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.

  1. 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'')

  2. 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

  3. 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