PHYSICS 3K03 Study Guide - Midterm Guide: Eigenfunction, Heat Equation, Residue Theorem

• School: McMaster University
• Department: Physics
• Course: PHYSICS 3K03
• Professor: Rajat Bhaduri

Document Summary

The method is applicable to pdes of the form. The pde reduces to two coupled odes along the trajectory defined by (the. Number of cars per unit distance at time t located at position x. Number of cars per unit time passing a fixed place x at time t. The car velocity depends only on the density (cars slows down as the traffic density increases) In this case, is only a function of becomes , or. The above two equations satisfies in any physical system in which density is conserved the flow is a function of. Velocity and density have a jump discontinuity shock wave . Terminologies: : locations that shock occurs, : position of the shock on the two sides of the discontinuity, : shock velocity. The assumptions, along with the fact that flow equals density times velocity (here relative velocity) , gives.