Homework

Comments: 

  • Homework will not be collected or graded, but the midterm exam will be based entirely on the assignments that precede it and the final exam will be based in part on the homework as well. 
  • Problems marked with a (+) are more challenging/fun.

 Assignment 1

      Chapter 5 - 5.1 5.2 5.4, 5.5, 5.6, 5.9, 5.12, 5.14, 5.16, 5.18(+).

Hints:

  • 5.6 -- It may be easier to differentiate the logarithms of the expressions.
  • 5.18 -- This is a constrained optimization problem (not an envelope problem).

Assignment 2

     Chapter 6 - 2, 3, 4, 18, 19.

Hints:

  • 6.4: surface integral means double integral.
  • 6.19: The substitution is suggested by the boundary curves of the original region.

Assignment 3

     Chapter 8 - 4, 11, 16, 29, 30(+), 37, 41(+).

 Assignment 4

     Chapter 10 - 4(+), 7(a,b,c,d), 12, 19.

Hints:

  • 10.4: Use vector methods, i.e., start with the vector form of the (differential) equation describing the motion of a body under gravity. If r(t) is the position of the stone at time t, show that the condition that the stone is always moving away from the thrower may be expressed in terms of the dot product r'(t)·r(t), and go from there.
  • 10.19: B is the magnetic field, E is the electric field and c is the speed of light, but you can do the whole problem as a pure math problem.

Assignment 5

       Chapter 6 -  4;  Chapter 11 -  1, 3, 4, 18, 28.

Comment:

  • There is an error in the statement of 11.28 - the corners of the rectangle should all be scaled by the parameter a (the same one that appears in the definition of the force field). E.g., B=(a,a,0).

Assignment 6

       Chapter 12 - 5, 6, 8, 14.

Comment:

  • The function |x| in 14 is very simlar to the example I did in class on Friday.

 Assignment 7

       Chapter 13 -  3, 4 (1st part and application (a)), 5, 12, 21, 22.

Comments/Hints:

  • 13.12 -- Not as hard as it looks at first.
  • 13.22 -- Use Partial fraction decomposition before finding the inverse transforms.

Assignment 8

       Chapter 24 - 1, 3, 6, 9, 10, 15, 18.

       Chapter 25 - 6, 7, 15.

Assignment 9

       Chapter 14 -  2, 4, 5(a), 8, 14, 24.

       Chapter 15 - 2, 4, 14 first part and (a).

Comments:

  • 14.14 - see section 14.2.8
  • 14.24 - see section 14.2.5