Question

Any good techniques to plot a function of two variables by hand - or how do we do it anyway?

Answer 1

The general way is to plot many different points that satisfy your equation and then to draw a curve through them.

Answer 2

Well i am reading in my math book "Functions of Several Variables" trying to figure out what they mean, but find it quite hard. They constantly refure to something called outlines and contours (don't know if it is called outlines but best translation i can do so far)

Answer 3

Oh, may be you are asking about surfaces.. I thought about equation \(F(x,y)=0\).

Answer 4

surfaces yea

Answer 5

you can hold one of the 3 variables constant and plot the remaining 2-variable equation... such as a y = mx + b line, with z or f(x,y) held constant is like looking at the edge of the plane that would occur if you extended that line into the 3rd dimension

Answer 6

or a parabola on an x-y plane would extend into a "trough" shape when you extend it.

More complicated functions in 2 variables are not simple 2 dimensional curves extended into 3 dimensional space, though.

Answer 7

Still i find it quite hard to see how they come up with this (see attachment)

Answer 8

that is the function f(x,y)=x^2-xy+y by the way

Answer 9

ouch... hurts my brain!

Answer 10

I am not sure how to generate those graphs easily by hand... sorry!