• What: Exam on series, residues, singularities, and contour integrals
• When: Handed out Wednesday, May 5
  Due: by start of class, Friday, May 7

You are on your honor to take this take-home exam as a closed-book exam and not to discuss it with anyone else before Friday's class. You may use one new 4"-by-6" note card with anything you want written on both sides, and you may use your previous note cards as well. There is no specific time for the exam, and no specific time limit. However, you are directed to take the exam at one "sitting" and to return the exam to Olin 307 when you are done.

The exam focuses on chapters 5 and 6 of our text. Many of the problems will be similar to problems you did for homework. Typical problems will include problems of the form "find a given type of series for a given function" or "evaluate a given contour integral (by Cauchy's residue theorem)."

Main topics

• Series
  • Power series, Taylor series, Maclaurin series
  • Series for e^z, sin z, cos z, sinh z, cosh z, 1/(1-z)
  • Laurent series
  • Basic theorems on convergence of series
• Residues and poles
  • Residues
  • Cauchy's residue theorem
  • Types of singular points
  • Residues at poles
  • Zeros and poles