Parametric Equations for Lines and Curves

John Belcher

Course Lectures

• Dot Product

  Denis Auroux

  Play

  John Belcher

• Determinants; Cross Product

  Denis Auroux

  Play

  John Belcher

• Matrices; Inverse Matrices

  Denis Auroux

  Play

  John Belcher

• Square Systems; Equations of Planes

  Denis Auroux

  Play

  John Belcher

• Parametric Equations for Lines and Curves

  Denis Auroux

  Playing

  John Belcher

• Velocity, Acceleration - Kepler's Second Law

  Denis Auroux

  Play

  John Belcher

• Review: Vectors and Matrices

  Denis Auroux

  Play

  John Belcher

• Level Curves; Partial Derivatives; Tangent Plane Approximation

  Denis Auroux

  Play

  John Belcher

• Max-Min Problems; Least Squares

  Denis Auroux

  Play

  John Belcher

• Second Derivative Test; Boundaries and Infinity

  Denis Auroux

  Play

  John Belcher

• Differentials; Chain Rule

  Denis Auroux

  Play

  John Belcher

• Gradient; Directional Derivative; Tangent Plane

  Denis Auroux

  Play

  John Belcher

• Lagrange Multipliers

  Denis Auroux

  Play

  John Belcher

• Non-Independent Variables

  Denis Auroux

  Play

  John Belcher

• Partial Differential Equations; Review

  Denis Auroux

  Play

  John Belcher

• Double Integrals

  Denis Auroux

  Play

  John Belcher

• Double Integrals in Polar Coordinates; Applications

  Denis Auroux

  Play

  John Belcher

• Change of Variables

  Denis Auroux

  Play

  John Belcher

• Vector Fields and Line Integrals in the Plane

  Denis Auroux

  Play

  John Belcher

• Path Independence and Conservative Fields

  Denis Auroux

  Play

  John Belcher

• Gradient Fields and Potential Functions

  Denis Auroux

  Play

  John Belcher

• Green's Theorem

  Denis Auroux

  Play

  John Belcher

• Flux; Normal Form of Green's Theorem

  Denis Auroux

  Play

  John Belcher

• Simply Connected Regions; Review

  Denis Auroux

  Play

  John Belcher

• Triple Integrals in Rectangular and Cylindrical Coordinates

  Denis Auroux

  Play

  John Belcher

• Spherical Coordinates; Surface Area

  Denis Auroux

  Play

  John Belcher

• Vector Fields in 3D; Surface Integrals and Flux

  Denis Auroux

  Play

  John Belcher

• Divergence Theorem

  Denis Auroux

  Play

  John Belcher

• Divergence Theorem (continued): Applications and Proof

  Denis Auroux

  Play

  John Belcher

• Line Integrals in Space, Curl, Exactness and Potentials

  Denis Auroux

  Play

  John Belcher

• Stokes' Theorem

  Denis Auroux

  Play

  John Belcher

• Stokes' Theorem (continued); Review

  Denis Auroux

  Play

  John Belcher

• Topological Considerations - Maxwell's Equations

  Denis Auroux

  Play

  John Belcher

• Multivariable Calculus Final Review

  Denis Auroux

  Play

  John Belcher

• Multivariable Calculus Final Review (continued)

  Denis Auroux

  Play

  John Belcher