Multivariable Calculus Concept

Multivariable Calculus Concept
Heegyung Kim
November 8, 2021
George Mason University MATH 401: Mathematics Through 3D Printing

The level set is the set of points in the domain of a function such that the function is constant. The level curve is the curve of points (x,y) where f(x,y) is some constant value. A horizontal slice is taken from a graph of z = f(x,y) at a constant value z = c, and can be also written as c = f(x,y). In other words, the level curve can show the graph of a function at height c. It lies in the xy plane.

For this assignment, my first thought was to illustrate the concept of level sets by creating the graph of a function f(x,y) and its level curves. Then, after I printed the object, I realized that the object didn’t represent the level curves (or it could say it shows the level curves in the direction of the x and y-axis). Rather, it showed the multiple lines of x = constant and y = constant on a plane and combined with the graph of a function 4x^2+ (1/3)