Harvard University,FAS
Fall 2002

Mathematics Math21a
Fall 2002

Multivariable Calculus

Course Head: Daniel Goroff
Office: SciCtr 427
Email: goroff@math.harvard.edu
News Syllabus Sections Calendar Homework Exams Supplements Lab Project Faq Links
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Week 1:                       Geometry of Space (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1         9.1          5, 8, 10         9/25 rsp 9/26
                         14,28                  .
  Solutions: HW 1a 

  2         9.2          20, 34           9/30 rsp 10/1
            9.3          18, 34                 .
  
  3         9.4          16, 18, 22             .
            9.5          20, 36, 48             .
  Solutions: HW 1b 
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Week 2:                    Functions and Graphs (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1       9.6          10,12,16,24,32     10/2 rsp 10/3   
  Solutions: HW 2a 

  2       9.6          14,18,20,22,26     10/7 rsp 10/8 

  3       9.7          6,8,16,28,30           .
  Solutions: HW 2b (page 1) 
  Solutions: HW 2b (page 2)
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Week 3:                     Curves and Surfaces (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1       10.1         5-10,16,18,20,28   10/9  rsp 10/10
  Solutions: HW 3a

  2       10.2         6,18,40,42,46      10/14 rsp 10/15 (*)

  3       10.3         2, 4,see handout 
  Solutions: HW 3b (for sections 10.2 and 10.3) 
  Solutions: HW 3b (for differential equations handout)
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Week 4:                                Surfaces (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1       Columbus day (no assignment)

  2       Review for first hourly

  3       10.5        11-16,17,18,22,32a   10/21 rsp. 10/22
  Solutions: HW 4
  Note that there was only one part for Homework 4; 
  hence, these 10 questions counted for 60 points.

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Week 5:                     Partial Derivatives (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1       11.1         24, 31-36, 
          11.2         14, 28, 34          10/23  rsp 10/24
  Solutions: HW 5a

  2       11.3         8, 14, 26, 48, 78   10/28 rsp. 10/29

  3       11.4         4, 12, 16, 30, 40
  Solutions: HW 5b
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Week 6:                              Chain Rule (Challenge problems)
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 assigned                                  due
 in hour    section      numbers            

  1       11.5         6, 17, 18, 24, 28   10/30 rsp 10/31
  Solutions: HW 6a

  2       11.5         10, 32, 43,         11/4  rsp 11/5

  3       11.6         8, 16, 20, 26, 30, 
                       42, 44
  Solutions: HW 6b
  
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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    11/6 rsp 11/7
  Solutions: HW 7a 

  2       11.8         8, 10, 24, 42a,42b  11/13 rsp 11/12

  3       11.8         6, 12, 18, 19, 36 
  Solutions: HW 7b
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Week 8:                        Double Integrals  (Challenge problems)
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  1       Veteransday

  2       12.2         2, 14, 20           11/15 rsp 11/14
          12.3         30, 40
  Solutions: HW 8a


  3       12.4         14, 22, 30          11/18 rsp. 11/19
          12.6         8, 22
  Solutions: HW 8b
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Week 9:                        Triple Integrals  (Challenge problems)
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  1      Spill over from last week  (MWF catchup for 2 holidays)

  2      Review for second hourly

  3      12.7:    4, 6, 8, 30, 34          11/25 rsp 11/26
  Solutions: HW 9
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Week 10:                         Line Integrals  (Challenge problems)
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  1       12.8:        2,4,10,16,30        12/2 rsp. 12/3
  Solutions: HW 10a

  2       13.1         6, 29-32,           12/4 rsp. 12/5 
          13.2:        10,14
  Solutions: HW 10b

  3       Thanksgiving
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Week 11:                    Integral Theorems I  (Challenge problems)
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  1       13.1,13.2     From last week     12/4 rsp. 12/5
  
  2       13.3          16, 26             12/9 rsp. 12/10
          13.4          8, 18, 20

  Solutions: HW 11a

  3       13.5          4, 6, 10, 12, 34   12/9 rsp. 12/10
  Solutions: HW 11b
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Week 12:                   Integral Theorems II, (Challenge problems)
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Homework assignments for this week are assigned
individually in section. The following suggestions 
probably will differ from what you get assigned in
your section:

  1       13.6          4, 8, 14, 34, 42

  2       13.7          2, 10, 12, 14, 18

  3       13.8          2, 4, 6, 20, 22

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Please send comments to math21a@fas.harvard.edu