The discussion revolves around the concept of "level sets" in the context of functions of two variables, specifically examining equations that define these sets. Participants express discomfort with understanding the definition and implications of level sets, as well as their graphical representation.
Some participants have provided definitions and examples to clarify the concept of level sets. There is ongoing exploration of how to graph these sets and interpret the equations, with no explicit consensus reached yet on the best approach to take.
Participants express uncertainty about their prior experience with similar problems and seek foundational knowledge. There is a recognition of the complexity introduced by multiple variables in the equations being discussed.
939 said:Homework Statement
I am very uncomfortable with the concept of "level sets" and don't quite get what it means.
Homework Equations
y = 2(x1)^2 - (x1)(x2) + 2(x2)^2
y = 2x1^(1/2) * x2^(1/2)
The Attempt at a Solution
I'm not even sure where to start... Can anyone please give me some basic knowledge of how to approach these problems?
Ray Vickson said:A level set of f(x1,x2) is the curve f(x1,x2) = constant. If z = f(x1,x2) describes a hill or mountain, a level set of f would be a path of constant elevation. That's all!
939 said:Thanks...
So in the top example above,
2(x1)^2 - (x1)(x2) + 2(x2)^2 = C?
What I'm confused about also is how I would graph it...
Ray Vickson said:For a given numerical value of C, the equation describes some type of curve; you need to figure out what that curve is, and draw it. Surely you must have done problems like that in the past!