MCS 321: Elementary Theory of Complex Variables
Spring 2004
College catalog's course description
Derivative and integral of a function of a complex variable,
Cauchy's integral theorem and formula, calculus of residues,
application to evaluation of integrals, conformal mappings,
and various other topics as indicated by the interests, needs,
and experiences of the students.
Prerequisite: MCS-222, i.e., Multivariable Calculus
"Complex variables" are variables whose values are complex numbers,
i.e, numbers of the form
z = x + iy
where x and y are real and i2 = -1.
In this course we study complex functions w = f(z)
where w = u + iv with u and v real, i.e.,
functions whose domain and range are in the complex numbers.
This study includes geometry (angles, images of regions, etc.)
and especially analysis (derivatives, integrals, series).
This subject is remarkable both for the beauty of its mathematics
and its power in applications.
Instructor: John Holte
Course web site
Textbook
Complex Variables and Applications 7/e
by James Ward Brown and Ruel V. Churchill,
McGraw Hill, 2004.
Class meetings
12:30-1:20 Monday, Wednesday, and Friday
Classroom: Olin 319
Regular attendance, both physical and mental, is required.
Class meetings will be used for a variety of activities: lectures,
discussions, and informal or formal presentations of solutions or
proofs.
| Dates
| Chapter
| Topics
| Tests
|
| Feb. 9-16
| 1
| Complex numbers
| Quiz
W 2/18
|
| Feb. 20-Mar. 3
| 2
| Analytic functions
|
|
| Mar. 5-12
| 3
| Elementary functions
Review
| Exam 1
M 3/15
|
| Mar. 17-31
| 4
| Integrals
| Exam 2
F 4/2
|
| Apr. 3-12
|
| Spring break
|
|
| Apr. 14-23
| 5
| Series
|
|
| Apr. 26-May 5
| 6
| Residues and poles
| Exam 3
5/5-7
|
| May 7-19
| 7-10
| Topics and projects
| Final exam
T 5/25 3:30-5:30
|
This is a tentative syllabus. Changes may be made during the semester.
Students are encouraged to discuss course topics with one another.
On assigned work, though, you are expected to do the work on your own.
Your discussion with other students should be confined to matters
related to understanding the problems and general approaches to doing
problems, and you should acknowledge those who help you in this way.
You should not collaborate on problem solutions unless directed otherwise.
- Acknowledge your sources (people and texts).
- In nontrivial problems, show how you get your answers.
- Turn in neat, well-written solutions, not messy first drafts.
Trim "fringes." Staple multiple-page submissions.
- Do not copy collaborative solutions; write up solutions in your own words.
- Turn in homework on time. Each class day late reduces the possible points
by 33%.
- Do extra credit problems entirely on your own.
Exams
There will be one quiz, three unit exams,
and one comprehensive final examination.
Your final exam score will count as two unit exam scores,
effectively making a total of five unit exam scores.
The worst unit exam score will then be thrown out.
Some or all of the unit exams may be take-home examinations due on the
class day following the day it is given out.
See the syllabus for the exam schedule.
Make-up exams will not be given except for medical or family emergency
reasons.
Students who will be absent from an exam for a school-sponsored event
should arrange with me in advance to have an exam sent along with the coach.
If you miss a class for any reason, you are still responsible for
learning what was covered in class and for getting any homework that is
due turned in on time.
The standard way for making up an absence is to turn in a handwritten
report on the material and examples that were covered in class.
Late homework will be penalized as stated under
Homework rules.
If there is a compelling reason for granting an
extension, you must negotiate the arrangements with me.
Grading
Your grade will be based on the following,
assuming satisfactory attendance and participation in class.
Absences that are not made up may reduce your score by
as much as 2.5 percentage points per day.
| Percent
| Work
|
| 30%
| Problem assignments and project(s)
|
| 6%
| Quiz
|
| 64%
| Best 4 of 5 exam scores
(3 unit exams and final exam counted as two scores)
|
Academic honesty
-
Page 31 of the Gustavus Adolphus College Academic Bulletin
states in part:
"The faculty of Gustavus Adolphus College expects all students to adhere
to the
highest standards of academic honesty... In all academic exercises,
examinations, papers, and reports, students shall submit their own work.
Footnotes or some other acceptable form of citation must accompany any use
of another's words or ideas."
The complete statement may be found at:
http://www.gac.edu/oncampus/academics/general_catalog/current/acainfo.cfm.
-
The following code will be written in full and signed on every examination
and graded paper:
"On my honor, I pledge that I have not given, received, or tolerated
others' use of unauthorized aid in completing this work."
-
"By enrolling classes at Gustavus, you have taken up membership in a
worldwide community of scholars, and like any community, Academia has ethical
standards to which you are expected to adhere.
You are expected to learn and follow the principles of honesty
and integrity that apply in academic life.
Among those
standards are that you faithfully represent your own work,
acknowledge any borrowing from the work of others,
avoid falsifying data or sources, be respectful of other
scholars' efforts and not interfere with their access to
resources (e.g., by misappropriating or damaging library materials),
do a fair share of the work in group efforts, give others
the benefit of your informed opinions and observations in
discussion, and be respectful of others' values, knowledge,
and feelings while developing your own....
Regrettably, serious and deliberate violations of ethics may
incur serious penalties.... If you are in doubt about whether
your work conforms to ethical standards, please inquire--you are,
after all, a learner."
--John Rezmerski, Advising and Registration Manual 1995-96, pp. 60-61.
- A first violation of the academic honesty policy
will result in a zero grade on the paper in
question and a report to the office of the Dean of the Faculty.
A second case will result in a failing grade for the course.
Extra help
-
I encourage you to see me during my office hours and at other
times when my office door is open.
-
If you have a disability that requires an accommodation, please
see me privately as soon as possible.