Math 231 - Calculus III - Homework Assigments/Solutions, Spring, 2008

 

  Date    

Assignment

Due

  Jan 9  

 

Vectors in the Plane/(10.1)
Assignment 1 - turn in the problems with (*)         

Page 794:
1, 2*, 3, 4*, 9, 10*, 17, 18*, 19, 20(a)*, 25, 26*

 

Extra points: 20(b), 32, 48, 47

 

Solutions

   Jan 11

  Jan 11

Vectors in Space/(10.2)
Assignment 2 - turn in the problems with (*)         

Page 802:
11, 12*, 17, 18*, 19, 20*, 23, 24*, 27, 28*

31, 32*, 33, 34, 35, 36, 37, 38*

 

Extra points: 44, 46

 

Solutions

   Jan 15

   Jan 15

The Dot Product/(10.3)

Assignment 3 - turn in the problems with (*)       

 

Page 811:

5, 9, 10*, 13, 14*, 15, 16*, 23, 24*, 31*(a)(b)(e)

 

Extra points: 

Let u=<3,1,-4> and v=<-2,2,1>. Verify the Cauchy-Schwartz inequality and the triangle inequality.

 

Solutions

   Jan 18

  Jan 18

The Cross Product/(10.4)

Assignment 4 - turn in the problems with (*)     

 

Page 825:

5, 6*, 15, 16*, 19, 20*, 23, 24*, 47*, 51*

 

Extra points:

54, 56, 58, 66

 

Solutions

  Jan 22

 

  Jan 22

Lines and Planes in Space/(10.5)

Assignment 5 - turn in the problems with (*)     

 

Page 834:

 

3, 5, 8*, 9, 10*, 13, 15, 16*, 17, 18*

23, 24*, 27, 28*, 19, 30*

55-62

 

Extra points:

42, 46, 54, 60, 62

 

Solutions

 

  Jan 25

  Jan 25

Surfaces in Space/(10.6)

Page 847: - turn in the problems with (*) 

1, 2* (trace: x=2, x= - 2)

3, 4* (trace: y=0, z=1)

15, 22* (trace: x=1, x= - 1)

23, 24* (trace: z=-1, z= 1)

41,42*

 

 Jan 29

 Jan 29

Vector-Valued Functions/(11.1)

Page 862: - turn in the problems with (*) 

 

1,2*, 5, 6*, 7, 8*, 9, 10*, 15, 16*

 

19-30, 23*, 33*, 37*

- use either calculator or Scientific Notebook

Scientific Notebook is installed on PCs in Thompson 220 and 215

 

Solutions

 

 Feb 4

 Feb 4

Calculus of Vector-Valued Functions/(11.2)

 

Page 874: - turn in the problems with (*)

 

3, 4*, 7, 8*, 9, 10*, 13, 14*, 17, 18*

 

Without using a calculator or Scientific Notebook:   20*, 21*

 

25, 26*, 31, 32*

 

35, 36*, 39, 40*

 

Extra points:  6, 12, 47, 48, 49

 

Solutions

 

 Feb 8

 Feb 8

 Motion in Space/(11.3) and Curvature/(11.4)

 

Page 884: - turn in the problems with (*)

 

5, 6*,  7, 8*, 13, 14*

 

Page 893: - turn in the problems with (*)

 

7, 8*, 9, 10*, 11, 12*, 13, 14*

 

15, 16*, 17, 18*,  21, 22*, 23, 24*

 

Extra points:  30, 32, 34, 36

 

Solutions

 

Feb 12

 Feb 12

Curvature/(11.4) and Tangent and Normal Vectors (11.5)

 

Page 894: - turn in the problems with (*)

33, 34*, 41, 42*, 45, 46*

 

Page 906: - turn in the problems with (*)

1, 2*, 5, 6*, 9, 10*, 11, 12*

 

Solutions

 

 Feb 15

 Feb 15

Tangent and Normal Vectors (11.5) and Function of Several Variables (12.1)

 

Page 906: - turn in the problems with (*)

21, 22*, 23, 24*

25-28, 26*, 28*

 

Page 930: - turn in the problems with (*)

1-6: 2*, 4*, 6*

7, 8*, 11, 12*, 19, 20*

37* c=0, c=1, c=4,  40* c= - 2, c=0, c=2

47, 49

51, 52* c= - 1, c=0, c=1

 

Extra points:  18, 42, 54

 

Solutions

 

 Feb 19

 Feb 19

Limits and Continuity (12.2)

 

Page 947: - turn in the problems with (*) on Friday, Feb 22

1-6: 2*, 6*

7-22: 10*, 12*, 20*

23-30: 26* (using polar coordinates for x,y)

