ObsidianVault/.trash/Class 10-30.md

Calculus 3

• Level curve
  • A 2D shape that results from setting a two-variable equation equal to a constant
  • can help to see the shape of a 3D function
  • basically like taking horizontal slices out of a two-variable function
• Vertical trace
  • similar to level curve, finding the 2D shape from a vertical slice
  • can find with either f(a, y) = z for constant x = a or f(x, b) = z for constant y=b
• Both of these are used to visualize 3D functions in 2D
• Functions of 3 variables
  • there is no great way to visualize these in 3 dimensions
  • have to take 3D "slices" out of the 4D shape