Queen's University
MTHE 228: Complex Analysis


Final Exam
The final exam is from 7-10 PM on Thursday, April 23rd in Bartlett Gym (Enter PEC).
Queen's Approved, Non-Programmable Calculators are permitted, but no other resources.
Here is an updated Review Guide
Here's a list of Conceptual Questions, and Conceptual Solutions
Practice Final, Practice Final Solutions
Office Hours in Jeff 512 (or nearby) from 9 AM-12 PM and 1-5 PM on April 20th-23rd, unless otherwise stated.
Here is a hastily made
video with the lost content from the last lecture. There will be a bonus question on the final concerning this material, but you are not otherwise responsible for it.

Midterm Exam
Exam, Exam Solutions
Practice Exam, Practice Exam Solutions

Lecturer: Dr. Thomas A. Hulse (you can call me "Tom")
Location:
Monday: Jeffery Hall 128, 10:30-11:20 AM
Tuesday: Jeffery Hall 126, 8:30-9:20 AM
Wednesday: Jeffery Hall 126, 10:30-11:20 AM
Office: Jeffery Hall 512 ph.: x3-6299
e-mail: hulse@mast.queensu.ca

TA: Andrew Staal, Meghan Beattie
Tutorial: Wednesdays 11:30 AM - 12:20 PM
Ahmed through Laurenzi will be in Jeff 225 with Meghan Beattie
Lewis through Xu will be in Jeff 234 with Andrew Staal

Book: The textbook for this course is Fundamentals of Complex Analysis with Applications to Engineering and Science Third Edition, by E. B. Saff and A. D. Snider (ISBN-10: 0139078746). This is available in the bookstore.

Course Information: It is required that you read and understand the course syllabus.

Homework: Watch this page for homework assignments and solutions.

Introduction: Calculus is a powerful mathematical tool which has proven to be of profound practical use in the sciences and one of the great achievements of human thought.

But you know that already.

The theory of calculus with complex numbers, also known as the theory of functions of a complex variable, is significantly richer than just the extension of calculus to the real plane. The beautiful underlying algebraic and geometric structure of the complex numbers allows us to describe a large class of extremely well-behaved and physically-relevant functions with a very small number of conditions and allows us to better understand functions of a real variable. It's an exciting twist on a well-known story, and will quite possibly answer many questions you never knew you had.

This course is an introduction to complex analysis, intended primarily for engineering students. Some attention will be paid to theory but mainly this course will be focused on developing your ability to work in the realm of calculus with complex numbers.

The Course So Far:

