Solving Sketch Level Sets: A Beginner's Guide

[939]

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]

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?

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]

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!

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]

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...

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!

 

[939]

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!

Thanks... The only thing I don't get is figuring out what the curve is when there is always two xs, i.e. y = ((x1)^(2))*((x2)^(2))... Do you use algebra to put it into a form you can understand better?

Sorry for the newb questions...