Presenter(s)

    Amanda Maylath

    Comments

    1:15-2:30, Kennedy Union Ballroom

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    Description

    Differential equations are essential in modeling systems in areas such as physics, biology, and engineering. This project explores delay differential equations (DDEs), a type of functional differential equation that builds on ordinary differential equations (ODEs) by including time delays. Incorporating delays allows for the rate of change or derivative to depend on the current state of the system and on its past states, making DDEs useful in modeling real-world systems where past states influence future outcomes. This project looks at several types of DDEs, including linear delay models, Hutchinson’s equation, and second-order delay equations. Solution methods include Laplace transforms and the method of steps in which traditional ODE techniques are applied, such as separation of variables, integrating factors, and variation of parameters. DDE solutions are compared with those of corresponding non-delayed models. Practical applications of DDEs include modeling population dynamics and analyzing engineering systems. These examples show the effectiveness of DDEs in providing a more accurate representation of real-world dynamical systems.

    Publication Date

    4-23-2025

    Project Designation

    Capstone Project

    Primary Advisor

    Sam J. Brensinger

    Primary Advisor's Department

    Mathematics

    Keywords

    Stander Symposium, College of Arts and Sciences

    Institutional Learning Goals

    Scholarship

    Delay Differential Equations: Methods and Practical Applications

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