Day Description Notes Practice Problems
Week One
M 1/5 Course Introduction. Complex Numbers, Operations Notes 1 Section 1.1: 6,7,10,15,16
T 1/6 Complex Plane, Geometric Objects, Conjugation Notes 2 Section 1.2: 4, 5, 7
W1/7 Vector Representation and Polar Form Notes 3 Section 1.3: 5,6,7,15,16
Week Two
M 1/12 The Exponential Function Notes 4 Section 1.4: 1,4,10,12,14
T 1/13 Powers and Roots Notes 5 Section 1.5: 4,5,11
W1/14 Planar Sets Notes 6
Tutorial Problems
Section 1.6: 2,3,4,8
Assignment 1 Due
Week Three
M 1/19 Properties of Domains, Boundedness, and Beginning Functions Notes 7 Section 1.6: 5,19,21
Section 2.1: 2
T 1/20 Functions of a Complex Variable, Visualizing the Range Notes 8 Section 2.1: 1,3,5, 6b
W1/21 Limits and Continuity Notes 9
Tutorial Problems
Section 2.2: 7,11,12
Assignment 2 Due
Week Four
M 1/26 Infinity, Admissibility, Differentiability Notes 10 Section 2.2: 11, 15, 25
T 1/27 Rules of Differentiation, Analyticity Notes 11 Section 2.3: 7,9,14 [L'Hopital's Rule]
W1/28 Cauchy-Riemann Equations Notes 12
Tutorial Problems
Section 2.4: 2,5,10,11,13
Assignment 3 Due
Week Five
M 2/2 Zero Derivative and Harmonic Functions Notes 13 Section 2.4: 12
Section 2.5: 1,4,5,6
T 2/3 More Harmonic Functions and The Fundamental Theorem of Algebra Notes 14 Section 2.5: 3
Section 3.1: 3
W2/4 Factoring, Polynomial Long Division and Taylor Expansions Notes 15
Tutorial Problems
[See also: Example 2 on Page 101-102]
Section 3.1: 5,8,11
Assignment 4 Due
Week Six
M 2/9 Partial Fractions Decomposition, Returning to the Exponential Function Notes 16 Section 3.1: 13, 15
Section 3.2: 1,2,4
T 2/10 Complex Trigonometric and Hyperbolic Functions, Logarithms Begin Notes 17 Section 3.2: 5,9, 11,13,15,17,19
W2/11 Complex Logarithms Notes 18
Tutorial Problems
Section 3.3: 1,3,5, 8, 9, 12, 13,
Assignment 5 Due
Week Off, 2/16-2/20
Week Seven
M 2/23 Boundary Value Problems for Harmonic Functions Notes 19 Section 3.4: All of them
T 2/24 Complex Powers Notes 20 Section 3.5: 1,3,4,6,15a
W2/25 Contours Notes 21
Tutorial Problems
Section 4.1: 1,6, 7, 8, 9
Assignment 6 Due
Week Eight
M 3/2 Intro to Contour Integrals Notes 22 Section 4.1: 5,10
Section 4.2: 3
Exam Tonight!
T 3/3 Evaluating Contour Integrals Notes 23 Section 4.2: 5,6,7,8,9,10,11
W3/4 Fundamental Theorem of Calculus on Contours Notes 24
Tutorial Problems
Section 4.2: 14
Section 4.3: 1,2,4,6,7
F3/6 Assignment 7 Due by 10:20 AM in Jeff 512 mail slot
Week Nine
M 3/9 Continuous Deformation and Cauchy's Integral Theorem Notes 25 Section 4.4: 1,3,9,10
T 3/10 Cauchy's Integral Formula Notes 26 Section 4.5: 1,2,3a,3b,3c
W3/11 Cauchy's Generalized Integral Formula Notes 27
Tutorial Problems
Section 4.5: 3d, 3e, 3f, 4,5,6,7
Assignment 8 Due
Week Ten
M 3/16 Liouville's Theorem and The Maximum Modulus Principle Notes 28 Section 4.6: 1,2,5,6,7,8,14
T 3/17 Using Max Modulus and Max/Min Principle for Harmonic Functions Note 29 Section 4.6: 10,16,17
Section 4.7: 1,2,4
W3/18 Dirichlet's Problem, Poisson's Integral Formula, and (Re-)Introduction to Series Notes 30
Tutorial Problems
Section 4.7: 6,8, 11
Section 5.1: 1,2,5,7
Assignment 9 Due
Week Eleven
M 3/23 Evaluations, More Series Examples Notes 31 Section 5.1: 13,14
T 3/24 Taylor Series Notes 32 Section 5.2: 1,3,4,5,6,8
W3/25 Power Series and Laurent Series Notes 33
Tutorial Problems
Assignment 10 Due
Section 5.3: 3, 5a, 5b, 10
Section 5.5: 1,2,3,5
Week Twelve
M 3/30 Finishing Laurent Series, Classifying Singularities Notes 34 Section 5.5: 6,9,11
T 3/31 Classifying Singularities, Cauchy's Residue Theorem Notes 35 Section 5.6: 1,2
Section 6.1: 1,3
W4/1 Using Cauchy's Residue Theorem to Evaluate Real Integrals Notes 36
Tutorial Problems
Assignment 11 Due
Assignment 12.
Section 6.2: 1,2,3,4,8
Section 6.3: (Optional) 1,2,3,4,5,6,7

Here's a picture of me wearing only one shoe and standing in front of the Oscar Mayer Weinermobile:

And here's a link to a video of my Linear Algebra Class being disrupted.