Course Outline - Carleton University

MATH 3007 Functions of a Complex Variable
Fall 2012
Instructor Dr. David Amundsen
Office 4259 HP
Email dave@math.carleton.ca
Phone ext. 2135
Office Hours Tues. 9:30-10:30, Fri. 11:00-12:00 or by appt.
Web page http://mathstat.carleton.ca/∼dave/
Text Basic Complex Analysis
J.E. Marsden & M.J. Hoffman (3rd ed.)
on 2-hour reserve in the library
Lectures Monday and Wednesday 14:30-16:00 in CB 2400.
TA Babak Moazzez
email:bmoazzez@math.carleton.ca
Office: 4356 HP, Tel: x8789
Office Hours: Tues. 4-5pm or by appt.
Tutorials Wednesdays 11:30-12:30 in TB 234 (starting Sept. 19).
Tests During tutorial: Oct. 3, Oct. 17, Oct. 31, Nov. 14.
Final Cumulative final during exam period.
Grading Tutorial work: 10 %
Term tests (best 3 of 4 ∗ ): 30 %
Final: 60 %
*- provided a minimum score of 30% is achieved on each of the four tests.
Accommodation Policies
• The Paul Menton Centre for Students with Disabilities (PMC) provides services to
students with Learning Disabilities (LD), psychiatric/mental health disabilities, Attention
Deficit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders (ASD),
chronic medical conditions, and impairments in mobility, hearing, and vision. If you
have a disability requiring academic accommodations in this course, please contact
PMC at 613-520-6608 or pmc@carleton.ca for a formal evaluation. If you are already
registered with the PMC, contact your PMC coordinator to send me your Letter of
Accommodation at the beginning of the term, and no later than two weeks before the
first in-class scheduled test or exam requiring accommodation. After requesting accommodation
from PMC, meet with me to ensure accommodation arrangements are
made. Please consult the PMC website for the deadline to request accommodations
for the formally-scheduled exam.
• Accommodations for other reasons such as religious obligation, or parental leave, will
be done only in accordance with University policy. These policies are administered
by the office of Equity Services.

1. Analytic Functions (Chapter 1)
Topics
• Introduction to complex numbers (1.1)
• Properties of complex numbers (1.2)
• Elementary Functions (1.3)
• Continuous Functions (1.4)
• Properties of Analytic Functions (1.5)
• Differentiation of elementary functions (1.6)
2. Cauchy’s Theorem (Chapter 2)
• Contour Integrals (2.1)
• Cauchy’s Theorem (2.2)
• Cauchy’s Integral Formula (2.4)
3. Series Representations of Analytic Functions (Chapter 3)
• Convergent series of analytic functions (3.1)
• Power series and Taylor’s Theorem (3.2)
• Laurent series and classification of singularities (3.3)
4. Calculus of Residues (Chapter 4)
• Calculation of Residues (4.1)
• Residue Theorem (4.2)
• Evaluation of definite integrals (4.3)
5. Conformal Mappings (Chapter 5)
• Basic theory of Conformal Mappings (5.1)
• Fractional linear mappings (5.2)
• Applications to fluid flow (5.3)