MITx Multivariable Calculus starts next week (edx.org)

Syllabus

  Unit 1: Functions of two variables

  Graphing functions and slicing
  Level curves
  Partial derivatives
  Tangent planes
  Linear approximation

  Unit 2: Geometry of derivatives

  Vectors
  Dot products
  Gradients
  Vector fields
  Directional derivatives

  Unit 3: Optimization

  Critical points
  Second derivative test
  Constrained optimization
  Lagrange multipliers
  Least squares approximation

  Unit 4: Matrices

  Systems of equations
  Matrix algebra
  Undetermined and overdetermined systems
  Linear functions as matrix maps

  Unit 5: Curves

  Parametric curves in 2 and 3 dimensions
  Chain rule
  Vectors and derivatives in three dimensions and higher