Lecture 1: Intro to Multivariable Functions

Coordinate Planes:

x=0 is yz-plane:

y=0 is xz-plane

z=0 is xy-plane

Distance between vectors (r_1) & r*(r_1)=((x_1),(y_1),(z_1)) r=(x,y,z)
d=√(,(x-(x_1))2+(y-(y_1))2+(z-(z_1))2)

Standard Sphere equation:
R2=(x−(x_0))2+(y−(y_0))2+(z−(z_0))2
Centered at ((x_0),(y_0),(z_0)) and of radius R

Midpoint of line segment:

M=(((x_1)+(x_2))/2,((y_1)+(y_2))/2,((z_1)+(z_2))/2)

Examples:

1. Sphere: x2+y2+(z-1)2=1

center: (0,0,1)

2. x2+y2=1 ⟸ circ...