Ph 385

8/18/2015 10:26 AM

 

Problem Assignments (Fall 2015)

(Changes in Schey Version 4)

 

Problem Set 1.  Ch. 1 P 1, New 4, 5, 6, New 10, 10a, 23, 26; computer problem Comp-1.

 

Problem Set 2.  Ch. 1 P {2, 3, 21 - all using Mathematica}, 12, 13,  15, 16, 17, 18, 19, 20, 25, 32; Ch. 2 P 1, 2, 3, 4.

 

Problem Set 3.  Ch 2 P 6, 7, 9; Ch. 3 P 2a (using Mathematica), 3, 7, 9, 10; Ch. 4 P 1.

 

Problem Set 4.  Ch. 4 P. 2, 3, 4, 6; Ch. 5 P. 1, 2 (using Mathematica), 3, 5.

 

Problem Set 5.   Ch. 5 P. 6; Ch. 6 P. 1, 3, 5, 6, 7, 8, 13, 15; Ch. 6a P 1, 2, 4, 5;  computer problem Wave-1.

 

Problem Set 6.  Ch. 7 P. 3, 5, 6, 7, 8; Ch. 8 P 1, 2; Ch. 9 P. 1, 3; computer problem Wave-2.

 

Problem Set 7.  Ch. 9 P. 4, 5, 6 (using Excel), 7; Ch. 10 P 1, 2, 3.

 

Problem Set 8.  Schey Ch. I P. 1 (plot F at 25 pts, x and y = -2, -1, 0, 1, 2; use reduced scale for the length of the vectors), 3, 6;

 

Problem Set 9. Ch. II P. 2, 4 part (a), 5 part (a),10, 12; computer problem Fourier-1.

 

Problem Set 10.  Ch. II P. 14, 15 parts (a) and (b), 17, 19, 21; computer problem Fourier-2.

 

Problem Set 11.  Ch. II P. 23, 24, 27, 28; Ch. III P. 1, 2

 

Problem Set 12.  Ch. III P. 3, 4 parts (a) and (b), P. 6 (use tensor notation), 9, 11 (note typo in problem 11 - should say "See Problem II-19"), 15 (OK to choose any capping surface you like).

 

Problem Set 13.  Ch. III P. 20, 24 (substitute the given expressions for the components of  into ; then look for a place to use ), 25, 26, Ch. IV P. 1 (see revised version below).

 

Problem Set 14.  Ch. IV P. 2 (see revised version below), 3 (use tensor notation), 24, 27.

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Schey Ch. IV Problem 1 (modified).  (a)  Calculate  for each of the following scalar functions:

 

 

 

 

   (b)  Verify that

for the specified function  determined in part (a) by choosing for the curve C:

            (i)  the square in the xy-plane with vertices at (0,0), (1,0), (1,1), and (0,1); use function (i) above.

            (ii)  the triangle in the yz-plane with vertices at (0,0), (1,0), and (0,1); use function (iii) above.

            (iii)  the circle of unit radius centered at the origin and lying in the xz-plane; use function (iv) above.

      (c)  Verify by direct calculation that  for all of the functions  determined in part (a).

Schey Ch. IV Problem 2 (modified).   Using tensor notation, verify the following identities, in which f and g are arbitrary differentiable scalar functions of position, and  and  are arbitrary differentiable vector functions of position: