Harvard University,FAS
Spring 2003

Mathematics Math21a
Spring 2003

Multivariable Calculus

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu
News Syllabus Sections Checks Calendar Homework Exams Addons Lab Project Faq Links
Challenge problems are an option for the project part. They are not turned in with the regular homework.
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Week 1:              Geometry of Space (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1         9.1          2, 8, 10         2/5 rsp. 2/6
                         14, 34                 .

  2         9.2          20, 34           2/7 rsp 2/11
            9.3          18, 34, 38             .
  
  3         9.4          16, 18, 26       2/10 rsp 2/11
                         32, 34                 .

   Solutions Week 1  (For questions about the posted 
   solutions, contact Jonathan (guberman@fas)).
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Week 2:              Lines, Planes, Functions (Challenge problems)
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 assigned                                  due
 in hour    section      numbers

  1         9.5          6, 8, 20            2/12 rsp. 2/13
                         26, 36                  .

  2         9.5          46, 48, 52,         2/14 rsp. 2/18
            9.6          4, 18                   .

  3         9.6          16, 20, 22          2/19 rsp. 2/18
                         26, 32                  .
Solutions Week 2
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Week 3:              Curves   (Challenge problems)
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 assigned                                  due
 in hour  section      numbers

  1         -          Holyday (Presidents day)

  2       10.1         18,28                 2/21 rsp 2/20
          10.2         10,18,46

  3       10.3         2,4,22                2/24 rsp 2/25
          10.4         12,34
Solutions Week 3
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Week 4:              Surfaces  (Challenge problems)
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 assigned                                  due
 in hour  section      numbers

  1        9.7         6,10,16,20,22       2/26 rsp 2/27

  2       10.5         4,11-16,18,22,32a   2/28 rsp 3/4

  3       11.1         18, 24, 31-36,      2/3  rsp 3/4
          11.2         28, 34
Solutions Week 4
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Week 5:              Partial derivatives (Challenge problems)
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 assigned                                  due
 in hour  section      numbers

  1       11.3         48, 62, 66, 70, 76  3/5 rsp 3/6
                        you can skip 76d)
 
  2       11.4         4, 12, 28, 30, 40   3/7 rsp 3/11   (*)  

  3       Review for midterm

 Solutions Week 5 

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Week 6:               Chain Rule (Challenge problems)
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 assigned                                  due
 in hour  section        numbers            
 
  1       11.5           6, 18, 24, 28, 30    3/12 rsp 3/13
  
  2       11.5           32, 42, 43           3/14 rsp 3/18
          11.6           8, 18

  3       11.6           20, 26, 30, 42, 44   3/17 rsp 3/18

 Solutions Week 6 
  
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Week 7:                Extrema  (Challenge problems)
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 assigned                                  due
 in hour    section      numbers

  1       11.7         4, 8, 12, 16, 26       3/19 rsp 3/20

  2       11.8         8, 10, 24, 42a,42b     3/21 rsp 4/1

  3       11.8         6, 12, 18, 19, 36      3/31 rsp 4/1
Solutions Week 7
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Week 8:                Double Integrals  (Challenge problems)
-----------------------------------------------
 assigned                                  due
 in hour    section      numbers

  1       12.1         14, 18              4/2 rsp 4/3
          12.2         4, 14, 20

  2       12.3         10, 14, 22          4/4 rsp 4/8
          12.4         10, 12

  3       12.3         30, 36              4/7 rsp 4/8
          12.6         8, 10, 22      

 Solutions Week 8 

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Week 9:                Triple Integrals  (Challenge problems)
-----------------------------------------------
 assigned                                  due
 in hour    section     numbers

  1         12.7        4, 16, 24          4/9 rsp 4/10
                        34, 46

  2         12.8        4, 8, 10           4/11 rsp 4/15
                        20, 32           

  3         12.9        4, 10, 22          4/14 rsp 4/15
            12.8        30, 16

 Solutions Week 9 
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Week 10:                Line Integrals  (Challenge problems)
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 assigned                                  due
 in hour    section     numbers


  1         13.1        4,6,28,29-32,34    4/16 rsp. 4/17

   Solutions 13.1 

  2         13.2        10,14,16,18,38     4/18 rsp. 4/22

  3         13.3        6,16,20,22,26      4/21 rsp. 4/22

   Solutions 13.2-13.3 
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Week 11:                Integral Theorems I  (Challenge problems)
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 assigned                                  due
 in hour    section     numbers

  1       Review        No homework 
                        due to exam

  2       13.4          2, 8, 18, 20, 22  4/25 rsp. 4/29

  3       13.5          4, 6, 10, 14, 34  4/28 rsp. 4/29

   Solutions Week 11 
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Week 12:                Integral Theorems II  (Challenge problems)
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 assigned                                      due
 in hour  section       numbers

  1       13.6          4, 8, 14, 34, 42       4/30 rsp 5/1

  2       13.7          2, 10, 12, 14, 18      5/2  rsp 5/4
                        (12 b,c with CAS 
                        are optional)

  3       13.8          2, 4, 6, 20, 22        5/3  rsp 5/4

   Solutions Week 12 

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Please send comments to math21a@fas.harvard.edu


Wed May 21 22:22:42 EDT 2003