Mathematics & Statistics Multivariable Calculus

Download multivariable calculus comps syllabus

Elementary vector analysis

• Dot or scalar product 
• Cross or vector product
• Lines and planes 
• Tangent vectors and tangent lines to parametrized curves
  

Definitions and computations involving functions of several variables

• Partial derivative
• Directional derivative
• Gradient
• Tangent plane to a surface

Maxima and minima of functions of several variables

• Finding critical points
• The second derivative test for local maxima/minima and saddle points
• The method of Lagrange multipliers

Double integrals 

• Cartesian and polar coordinates
• Finding area and volume

Triple integrals 

• Cartesian, cylindrical and spherical coordinates
• Finding volume
  

Line integrals 

• Fundamental Theorem of Calculus for Line Integrals
  
• Green's Theorem