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I'm starting learning pde by myself , using "linear partial differential equations for scientists and engineers"

I'm having some problems with the basics "I took ODE". The following differentiation is totally new to me, can some one explain to me?

f(x,y,z,a,b)=0, a and b are parameters

Differentiating the function with respect to x we get:

f_{x}+ pf_{z}=0

And with respect to y we get:

f_{y}+ qf_{z}=0

Where q=∂z/∂y , p=∂z/∂x.

How? Why?

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# First-order pde

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