The Math of Traffic: Driving Through Differential Equations

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Ever wonder why traffic jams seem to pop up out of nowhere and then mysteriously disappear? "How mathematics models traffic flow" takes you on a captivating journey into the mathematics that unravels this everyday puzzle. The video explores the macroscopic LWR model, a cornerstone of traffic flow theory, showing how traffic density, velocity, and flux come together through the continuity equation to predict roadway behavior

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Further reading:
Paper mentioned: https://sci-hub.se/10.1063/1.1721265
Dr Trefor's video:    • The Problem of Traffic: A Mathematica...  
Notes for Introduction to Partial Di↵erential Equations - Esteban G. Tabak (2018)
The method of characteristics applied to quasi-linear PDEs - Matthew J. Hancock (2006)
Traffic Flow Problem with Differential Equations - Abdul Salaam.A.AIkhazraji
An introduction to non-linear partial differential equations - J. David Logan

CHAPTERS:
00:00 Introduction
00:53 #1 Problem setting, history and terminology, prerequisites
15:40 #2 Sponsor Segment: Brilliant
17:29 #3 Introducing variables and equations
22:35 #4 Quasi-linear PDEs: Overview
24:40 #5 Explaining the method of characteristics
29:55 #6 Linear interpolation model, using characteristics to analyze the solution’s
behavior
42:28 #7 Different settings : Red light, heavy traffic heading to light traffic, light traffic
heading to heavy traffic, etc...
50:34 #8 Shock waves and their propagation
55:30 #9 Summary and closing statement