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Published online by Cambridge University Press: 02 April 2020
Taking the continuum limit of the chains of masses from the previous chapter, we arrive at the wave equation, the physical subject of this chapter.The connection to approximate string motion is an additional motivation.Viewed as a manifestation of a conservation law, the wave equation can be extended to other conservative, but nonlinear cases, like traffic flow.Mathematically, we are interested in turning partial differential equations (PDEs) into ODEs, making contact with some familiar examples.Making PDEs into ODEs occurs in a couple of ways --- the method of characteristics, and additive/multiplicative separation of variables are the primary tools.
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