Outline of the course

• Curves defined by parametric equations
  
• Vector functions and space curves
  
• Derivatives and integrals of vector functions
  
• Arc length and curvature
  
• Motion in space: velocity and acceleration

10.1
13.1
13.2
13.3
13.4

• Functions of several variables
  
• Partial derivatives
  
• Linear approximations
  
• Directional derivatives and the gradient vector
  
• Lagrange Multipliers
  

12.6,14.1
14.3
14.4
14.6
14.8

• Double integral over general region
  
• Double integral in polar coordinates
  
• Applications of double integrals
  
• Triple integrals
  
• Change of variables in multiple integrals
  

15.3
15.4
15.5
15.6-15.8
15.9

• Vector fields
  
• Line integrals
  
• The fundamental theorem of line integrals
  
• Green's Theorem
  
• Curl and divergence
  
• Parametric surfaces and their areas
  
• Surface integrals
  
• Stoke's theorem
  
• Divergence theorem
  

16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9