Multivariable Calculus

Multivariable calculus involves functions of more than one variable such as or . Similarly to single variable calculus there are techniques for differentiating, integrating and optimising these functions.

1. Multivariable Functions
   • Partial Derivatives and Tangent Planes
   • Gradient Vector and Linearization
   • Chain Rule
   • Implicit Function Theorem
   • Directional Derivatives
   • Taylor Series
   • Vector Functions
2. Optimization
   • Critical Points and 2nd Partials Test
   • Techniques when 2nd Partials Test Fails
   • Lagrange Multipliers
3. Integration
   • Integration Summary
   • Line Integrals
   • Line Integrals and Vector Fields
   • Double Integrals including Polar Coordinates
   • Greens Theorem
   • Triple Integrals including Polar Coordinates
   • Surface Integrals
   • Flux Integral
   • Divergence Theorem
   • Stokes Theorem