MATH 655, Review for the Final Exam

Test topics

1. Properties of analytic functions.

2. Elementary functions (linear, powers, fractional linear, exponential, logarithmic, trigonometric and their inverses). Mapping properties of elementary functions.

3. Conformal mappings.

4. Cauchy's Theorem and Cauchy's Integral Formula.

5. Singularities: removable, poles, essential, accumulation points, branch points.

6. Taylor and Laurent Series.

7. Analytic Continuation.

8. Techniques of contour integration. Evaluation of integrals along the real axis.

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. Complete solutions to most homework problems are available on the main page.
• Review old tests, paticularly the questions belonging to final exam topics.
• A list of review problems (some of which may end up on the exam) 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 2 hours.