Math 53
Math 53  Multivariable Calculus  [4 units]
Course Format: Three hours of lecture and two hours of discussion/workshop per week; at the discretion of the instructor, an additional hour of discussion/workshop per week.
Prerequisites: 1A1B or equivalent
Description: Parametric equations and polar coordinates. Vectors in 2 and 3dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes. (F,SP)
Textbook: Multivariable Calculus  Early Transcendentals for UC Berkeley
Outline of the Course:
Chapter 10: Parametric Equations and Polar Coordinates 
4.5 hours 
Omit Section 10.6. Discuss only the highlights of Section 10.5. 

Chapter 12: Vectors and the Geometry of Space 
4.5 hours 
Chapter 13: Vector Functions 
1 hour 
Cover only Sections 13.1 and 13.2. 

Chapter 14: Partial Derivatives 
8 hours 
Chapter 15: Multiple Integrals 
10 hours 
Some students have difficulty with Sections 15.3 and 15.7 because of the 3D geometry involved. 

Chapter 16: Vector Calculus 
12 hours 
Total 
40 hours 
Midterms 
2 hours 
Holidays & Reviews 
3 hours 

45 hours 
Comments: The final chapter, Vector Calculus, is the heart of the
course. Try not to rush through this material. Several topics in
earlier chapters have been omitted so as to leave more time for Chapter
16.
Lectures may, of course, deviate at their discretion from the suggested
lecture hours. The Calculus Committee welcomes recommendations from the
faculty and GSIs for modifications in the course outline.