17 sample documents related to MATH 511

• 
  sol2.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 2 Solution 1. Evaluate z dz, where is the rectangle with vertices 3 i with counter8+z clockwise direction. Solution: Let 1 (t) = t - i, -3 t 3, 2 (t) = 3 + ti, -1 t 1, 3 (t) = -t + i, -3 t 3, 4 (t) = 3 - ti,
   
• 
  assignment2.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 2 Due date: Monday, February 16, 2009 1. Evaluate z dz, where is the rectangle with vertices 3 i with counter8+z clockwise direction. 2. Let f (x + iy) = x3 y 2 + i x2 y 3 . Find all the points P in C where f (P )
   
• 
  assignment4.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 4 Due date: Monday, March 23, 2009 1. Let R(z) = P (z) , where P and Q are two polynomials with no zeros in common. Let Q(z) P1 , P2 , . . . , Pk be the zeros of Q. Suppose f is holomorphic on C \\ {P1 , P2 , . . . , Pk
   
• 
  assignment3.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 3 Due date: Friday, March 6, 2009 1. Find the power series expansion of the following holomorphic functions at the given point and nd the radius of convergence. 1 at z0 = 2 i. z z1 2 (b) f (z) = at z0 = 0. 1 z 2 (a) f
   
• 
  sol3.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 3 Solution 1. Find the power series expansion of the following holomorphic functions about the given point and nd the radius of convergence. (a) f (z) = 1 at z0 = 2 i. z Solution: 1 1 1 = = z (2 i) + (z (2 i) (2 i
   
• 
  sol4.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 4 Due date: Monday, March 23, 2009 1. Let R(z) = P (z) , where P and Q are two polynomials with no zeros in common. Let Q(z) P1 , P2 , . . . , Pk be the zeros of Q. Suppose f is holomorphic on C \\ {P1 , P2 , . . . , Pk
   
• 
  assignment5.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 5 Due date: Friday, April 10, 2009 1. Find the number of zeros of f (z) = z 10 + 10zez+1 9 in {z : |z| < 1}. 2. Find the number of zeros of f (z) = 2z 5 6z 2 + z + 1 in {z : 1 < |z| < 2}. 3. Find the number of zeros
   
• 
  HW1a.pdf

  Iowa State MATH 511
  

  Homework 2. Due: Mon. Feb 18 1) Prove y 3 - 3x2 y + 3y is harmonic and find its harmonic conjugate. 2) Let G C be open and symmetric with respect to the real axis. Find all analytic functions f on G such that f () is also analytic. z p. 33 problem 7
   
• 
  hw7.pdf

  Iowa State MATH 511
  

  Math 511 Professor Lieberman Summer, 2005 HOMEWORK ASSIGNMENT 7 Read Chapters 5 and 6 Turn in the problems whose numbers are enclosed in a box. p. 110, #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 p. 121, #1, 2, 3, 4, 5, 6, 7, 8, 11 p. 126, #1, 2, 3, 4
   
• 
  511s5.pdf

  Iowa State MATH 511
  

  Math 511 Professor Lieberman Summer, 2005 SOLUTIONS TO HOMEWORK ASSIGNMENT 5 p. 73, #2. Since /z is continuous, it follows that (w, z + t) dt, 0 z for all suciently small h. Moreover, by uniform continuity, for any > 0 there is a > 0 such that
   
• 
  sol5.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 5 Due date: Friday, April 10, 2009 1. Find the number of zeros of f (z) = z 10 + 10zez+1 - 9 in {z : |z| < 1}. On D(0, 1), let g(z) = 10zez+1 , then |f (z) - g(z)| = |z 10 - 9| |z 10 | + 9 = 10 10eRe (1) (2) z+1 = |
   
• 
  assignment6.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 6 Due date: Monday, April 27, 2009 1. Find a holomorphic function f on D(0, 1) such that f (D(0, 1) = C. 2. Suppose f : C \\ {0} C \\ {0} is conformal. Prove that there exists a C \\ {0} such that f (z) = az or f (z) =
   
• 
  sol6.pdf

  Iowa State MATH 511
  

  Spring 2009 Math 511 Assignment 6 Due date: Monday, April 27, 2009 1. Find a holomorphic function f on D(0, 1) such that f (D(0, 1) = C. Let U = D(0, 1). (a) Let f1 (z) = z+1 . Then f1 (U ) = U1 = {x + iy C : x < 0}. z-1 (b) Let f2 (z) = z + 1. The
   
• 
  ec.pdf

  Iowa State MATH 511
  

  MATH 165 Extra credit problem (6 pts.) Due: Wed. 16 1. Let x = t cos t, y = t sin t; -2 t 2 describe the motion of a particle in the xy-plane. a) Find the slope of the tangent to the curve at (0, 0). b) Sketch the path the particle takes in the
   
• 
  p1.pdf

  Iowa State MATH 511
  

   
   
• 
  p2.pdf

  Iowa State MATH 511
  

  MATH 165 Practice Exam III Fall 2002 Name PART 1: Mulitple-Choice Problems Each problem is worth 5 points: NO partial credit will be given. Calculators may NOT be used on this part. 1. The function f (x) = 3x + sin x is one-to-one. If g is the inv
   
• 
  p3.pdf

  Iowa State MATH 511