homework - Homework List for Math 254.01 (Autumn 2010) Kiam...

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Unformatted text preview: Homework List for Math 254.01 (Autumn 2010) Kiam Heong Kwa November 26, 2010 Remark 1. This list will be updated throughout the quarter. Remark 2. A problem with an asterisk (*) is relatively more difficult. Remark 3. Turn in only boxed problems. Final is on December 6 (Monday) from 11:30am to 1:18pm. *** Note the time!!! *** Sec 16.9 5, 7, 13 Problem 7: Use the cylindrical coordinates y = r cos , z = r sin , x = x . Sec 16.8 3, 6, 7, 9 Problem 3: The boundary curve of S , i.e., the part of the paraboloid z = x 2 + y 2 that lies inside the cylinder x 2 + y 2 = 4 , has the vector equation r ( ) = 2 cos i + 2 sin j + 4 k , 2 , if oriented in the counter- clockwise direction when viewed from above. Problem 6: The boundary curve of S , i.e., the hemisphere x = p 1- y 2- z 2 , is the unit circle y 2 + z 2 = 1 , x = 0 , in the yz-plane. Note that the unit disk D , i.e., y 2 + z 2 1 , x = 0 , in the yz-plane has the same boundary curve. Hence RR S F d S = RR D F d S . Sec 16.7 due 12/01: 5, 7, 9, 13, 15, 17, 19, 21, 23 Sec 16.6 due 12/01: 4, 5, 13, 14, 15, 16, 17, 18, 21, 22, 23, 25, 33, 35, 37, 39, 43, 47 Problem 4: Use the identity sin 2 u + cos 2 = 1 . 1 Problem 5: It is a hyperbolic paraboloid. See Table I on p. 808 of the text. Problem 13: Set x = u cos v , y = u sin v , and z = v . Then grid curves of constant u are circles with radii | u | because x 2 + y 2 = u 2 . Note that these are also traces parallel to the xy-plane. The grid curve of a constant v is a straight line in the plane z = v such that y = x cot v except when u = 0 ....
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homework - Homework List for Math 254.01 (Autumn 2010) Kiam...

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