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Math Help - D Alemberts Solution Query - Characteristic Triangle

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    Senior Member bugatti79's Avatar
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    D Alemberts Solution Query - Characteristic Triangle

    Folks,

    I am struggling to understand what is goin on in this attachment. Given that g(x)=0 and a=1 and


    f(x) = \left\{\begin{array}{cl}0 & x \leq -1\\ 1-x^2 & -1 \leq x \leq 1 \\ 0 & x \geq 1\\ \end{array}\right.

    For region 1:

    How do we know that x+t \leq -1 and how how do we know that  x-t \leq -1
    Then how is u(x,t) zero in this region?

    If I can understand region 1 I should infer the rest.

    Thanks
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