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.
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Material |
Number of Lectures |
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Introduction, parametric equations |
4 |
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Vectors and Planes |
4 |
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Partial Derivatives |
9 |
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Multiple Integrals |
10 |
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Vector Calculus |
12 |
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Review (RRR Week) |
3 |
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Total |
42 |
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Tests |
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Exam |
Date |
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Material covered |
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Midterm # 1 |
September 24 |
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Lectures |
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Midterm # 2 |
November 5 |
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Lectures |
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Final Exam |
December 15, 11:30-2:30 PM |
All Lectures with 28-39 emphasized |
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Grades |
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Work |
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Percentage of final grade |
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Homework and Quizzes |
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20 % |
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Midterm #1 |
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20 % |
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Midterm #2 |
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20 % |
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Final Exam 20 |
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40 % |
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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
3
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Date |
Topic |
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1 |
August 29 |
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2 |
September 3 |
Parametric curves |
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3 |
September 5 |
Tangents and Area |
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4 |
September 8 |
Polar coordinates |
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5 |
September 10 |
More on polar coordinates |
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6 |
September 12 |
Vectors |
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7 |
September 15 |
Lines and planes |
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8 |
September 17 |
Quadric surfaces |
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9 |
September 19 |
Space curves |
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10 |
September 22 |
Cylindrical and spherical coordinates |
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11 |
September 26 |
Functions of several variables |
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12 |
September 29 |
Partial Derivatives |
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13 |
October 1 |
Tangent planes and differentials |
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14 |
October 3 |
Chain rule |
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15 |
October 6 |
More on chain rule, implicit differentiation |
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16 |
October 8 |
The gradient |
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17 |
October 10 |
Maxima and minima |
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18 |
October 13 |
Lagrange multipliers |
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19 |
October 15 |
Double integrals |
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20 |
October 17 |
Iterated integrals |
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21 |
October 20 |
More on double integrals |
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22 |
October 22 |
Applications |
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23 |
October 24 |
Surface area |
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24 |
October 27 |
Triple Integrals |
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25 |
October 29 |
Integrals in cylindrical and spherical coordinates |
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26 |
October 31 |
Change of variables, Jacobians |
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27 |
November 3 |
More on change of variables |
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28 |
November 7 |
Vector fields |
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29 |
November 10 |
Line integrals |
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30 |
November 12 |
Fundamental Theorem of line integrals |
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31 |
November 14 |
Green's Theorem |
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32 |
November 17 |
Proof of Green's Theorem |
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33 |
November 19 |
Curl and divergence |
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34 |
November 21 |
Parametric surfaces |
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35 |
November 24 |
Surface integrals |
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36 |
November 26 |
Stokes's Theorem |
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37 |
December 1 |
Applications |
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38 |
December 3 |
Divergence Theorem |
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39 |
December 5 |
Applications |
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40 |
December 8 |
Review |
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41 |
December 10 |
Review |
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42 |
December 12 |
Review |
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