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All Journal Jurnal Arjuna : Publikasi Ilmu Pendidikan, Bahasa dan Matematika Bilangan: Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Vena Yurinda Saragih
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Astronomy Education Health Professions Languange, Linguistic, Communication & Media Mathematics Social Sciences

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Penerapan Python dalam Perhitungan Turunan Fungsi Dua Peubah dan Visualisasi Grafik 3D Vena Yurinda Saragih; Bunga Diviya Kusfa; Rizky Iqna Fitria
Jurnal Arjuna : Publikasi Ilmu Pendidikan, Bahasa dan Matematika Vol. 3 No. 1 (2025): Jurnal Arjuna : Publikasi Ilmu Pendidikan, Bahasa dan Matematika
Publisher : Asosiasi Riset Ilmu Pendidikan Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.61132/arjuna.v3i1.1419

Abstract

This study aims to analyze the derivatives of a two-variable function and visualize the results in the form of a 3D graph using Python. Derivatives of two-variable functions are essential in multivariate analysis, such as optimization and surface analysis. The study uses Visual Studio Code as the Integrated Development Environment (IDE) to develop and run Python code, utilizing libraries such as NumPy, SymPy, and Matplotlib for mathematical computations and visualization. The first step involves programming partial derivatives of a two-variable function using SymPy. Subsequently, the derivative results are visualized in 3D using Matplotlib to illustrate the surface and gradient of the function. The goal of this research is to provide a deeper understanding of the application of derivatives in two-variable functions and the benefits of visualization in analyzing these derivative results. The findings are expected to contribute to the fields of mathematics education and numerical computation applications.
Implementasi Metode Runge-Kutta dalam Simulasi Lintasan Peluru pada Medan Gravitasi Bumi Vena Yurinda Saragih; Giovani Br Surbakti; Nia Elovani Br Munthe; Syabila Amalia Wardani
Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa Vol. 2 No. 5 (2024): Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/bilangan.v2i5.272

Abstract

This study examines the implementation of the fourth-order Runge-Kutta method in simulating bullet trajectories in the Earth's gravitational field. Bullet trajectory simulation is important in various fields such as ballistics and engineering, where the accuracy of predicting the trajectory of a moving object is crucial. The introduction explains the importance of using numerical methods in solving complex equations of motion, considering that analytical solutions are often inadequate. The purpose of this study is to apply the Runge-Kutta method to solve nonlinear differential equations describing the motion of a bullet under the influence of gravity. The research methods include modeling the motion system using Newton's laws and applying the Runge-Kutta method to predict the trajectory based on initial conditions such as velocity and firing angle. The simulation results show that the Runge-Kutta method provides accurate predictions of bullet trajectories, with low relative errors compared to other numerical methods. In conclusion, this method is effective and efficient in simulating bullet trajectories, providing reliable results in practical applications.
Co-Authors Bunga Diviya Kusfa Giovani Br Surbakti Nia Elovani Br Munthe Rizky Iqna Fitria Syabila Amalia Wardani