MATH 655, Review for Midterm Test 2

Test topics

1. Analytic Functions
   1. Cauchy's Integral Formula. Derivative Formulas (2-3)
   2. Maximum Modulus and Liouville's Theorems (2-4)
   3. Harmonic functions. Harmonic conjugates (2-5)
   4. Dirichlet and Neumann problems. The Maximum Principle and Integral Identity techniques (2-5)
   5. Taylor Series (2-6)
   6. Laurent Series (2-7)
   7. Classification of Singularities. Behavior at Inifinity (2-7)
   8. Analytic Continuation. Singular Points (2-8)

2. Contour Integration
   1. Examples of Complex Variable techniques for evaluation of integrals (3-1)

Test Preparation

• Read the material in the textbook(s) closely, fill in the missing details as necessary
• Work through examples in the book and on the homework.
• Practice problems as well as review problems (some of which may end up on the midterm) are available (see the main page).

General rules

• All tests are closed books/notes; graphing calculators, cell phones or other electronic devices are not permitted.
• The duration of the test is 75 minutes.
• Problems will come in the same format as on the quizzes: you will need to write a concise proof to answer each question.