Professor: Jeff Johannes
MWF 12:30-1:20p Sturges 113
Office Hours: Monday 11:30a - 12:20p, Wednesday 4-5p, Thursday 1-2p, 8-9p, Friday 2:30 - 3:30p, and by
appointment or visit
Email Address: Johannes@Geneseo.edu
An Introduction to Complex Analysis and Geometry by John P. D'Angelo
Extending almost all mathematics to complex numbers.
High school algebra and geometry, calculus, linear algebra,
differential equations, abstract algebra, topology, …
Because of the fact that we will be extending so
many areas, this is a perfect opportunity to solidify everything that
you have done before, or to get little tastes of things you haven't
seen before. We'll start with some basics of real
numbers, then earn the basics of what and why complex numbers are.
After that we will see interplay with geometry, linear algebra,
and then head toward topics from calculus: series,
differentiation and end with the richest area of all - integration.
Half of your grade will come from problem sets.
Another tenth will come from a final project and each of two
midterm exams. The final fifth will come from the final exam.
After we finish each chapter problem sets will be
collected. They will be returned with a letter grade based on the
following factors: number of exercises correctly completed,
difficulty of exercises correctly completed, number of exercises
completed by classmates, and some subjective determination on my part
as to what seems appropriate. Each problem set will be scaled
using a linear function of the number of exercises completed (problems
correctly completed by only one student will earn two points).
Submitting no problem set by the day it is due will earn a score
of zero. I strongly recommend consulting
with me as you work on these problem sets. I also recommend
working together on them, however I want to carefully emphasise that
write up their own well-written solutions. A good rule for this
is it is encouraged to speak to each other about the problem, but you
should not read each other's solutions. A violation of this
policy will result in a zero for the entire assignment and reporting to
the Dean of Students for a violation of academic integrity.
Your final project will constitute writing up a
detailed explanation (filling in the gaps) of a topic in the text that
we will omit (or another topic selected by you and approved by me) ,
and a completion of a problem set (graded as above) from the exercises
in that section.
The exams will consist of a few straightforward
problems designed to emphasise a personal understanding of the basics.
Occasionally you will be given anonymous feedback
Please use them to share any thoughts or concerns for how the course is
Remember, the sooner you tell me your concerns, the more I can do about
I have also created a web-site
which accepts anonymous comments. If we have not yet
this in class, please encourage me to create a class code. This
may also be accessed via our course page on
link entitled anonymous
feedback. Of course, you are always welcome to approach me
of class to discuss these issues as well.
While working on homework with one another is
encouraged, all write-ups of solutions must be your own. You are
expected to be able to explain any solution you give me if asked.
Student Academic Dishonesty Policy and Procedures will be followed
should incidents of academic dishonesty occur.
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning
disabilities. Students should consult with the Director in the
Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin,
firstname.lastname@example.org) and their individual faculty regarding any needed
accommodations as early as possible in the semester.
It is my policy to give students who miss class
of observance of religious holidays the opportunity to make up missed
You are responsible for notifying me by September 11 of plans to
Schedule (loose and subject to variations)
August 29 Introduction
Chapter 1 (1-3, 4, 5)
14 Chapter 2 (1, 2, 6, 7, 8)
16 PS1 due
Chapter 3 (1, 2, 4, 5) PS2 due
October 3 exam (Chapter 1-2)
17 Chatper 4 (2.3, 2.4, 2.5, 1, 2)
21 PS3 due
November 2 Chapter 5 (1, 2, 3, 4, half of 5) PS4 due
7 exam (Chapter 3-4)
18 Chapter 6 (1, 2, 4, 5)
21 PS5 due
5 Chapter 7 (1, 2)
12 Review, PS6-7 due, Final Project due
Monday, December 19 12N - 3p
Final Exam (half 5-7, half 1-4)
Upon successful completion of this course, a student will be able to
- Express complex numbers in the important equivalent forms - rectangular, polar and exponential.
- Perform the basic arithmetic operations on complex numbers, including powers and roots (using DeMoivre's Theorem).
- Represent complex numbers as points in the complex plane and vice-versa.
- Determine various basic topological properties of sets of complex numbers in the plane.
- Determine convergence of sequencees and series of complex numbers.
- Determine the continuity and differentiability of complex valued functions of a complex variable.
- Determine the analyticity of complex valued functions of a complex variable using the Cauchy-Riemann equations.
- Determine the harmonicity of complex and real valued functions of a complex varaible.
- Perform computations with the elementary compelx functions - exponential, trigonometric, and logarithmic.
- Evaluate contour integrals directly and using the appropriate form of Cauchy's theorems.
- Expand analytic functions in power series of a complex variable.
- Determine the radius and interval of convergence of a complex power series.
- Calculate the residue ofa complex function at a singularity.
- Use the residue theorem to compute definite integrals.