MATH 253 Sec 504-506 Spring 2004: Homework

Text: Calculus, with Early Vectors, by James Stewart.

Homework 1

Chapter 11

• Section 11.1 -- #3, 5, 7, 13, 25, 29, 31, 33, 35, 39, 45, 47.
• Section 11.2 -- #5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31, 33, 35.
• Section 11.3 -- #3, 5, 7, 9, 11, 19, 21, 23, 31.
  
•  Let A₁ and B₁ be the vectors (1,2,0) and (-3,1,0), respectively. Let A₂ and B₂ be the vectors obtained by rotating A₁ and B₁ by an angle of 60 degrees in the counterclockwise direction about the Z-axis. Compute the vectors A₂ and B₂ and show that the cross product of A₂ with B₂ is the same as the cross product of A₁ with B₁.
  Hint: to compute A₂ and B₂, express the x,y-coordinates of A₁ and B₁ using polar coordinates.
  Answer: A₂=(-1.232, 1.866, 0); B₂=(-2.366, -2.098, 0) and A₁ x B₁ = (0,0,7) = A₂ x B₂.

Homework 2

Chapter 11

• Section 11.4 -- #3, 7, 13, 15, 17, 19, 25, 29, 31, 37, 43, 47, 49, 51, 55, 63, 65.
• Section 11.5 -- #17-24, Use Maple on (25, 27, 28, 29, 30, 31), 41, 43.
• Section 11.6 -- #1-6, 9, 17, 21, 25, 31, 37, 41, 43, 47, 51, 57, 61, 74.
• Section 11.7 -- #1, 3, 9, 12(Find v, a, j, T, B, N, curvature and torsion).
• Section 11.8 -- #3, 5, 9, 15, 17, 21, 25.

Homework 3

Chapter 12

• Section 12.1 -- #3, 7, 10, 21, 24, Use Maple:(33, 35, 37, 39, 41, 43, 45), 53, 55, 57, 59-64.
• Section 12.2 -- #5, 7, 9, 15, 33, 39, 45.
• Section 12.3 -- #1, 5, 7, 10, 23, 29, 31, 47, 50, 57, 63, 75, 85, 91.
• Section 12.4 -- #1, 5, 7, 15, 19, 25, 31.

Homework 4

Chapter 12

• Section 12.5 -- #1, 7, 11, 13, 17, 19, 35, 39.
• Section 12.6 -- #1, 5, 7, 11, 15, 19, 25, 27, 30, 35, 37, 41, 49, 55.

Homework 5

Chapter 12

• Section 12.7 -- #1, 3, 7, 9, 17, 25, 31, 37, 43, 49.
• Section 12.8 -- #3, 5, 7, 9, 17, 27, 33, 39.

Homework 6

Chapter 13

• Section 13.1 -- #1, 5, 10(divide into 3x3), 13.
• Section 13.2 -- #5, 13, 17, 21, 23, 27, 29, 31, 35.
• Section 13.3 -- #3, 9, 13, 17, 21, 25, 27, 29, 33, 35, 39, 41.
• Section 13.4 -- #3, 9, 15, 19, 23, 25, 27, 29, 31, 33, 39, 43, 51.
• Section 13.5 -- #3, 5, 9, 13, 17, 19, 25, 27, 31.

Homework 7

Chapter 13

• Section 13.6 -- #1, 3, 5, 9, 11, 13, 15.
• Section 13.8 -- #3, 5, 7, 9, 11, 15, 17, 21, 25, 31.
• Section 13.9 -- #3, 9, 17, 23, 27, 31, 39, 45, 47, 53, 55, 57, 59, 61, 63.
• Section 13.10 -- #1, 3, 7, 13, 17, 21, 23, 24, 29, 33, 35.

Homework 8

Chapter 13

• Section 13.11 -- #1, 3, 5, 7, 9, 11, 13, 15, 19, 21.
• Also compute the Jacobian for spherical coordinates.