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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2010 • Question 8

Question

Math 6420 • PDE Fall 2010 • Question 8

Use antiderivatives to evaluate the contour integral \[ I=\int _C\frac {1}{z+i} \] where \(C\) is a contour (possibly with loops) starting at \(z=0\) and ending at \(z=1\). Express your answer in the form \(I=a+ib\) where \(a\) and \(b\) are real. The answer is multivalued. Explain the interpretation of the different values, and account for the difference between successive values using the residue theorem.

Raw LaTeX

Use antiderivatives to evaluate the contour integral
\[
  I=\int_C\frac{1}{z+i}
\]
where \(C\) is a contour (possibly with loops) starting at \(z=0\) and ending at \(z=1\). Express
your answer in the form \(I=a+ib\) where \(a\) and \(b\) are real. The answer is multivalued.
Explain the interpretation of the different values, and account for the difference between
successive values using the residue theorem.

Topic Tags

Contour Integration and Residue Calculus Finite Difference Boundary Value Problems Isolated Singularities and Residues Linear Programming and Optimization