Hi group,(adsbygoogle = window.adsbygoogle || []).push({});

In order to understand the methods of characteristics, I've been reading its wiki entry plus other sources. However, one of the first step of finding the normal surface vector given the PDE remains baffling to me in terms of how it's derived. In short, when provided with

[itex]

a(x, y, z) \frac{\partial{z}}{\partial{x}} + b(x, y, z) \frac{\partial{z}}{\partial{y}} = c(x,y,z)

[/itex]

how does one derive the surface normal as

[itex]

\left( \frac{\partial{z}}{\partial{x}}(x,y), \frac{\partial{z}}{\partial{y}}(x,y), -1 \right)

[/itex]

? What are the in-between steps? Thanks!

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# Derivation of normal surface vector of a quasilinear PDE

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