homework2 - dened. a ) lim z z 2 z 2 ; b ) lim z i z 2 z 2...

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Due 01-23-09 Physics 132 Winter 2009 P. Kraus HOMEWORK #2 Hand into box marked “132” outside 1-707D PAB by 3pm Fri. —————————————————————————————————————————— 1) We can write a function f ( z ) in the form f ( z ) = u ( x,y ) + iv ( x,y ) where z = x + iy . Work out u ( x,y ) and v ( x,y ) for the following: a ) f ( z ) = z 2 z ; b ) f ( z ) = 2 z 2 + 3 z ; c ) f ( z ) = ze z 2) Draw the image of the line x = 2 under the mapping w = z 2 + 1. 3) BC p. 44 problem 7: Find the image of the semi-infinite strip x 0 , 0 y π under the transformation w = exp z and label corresponding portions of the boundaries. 4) Which of the following limits are well defined? Write the result when the limit is well
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Unformatted text preview: dened. a ) lim z z 2 z 2 ; b ) lim z i z 2 z 2 ; c ) lim z ( z + 1) 2 z + 2 ; d ) lim z z 2 z 5) BC p. 56 problem 7: Use denition (2), Sec. 15, of limit to prove that if lim z z f ( z ) = w then lim z z | f ( z ) | = | w | Is the converse true? If not, give an explicit counterexample. 6) BC p. 56 problem 10: Use the theorem in Sec. 17 to show that a ) lim z 4 z 2 ( z-1) 2 = 4 ; b ) lim z 1 1 ( z-1) 3 = ; c ) lim z z 2 + 1 z-1 = 1...
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