35-40:  36*, 37*, 40*

 

On Tuesday, Feb 26

14*,  22*,  28*, 38*

55-58:  56*

Extra points: 42, 44, 52, 58

 

 

 Feb 22/26

 Feb 26

Partial Derivatives (12.3) and Tangent Plane and Normal Line (12.4) – HW13

 

Page 957: - turn in the problems with (*)

1-8: 6* (without using a calculator)

9-16: 12*, 14* (without using a calculator)

17, 18*, 19, 20*

29, 30*, 43*

 

 

Page 970: - turn in the problems with (*)

1-6: 2(b)*, 4(b)*

7-12: 8(a)*, 10(a)*

 

Solutions

 

Feb 29

Feb 29

Chair Rule (12.5) –HW14

 

Page 981: : - turn in the problems with (*)

3-6: 4*, 6*

7-10: 8*, 10*

17-20: 18*, 20*

21-24: 22

25*

Extra points: 26, 27

 

Solutions

 

Mar 4

Mar 4

Directional Derivatives (12.6) – HW15

 

Page 992: : - turn in the problems with (*)

1-4: 4*

5-10: 6*, 8*

11-26: 12*, 16*, 18*, 22*

27-36: 30*

47-50: 48*

Extra points: 36, 46, 50

 

Solutions

 

 Mar 7

Mar 7

Extrema of Functions of Several Variables (12.7) – HW16

 

 

Page 1008: : - turn in the problems with (*)

51-54: 52*, 54*

55-60: 58*

1-8: 2*, 4*, 6*

35-38: 35*, 38*

Extra points: 44(b), 46

 

Solutions

 

Mar 11

Mar 11

Double Integrals (13.1)

 

Page 1043: : - turn in the problems with (*)

7-10: 10*

11-14: 14*

15-22: 18*, 20* - without using a calclulator

25-32: 28*, 30*

37-42: 38*, 40*, 42*

44-47: 44*, 46*

49-52: 52*

Mar 18

Mar 18

Applications (13.2) and Polar Coordinates (13.3)

 

Page 1055:  - turn in the problems with (*)

7-18: 8*, 16*

23-28:  24*

43-46: *44

 

Page 1064: - : - turn in the problems with (*)

1-6:  *4, *6

7-12: *8, *10

13-16: *16

17-26: *18, *22, *24

27-32: *28, *31

Mar 21

Mar 21

Surface area (13.4)/Triple Integrals (13,5)

 

Page 1071: - turn in the problems with (*)

1-12:  2*,  6*

16*

 

Page 1082: - turn in the problems with (*)

1-4: 2- without using a calculator

5-16: 6*, *9, 10* - for each problem, sketch the solid Q first

 

Solutions

 

April 1

Apr 1

Triple Integrals in Cylindrical and Spherical Coordinates (13.5)/(13.6)/(13.7)

 

Page 1082- turn in the problems with (*)

17-28: 20*, 28*

29-36: 30*

37-42: 38*, 40*

Extra points: 42

 

Page 1090: -  turn in the problems with (*)

9-20: 12*, 16*.   Extra points:  18, 20

33-38: 34*, 38*.  Extra points: 36

 

Page 1098: - turn in the problems with (*)

1-8: 6*

9-16: 14*  Extra points 16

17-23:  20*

25-32:  28*, 30*  Extra points 32

43-52: *44, *50   Extra points 52

 

Solutions

 

April 4

Apr 4

Vector Field (14.1) and Line Integrals (14.2)

 

Page 1127- turn in the problems with (*) - April 8

1-10:  4*, 6*,  x=-2,-1,0,1,2, y=-2,-1,0,1,2

11

13-18, 14*

23-34:  28*, 30*, 34*

35-42:  38*, 40*

Extra points: 22, 48, 52

 

Solutions

 

Page 1142 - turn in the problems with (*) - April 9

1-24:  6*, 8*, 12*, 14*, 18*, 22*

25-36: 28*, 35*,  Extra points: 36

 

Solutions

 

April 8/9

 

April 14

Independence of Path (14.3)

 

Page 1153 - turn in the problems with (*)

1-12: 2*, 10*, Extra point 12

13-18: 14*, 18*

19-30: 20*, 21*, Extra point - 30

41-44

Extra point: 45

 

Solutions

 

April 18

April 18

Green’s Theorem (14.4)

 

Page 1164 - turn in the problems with (*)

1-4: 2*

5-20: 8*, 10*, 13*, 15*, Extra points 18

34*, 35*

 

Solutions

 

April 22

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