Math 252 Homework Assignment 04

- Due 8:30 AM Friday February 5th, 1999.

• Section 3.1, pages 112-114:
  
  
  • 5, 8, 10, 12, 17, 21, 23, 29, 32
  
  
• Section 3.2, page 117:
  
  
  • 2
    
    
  • jh04.1:
    1. Plot in Maple the isotimic surfaces given by x^2 + y^2 - z^2 = C^2 for C=1, C=2, and C=3.

    2. What is the gradient field of x^2 + y^2 - z^2 ?

    3. Plot this gradient field in Maple.

    4. What are the equations of the flow lines for this gradient field? In particular, what are the equations of the three flow lines through the points (1,1,1), (1,1,2), and (1,1,3)?

    5. Plot these three flow lines in Maple, along with the isotimic surfaces on the same graph.
  
  
• Section 3.3, page 124:
  
  
  • 4, 5, 6, 11
    
    
  • jh04.2:
    1. Let . What is ?
    2. Plot a set of flow lines in the xz-plane. Do they appear to be converging in some places and diverging in others? How can the divergence of the vector field be constant? Plot the vector field in the xz-plane, in order to assist with explanation.