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.
- Functions: writing functions in terms of real and imaginary parts, mappings from the z-plane to the w-plane,
mapping the exponential function
- 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
- 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)
- Harmonic Functions: Heat equation, Laplace's equation, definition of a harmonic function, the harmonic conjugate,
finding harmonic conjugates