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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2009 • Question 6

Question

Math 6420 • PDE Spring 2009 • Question 6

  1. Verify that the real and imaginery parts of a complex analytic function satisfy Laplace’s equation.
  2. Give an interpretation of the complex function \[ w(z)=z+\frac {a^2}{z} \] as a flow past some object. That is, determine the streamlines for this function. Where are the stagnation points?

Raw LaTeX

\begin{enumerate}
\item[(a)] Verify that the real and imaginery parts of a complex analytic function satisfy
Laplace's equation.

\item[(b)] Give an interpretation of the complex function
\[
  w(z)=z+\frac{a^2}{z}
\]
as a flow past some object. That is, determine the streamlines for this function. Where are
the stagnation points?
\end{enumerate}

Topic Tags

Complex Potential Flow and Blasius Formula Holomorphic Functions and Cauchy-Riemann Equations Laplace Equation Linear Programming and Optimization