Summary
Level curve
- can be thought of as a slice of the curve at z=k
Contour plot
- multiple level curves at discrete values of k
- flattened to the xy-plane
Cylinder
- any equation in R³ thats missing one variable is a cylinder
x is not in the equation, the circle formed in the yz-plane is the same for all x
Elliptic paraboloid
- bowl
Ellipsoid
- closed shape
- ie. spheres
Level surface
- projection of trivatiate functions onto 3D space
- ie. planes
Concept
Bivariate functions of a surface
- accepts an ordered pair
- above or below(z-axis) the domain of the function
Quadratic curves
- focus on elliptic paraboloid and ellipsoids
Trivariate functions
- accepts an ordered triple
- lies in 4 dimensional space
Application
Domain of a bivariate function