Research Article

Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis

Volume: 4 Number: 1 June 30, 2026
TR EN

Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis

Abstract

This study presents a MATLAB-based computational visualization system for the three-dimensional representation of multivariable functions and their partial derivatives. The proposed framework integrates symbolic differentiation, numerical evaluation, and 3D graphical rendering within a reproducible computational environment. The system, implemented in MATLAB (R2023b), uses the Symbolic Math Toolbox together with built-in visualization functions such as surf and quiver3. A benchmark function, z=x^2-y^2, is used to demonstrate the visualization of saddle surface geometry and corresponding derivative fields. Results show that the system effectively represents multivariable functions and their partial derivatives in a geometrically consistent manner. Unlike static visualization methods, the proposed approach enables integrated and dynamic exploration of mathematical structures. However, the study does not include empirical evaluation of learning outcomes; thus, educational implications are considered conceptual. Overall, the framework provides a reproducible and efficient tool for visualizing multivariable calculus concepts in a computational environment.

Keywords

MATLAB, Multivariable calculus, MATLAB visualization, partial derivatives, computational mathematics education, 3D function plotting

Supporting Institution

No funding was received for this study.

Project Number

Not Applicable

Ethical Statement

This study does not require ethical approval.

Thanks

N/A

References

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APA
Türkoğlu, A., & Soylu, Y. (2026). Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis. Journal of Studies in Advanced Technologies, 4(1), 50-59. https://doi.org/10.63063/jsat.1927466
AMA
1.Türkoğlu A, Soylu Y. Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis. JSAT. 2026;4(1):50-59. doi:10.63063/jsat.1927466
Chicago
Türkoğlu, Ali, and Yasin Soylu. 2026. “Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis”. Journal of Studies in Advanced Technologies 4 (1): 50-59. https://doi.org/10.63063/jsat.1927466.
EndNote
Türkoğlu A, Soylu Y (June 1, 2026) Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis. Journal of Studies in Advanced Technologies 4 1 50–59.
IEEE
[1]A. Türkoğlu and Y. Soylu, “Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis”, JSAT, vol. 4, no. 1, pp. 50–59, June 2026, doi: 10.63063/jsat.1927466.
ISNAD
Türkoğlu, Ali - Soylu, Yasin. “Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis”. Journal of Studies in Advanced Technologies 4/1 (June 1, 2026): 50-59. https://doi.org/10.63063/jsat.1927466.
JAMA
1.Türkoğlu A, Soylu Y. Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis. JSAT. 2026;4:50–59.
MLA
Türkoğlu, Ali, and Yasin Soylu. “Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis”. Journal of Studies in Advanced Technologies, vol. 4, no. 1, June 2026, pp. 50-59, doi:10.63063/jsat.1927466.
Vancouver
1.Ali Türkoğlu, Yasin Soylu. Derivative and 3D Graph Simulation in MATLAB: Mathematical Exploration and Visual Analysis. JSAT. 2026 Jun. 1;4(1):50-9. doi:10.63063/jsat.1927466