can someone please explain to me how to do contour diagrams and cross sections in general ? Thanks

Question

kainui · Answer

When you think of a contour diagram, what do you see in your mind? It's a line drawn that is completely all in the same plane. It's basically just a 2D shape which is part of a 3D shape where one of the dimensions has been specified to be constant.

Suppose you have the graph:

z=x^2+y^2 how would this look if we make contours? Well there are three dimensions here to consider, so how about we choose to look at the one slice where y is kept constant, and for simplicity we'll choose y=0.

Plug it in and you get z=x^2. That's just a parabola! |dw:1398158444705:dw| Let's pick another point when y=2, what do we get?

kainui · Answer

|dw:1398158497656:dw| See we just have z=x^2+4 now. So  we sort of stacked another parabola nearby to draw this contour line. Add more and you'll see a a surface that they all lie on.