{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ComplexAnalysis2008Aug - Qualifying Exam Complex Analysis...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Qualifying Exam, Complex Analysis, August 2008 i. Let f be an entire function, a E (C and 7“ > la]. Show that 1 (1/2) 2m dz = f(0). werz— Z—i 3+1” 2. Find the image of the first quadrant {as > 0, y > 0} under the Mobius map in = 3. Find all the continuous functions 11 : (C —> R which have the property that for every rectangle R C C with sides parallel to the coordinate axes /vd3:=—areaR, /vdy=0, .1 6'}? where 8B is traversed counterclockwise. (Hint: Consider the function f(2) = a: + iv(:r, y), where z = a: + 1y.) 4. Suppose that f(z) =l+clz+0222+... is a holornorphic function on the closed unit disc X such that lf(z)| S M for |zf = 1. ll 20 E A is a zero of f show that 1 > . Vd— 4+1 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern