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From calculating routes to the optimized amount of cars that can be fit on a road, it becomes easy to see how much math has played a part in some many peoples' day to day living.
For the majority of traffic design and highway development can be modeled by equations express vehicles average speed and space in between the bumpers. Design engineers have to take this into account when figuring out where all the worst traffic jams are.
(d^2)xn+1(t+T)dt^2=λ[dxn(t)dt−dxn+1(t)dt]
(d^2)xn+1(t+T)dt^2=λ[dxn(t)dt−dxn+1(t)dt]
Time is an important asset to everyone, but even more important than that is personal safety for the populous. With this is mind, roads need to conform around the event of a serious evacuation on a city wide scale. Luckily, math is still able to cover for this as well.
∂W ∂t = L t,x,v * ( ) + v * ∇W + σ2 2 ΔW where v * = −c0∇W
∂W ∂t = L t,x,v * ( ) + v * ∇W + σ2 2 ΔW where v * = −c0∇W
This page by Smitty B. ('18)
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