BE 500: Introduction to Differential Equations for Bioengineers - Lecture 04

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

The lecture introduces second-order linear differential equations and their applications in bioengineering, focusing on homogeneous and non-homogeneous equations, characteristic equations, and the behavior of oscillatory systems. The lecture explains how to classify these equations by order and degree, solve them using characteristic equations, and interpret the roots (i.e., real, repeated, or complex) to determine system behavior such as exponential decay, critical damping, or oscillatory motion. It also covers practical applications including biomechanical systems like heart rate dynamics and spring-mass models, and introduces phase plane analysis for understanding stability and response types. The lecture further explores real-world biological systems through case studies and includes hands-on computational labs using Python and MATLAB to simulate undamped, underdamped, critically damped, and forced oscillations, providing students with both analytical and numerical tools to model dynamic biological processes such as cardiac rhythms and muscle movements.

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

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