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Description

Mathematical modeling through differential equations provides a basis for understanding change in physical and engineering systems. My project explores the transition from single-variable derivatives to multivariable partial derivatives and their applications in describing engineering applications. Beginning with the Fundamental Theorem of Calculus, derivatives are introduced as measures of change, quantifying relationships such as velocity and acceleration. The study then extends to partial derivatives, which represents systems influenced by multiple variables, including spatial and temporal factors. These principles are applied to model fluid motion, and pressure gradients, including the Navier–Stokes equations governing fluid dynamics. By linking mathematics with engineering applications, this project highlights how derivatives form the foundation for analyzing changes in modern scientific and engineering systems.

Publisher Location

Las Vegas (Nev.)

Publication Date

Fall 11-21-2025

Publisher

University of Nevada, Las Vegas

Language

English

Keywords

partial derivatives; fluid dynamics; mathematical modeling; differential equations; derivatives

Disciplines

Physical Sciences and Mathematics

File Format

PDF

File Size

407 KB

Permissions

Google Drive\Institutional Repository\OUR_OfficeOfUGResearch\Symposia\2025 Fall Symposium

Comments

Mentor: Monika Neda

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

The Mathematics of Motion: Applying Derivatives to Fluid Systems


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