ASSIGNMENTS


ALL ASSIGNMENTS SHOULD BE HANDED IN BY 3:00pm (FIRM) ON DUE DAYS.
THE DEPOSIT BOXE IS LOCATED THE OUTSIDE OF BSB-B157. 

LATE HAND-IN WON'T BE ACCEPTED.

SOLUTIONS TO THE ASSIGNMENTS WILL BE AVAILABLE IN THODE LIBRARY
DAY AFTER THE DUE DAY.

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Assignment 1: (due on January 20)
 
Chapter 1: #1, (b), (f), 
           #3, (a), (d), 
           #5, 
           #28, (b), (c),
           #30,
           #47.
Chapter 2: #2,
           #10,
           #18, (b), (c).

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Assignment 2: (due on February 3)

Chapter 2: #23,
           #37,
Chapter 3, #1,
           #10,
           #15,
           #29,
           #31,
           #42,
Chapter 4, #3,
           #5, (a), (d).

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Assignment 3: (due on February 17 ), 

Chapter 4, #6, 
           #13, (c), (d)
           #17, (a), (d)
           #35, (b), (f),
           #49, 
           #58,
           #62,
Chapter 5, #2,
           #10, (c),

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Assignment 4: (due on March 16)

Chapter 5, #7,
           #16,
Chapter 6, #1,
           #8,
           #30,
           #32,
And plus the following problems:
Problem 1, If f(z) is holomorphic in the unit disk |z|<1, and 
           |f(z)|<1 for all |z|<1. If |f'(0)|=1, prove that
           there is a constant A, such that |A|=1, and f(z)=Az
           for all |z|<1.
Problem 2, Show that composition of two linear fractional transformations
           is still a linear fractional transformation.
Problem 3, Find a linear fractional transformation which maps points
           -1, i and 0 to 0, 1, -i respectively. Find the images of
           the lower half plane {Im(z)<0} and the real line under
           this mapping respectively.
Problem 4, Find the image of the upper half plane Im(z)>0 under
           the transformation w=Log{(z+1)/(z-1)}.
           Sketch the images of the real line under the mapping.

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Assignment 5: (due on March 30)

Chapter 6, #19,
           #20, 
Chapter 7, #2,
           #18,
           #19,
           #28,
           #31,
           #32,
           #53 (b): with the boudary function changed to: equal
                    to 1 in the upper half circle, and equal to
                    -1 in the line segement {-1< x <1}.


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