Multivariable & Vector Calculus

Summer 2016

3D Coordinate Systems

• octants
• a point in 3D space
• a point in 3D space (user input)
• planes of the form variable = constant
• coordinates of the corners of a box
• circle vs. cylinder
• circle vs. cylinder + line vs. plane

Spring 2016

Vector Fields

• Simple 2D vector field.   (slide)
• Interesting 2D vector field.   (slide)
• Simple 3D vector field.   (slide)
• Interesting 3D vector field.   (slide)

3D Coordinate Systems

• Cylindrical coordinates.   (slide)
• Spherical coordinates.   (slide)
  • Finding r and z.   (slide)
  • Equation of a sphere.   (slide)
  • Equation of a half-plane.   (slide)
  • Equation of a half-cone.   (slide)
  • An "ice cream cone."   (still)   (slide)
  • Part of a spherical annulus   (slide)

Line Integrals

• On a quarter-circle.   (slide)
  • ds vs. dx vs. dy.   (slide)
  • Reverse orientation; ds vs. dx vs. dy.   (slide)
• On a half-circle.   (slide)
• On a helix.   (slide)
• Introduction to line integrals.

Parametric Curves & Surfaces

• Interactive helix.   (slide)
• Interactive helicoid surface.   (slide)
• Interactive planar surface.   (slide)