Mathematics 53  Multivariable Calculus
Professor M. Zworski
Office Hours:
Class meetings: The main lectures are TT 11:30
Course Webpage: The handouts and assignments on bCourse.
Text: J. Steward, Custom version of Calculus (Early Transcendentals), 8th edition for Math 53
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2
Overview

Material 
Number of Lectures 




Introduction, parametric equations 
4 




Vectors and Planes 
4 




Partial Derivatives 
9 

Multiple Integrals 
10 

Vector Calculus 
12 

Review (RRR Week) 
3 




Total 
42 







Tests 










Exam 
Date 


Material covered 


Midterm # 1 
September 24 


Lectures 










Midterm # 2 
November 5 


Lectures 










Final Exam 
December 15, 11:302:30 PM 
All Lectures with 2839 emphasized 












Grades 












Work 

Percentage of final grade 













Homework and Quizzes 

20 % 













Midterm #1 

20 % 













Midterm #2 

20 % 





Final Exam 20 

40 % 


Grades will be computed in the following way. You will be given a letter grade (+ or, if appropriate) for each item of work above and we will later combine these grades as indicated in the table to obtain the nal grade for the course. The TAs will lastly identify borderline cases, for which we will carefully look at the numerical grades on the variou s tests to determine the grade.
If you do not take Midterm #1, Midterm # 2 will count for 40 % of your grade. If you take Midterm #1 but not Midterm #2, the Final Exam will count for 60 % of your grade. If you take neither Midterm #1 nor Midterm #2, you will fail the course. Consequently, please mark them in your calendars.
Homework and Quizzes: There will be a weekly quizz given each Tuesday in sections. There will be no
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Date 
Topic 

1 
August 29 


2 
September 3 
Parametric curves 





3 
September 5 
Tangents and Area 





4 
September 8 
Polar coordinates 





5 
September 10 
More on polar coordinates 





6 
September 12 
Vectors 

7 
September 15 
Lines and planes 

8 
September 17 
Quadric surfaces 

9 
September 19 
Space curves 





10 
September 22 
Cylindrical and spherical coordinates 





11 
September 26 
Functions of several variables 





12 
September 29 
Partial Derivatives 





13 
October 1 
Tangent planes and differentials 





14 
October 3 
Chain rule 

15 
October 6 
More on chain rule, implicit differentiation 

16 
October 8 
The gradient 

17 
October 10 
Maxima and minima 





18 
October 13 
Lagrange multipliers 





19 
October 15 
Double integrals 





20 
October 17 
Iterated integrals 





21 
October 20 
More on double integrals 





22 
October 22 
Applications 

23 
October 24 
Surface area 

24 
October 27 
Triple Integrals 

25 
October 29 
Integrals in cylindrical and spherical coordinates 





26 
October 31 
Change of variables, Jacobians 





27 
November 3 
More on change of variables 





28 
November 7 
Vector fields 





29 
November 10 
Line integrals 





30 
November 12 
Fundamental Theorem of line integrals 

31 
November 14 
Green's Theorem 

32 
November 17 
Proof of Green's Theorem 

33 
November 19 
Curl and divergence 





34 
November 21 
Parametric surfaces 





35 
November 24 
Surface integrals 





36 
November 26 
Stokes's Theorem 





37 
December 1 
Applications 

38 
December 3 
Divergence Theorem 

39 
December 5 
Applications 

40 
December 8 
Review 

41 
December 10 
Review 





42 
December 12 
Review 



