Level Curves & Surfaces Flashcards
1
Q
Level Curve
A
z = f(x,y) -> c = f(x,y)
a slice of a function
2
Q
Open Disc
A
Point Pₒ = (xₒ, yₒ) in ℝ
disk = {(x,y) includes ℝ^2 | (x,y)^2 +(xₒ, yₒ)^2 < r^2}
3
Q
Interior Point
A
A Point is an interior point if an open disc caintained in R exists
4
Q
Interior Set
A
All interior points = Rₒ (but ₒ is above)
5
Q
Open Set
A
if R = Rₒ
eg: x^2+y^2 < 9 (boundary not included)
6
Q
Boundary Point
A
If an open disc around the point contains both R and not R
7
Q
Boundary Set
A
∂R ( All boundary Points )
8
Q
Closure of R
A
R_ (line above) = R ∪ ∂R
9
Q
Closet Set
A
If R = R_
10
Q
Bounded Set
A
If a disc around it can be drawn
eg. Rectangle or sphere
11
Q
Unbounded
A
Strip around it can not be drawn
eg. Strip or half-plane
12
Q
Compact Set
A
Bounded + Closed
If a disc around it can be drawn + R = R_
note: Compact always have a global max and min
