computing software users in selecting appropriate numerical integration methods based on function complexity and accuracy requirements.
Visualisasi Interaktif Permukaan dalam Ruang Tiga Dimensi: Analisis Geometris dengan GeoGebra Bali Sahputri Tarigan; Lauren Teresia Tamba; Tantory Yahya Purba
Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam Vol. 2 No. 4 (2024): Desember: Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/pentagon.v2i4.317

Abstract

Surfaces in three-dimensional space can be represented through explicit, parametric and implicit equations, which describe the relationship between the variables x, y and z. Graphs of linear equations produce flat planes, while quadratic equations form objects such as spheres or ellipsoids. In this research, a theoretical approach is combined with interactive visualization to analyze various surface shapes. Through the use of GeoGebra software, this analysis makes it easier to understand surface orientation and shape, such as normal vectors and curvature, as well as applications in vector fields. This research also investigates the concepts of Cartesian coordinates in three-dimensional space, by depicting surfaces in the form of graphs of functions of two variables. It is hoped that the results of this research can provide deeper insight into the geometric properties of surfaces and how to visualize them effectively in mathematics and physics applications.
Co-Authors Bali Sahputri Tarigan Bes Hendi Rio Pardede Bunga Diviya Kusfa Tantory Yahya Purba