Contents

• Graphic Representations of Two Dimensional Functions
  • Objectives
  • Opening the Notebook
  • Inserting Text
  • Graphing Contours
  • Graphing Surfaces
  • Finally
• Limits and Continuity of Two Dimensional Functions
  • Objectives
  • The Two Functions
  • Graphics for Functions
  • Distinguished Limits
  • Finally
• Partial Derivatives, Differentials, and Differentiability
  • Objectives
  • Comparing Differentiable and Non-Differentiable Functions
  • Symbolic Derivatives
  • Finally
• Chain Rule for Partial Derivatives
  • Objectives
  • Derivatives Along Paths
  • Multi-Variable Chain Rule
  • Finally
• Gradients, Normals, Level Curves
  • Objectives
  • The Gradient as a Vector Operator
  • Gradients and Level Curves
  • Finally
• Extrema of Functions
  • Objectives
  • Finding Critical Points
  • A More Complicated Extremization
  • The Second Derivative Test
  • Finally
• Polar Coordinates
  • Objectives
  • Graphing Polar functions
  • Center of Mass in Polar
  • Finally
• Change of Variables
  • Objectives
  • Change of variables, spherical
  • Change of variables, sample problem
  • Finally
• Line Integrals
  • Objectives
  • Center of mass
  • Work
  • Finally
• Divergence and Stokes Theorem
  • Objectives
  • Initialization
  • Divergence
  • Stokes Theorem