Multivariable Calculus
Independent Study
Week 
Topic(s) 
Quiz Due 

Problem set 
Problem set 
1 
Parametric equations and curves 


2 
Polar coordinates 


3 
Conic sections 


4 
3D coordinate systems, vectors 


5 
Dot product and cross product 


6 
Equations of lines and planes 


7 
Equations of cylinders and quadratic surfaces 


8 
Vector functions and their derivatives 


9 
Arc length and curvature,
motion in space 


10 
Functions of several
variables 


11 
Partial derivatives 


12 
Tangent planes and linear
approximations 


13 
The chain rule 


14 
Directional derivatives and
the gradient vector 


15 
Minimum and maximum values,
Lagrange multipliers 


16 
Introduction to double
integrals and iterated integrals 


17 
Double integrals 


18 
Applications of double integrals
and surface area 


19 
Triple integrals 
