Complex Analysis     MATH 305

Quiz #2

Friday, Oct. 7, in class

The second quiz covers Chapter 2 of the course text. You should go over the third homework assignment (which you should have back on Wednesday), the textbook and your class notes. The quiz will be short (10-15 minutes) and focus on basic concepts and calculations from Chapter 2. Types of possible questions include: short answer, fill in the blank, true/false, multiple choice, etc. You may be asked to define some terms or state some theorems precisely. You may also be asked to do some short calculations.

Note: No calculators are allowed on the quiz so be prepared to answer questions without your personal calculator.

The following topics and definitions are important material for the quiz.

  1. Functions: writing functions in terms of real and imaginary parts, mappings from the z-plane to the w-plane, mapping the exponential function

  2. Limits: epsilon-delta definition, approaching from different directions, CR Limit Theorem, Big Limit Theorem (BLT), limits involving infinity, the Riemann Sphere, LIPI Theorem, definition of a continuous function

  3. Derivatives and Analytic Functions: definition of the derivative, basic differentiation formulas, Cauchy-Riemann equations (in both rectangular and polar coordinates), SCD Theorem, definition of an analytic function, entire functions, singular points, finding where a function is analytic (if at all)

  4. Harmonic Functions: Heat equation, Laplace's equation, definition of a harmonic function, the harmonic conjugate, finding harmonic conjugates