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[tex]\frac{\partial^2 u}{\partial t^2} \;=\; c^2\frac{\partial^2 u}{\partial x^2} \;\;,\;\; u(x,0)\; =\; f(x) \;\;,\;\; \frac{\partial u}{\partial t}(x,0) \;=\; g(x)[/tex]

D'Alembert Mothod:

[tex] u(x,t)\; = \;\frac{1}{2} f(x\;-\;ct)\; +\; \frac{1}{2} f(x\;+\;ct)\; +\; \frac{1}{2c} \int_{x-ct}^{x+ct} \; g(s) ds \;\;[/tex]

Why the book call [tex]f(x\;-\;ct)\; ,\; f(x\;+\;ct)[/tex] odd extention of f(x)?

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# Why the book call f(x+ct) and f(x-ct) odd extension of D'Alembert Method?

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