Complex Analysis MATH 305
Quiz #3 (last one)
Friday, Nov. 18, in class
The third quiz covers Chapter 4 of the course text.
You should go over homework problems, the textbook and your class notes. The quiz will be short
(10-15 minutes) and focus on basic concepts and calculations from Chapter 4.
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.
- Contour Integrals: Set-up and evaluation of contour integrals, parametrizations of lines and circles,
properties of contour integrals, upper bounds for the moduli of contour integrals (the ``ML Theorem'')
- Important Integration Theorems and Formulas:
AD Theorem (antiderivative = path independence, etc.), Cauchy-Goursat Theorem, simply versus multiply
connected domains, Principle of Deformation of Paths (PDP),
Cauchy integral formula, extension of the Cauchy integral formula
- Applications of Cauchy's Integral Formulas: Analytic functions have analytic derivatives of all orders,
Liouville's Theorem, the Fundamental Theorem of Algebra, the Maximum Modulus Principle