BE 500: Introduction to Differential Equations for Bioengineers - Lecture 03

BE 500: Introduction to Differential Equations for Bioengineers (Summer 2025)

The lecture began with an introduction to first-order differential equations, which involve only the first derivative of the dependent variable with respect to the independent variable and are foundational tools for modeling dynamic systems in various fields including biology, engineering, physics, and economics; these equations help in understanding processes like growth, decay, diffusion, and oscillations, with applications ranging from population dynamics and pharmacokinetics to chemical kinetics. The lecture then delved into key solution techniques for first-order differential equations, such as separable equations where variables can be separated and integrated independently, and integrating factors that transform linear first-order DEs into exact equations. Examples were provided to demonstrate solving separable equations by separating variables, integrating both sides, and solving explicitly for the function, as well as using integrating factors to solve linear first-order DEs through a systematic approach. The lecture also covered specific examples like logistic growth models and drug concentration dynamics, illustrating how to apply these methods practically, while emphasizing real-world bioengineering applications. Additionally, hands-on lab exercises were introduced to show how to solve these equations analytically and numerically using Python or MATLAB, allowing students to compare analytical solutions with numerical results and visualize the behavior of the solutions, thereby bridging theoretical knowledge with practical problem-solving skills in bioengineering contexts.

Codes can be accessed using: https://github.com/HossamBalaha/BE-50...

Playlist from Summer 2025:    • BE 500: Introduction to Differential Equat...