General Information for Math 103 Complex Analysis Seminar

Instructor: My name is Thomas Hunter. My office in the mathematics department is in Dupont 185. You can reach me by phone at 328-8244 or by email at thunter1@swarthmore.edu

Office Hours: Tuesdays from 10 to 11am, Wednesdays from 8 to 10 pm, Thursdays from 3 to 4 and by generous appointment. The stated slots are times you can be sure to find me in my office and willing to talk. Other times are fine, but to be sure that I am available, you should make an appointment with me. Of course you should feel free to stop by anytime and see whether I am available.

Text: We will use the text An Introduction to Complex Function Theory by Bruce Palka. It is available at the bookstore.

General Game Plan: I hope that we can cover III, IV, V, VII, and VIII of the book together with the first three sections of IX. Chapter II should already be familiar to all of you and Chapter I will be referred back to as necessary. We may cover more or less than this depending on the desires of the students.

Seminar Meetings: We will meet 7:00pm--10:00pm on Monday in Dupont 189. The two main activities during each meeting will be student presentation of the two main points of the reading and student discussion of the problems.

Student Presentations: Each meeting will have two student presentations on topics I will select from the readings. These presentations will be thirty to forty-five minutes long and will take the place that would be occupied by lectures were this not a seminar. Each student will be responsible for three presentations during the semester. From time to time I will assign two students to collaboratively prepare one presentation.

Student Conferences: At the beginning of the semester I will meet individually with each student each week to discuss how things are going. Later in the semester, I may meet less often with some or all of you, but those students giving presentations will always have to meet with me during the week before their presentations.

Homework: Each week, I will list five to ten "common" problems. I expect each of you to work through all of these doing as many as you can. In addition I each student to do one or more other problems, selected by that student from the text's problems, difficulties encountered in the reading, or any other source. The number of such additional problems will vary from student to student depending on their difficulty and the difficulty the student had that week with the common problems and the reading.

Notebooks: I ask that each of you keep an organized notebook containing your work for the course. In it, you should keep your notes on the reading and the seminar meetings, your problems and rewrites, your presentation outlines, and anything else pertinent to the course which you choose to include.

Give to me:I ask each student to give to me the following things for evaluation and comment.

Exams: I expect all students in the course to take the written honors exam. I will grade the exams of the students who are not standing for honors.

Grades: For those students to whom I must assign grades, I will base my evaluation on the exam, the weekly handed-in problems, the presentations (including the handed-in outlines), and class participation (including the quality and veracity of your lists of completed problems).

Computer and Electronic resources: There is a web page (you may be reading it right now) associated to this course. You may find it via my home page at http://www.swarthmore.edu/NatSci/thunter1/. Other resources you may find useful are the Macintosh graphing calculator, Mathematica, and Maple. Use of these or any other computational tool will not be a required part of the course.

Late work: Generally speaking late work will never be accepted and exams may never be taken late. In the case of irreconcilable conflicts you may schedule an exam earlier than the official time, but make up exams will not be given after the regularly scheduled exam except for the most extraordinary circumstances. (For example, global invasion by extraterrestials.)

Date

Topic

Presenters

Food

Related Common Problems

Mon. Jan. 20

Introduction & Chap I: Complex Numbers

Hunter

Hunter

Mon. Jan. 27

III.1 & III.2: Derivatives and the Cauchy Riemann Equations

Joan & Terrill

Sonya

III.6: 3, 5, 7, 8, 11, 12, 16, 17, 18, 21.

Mon. Feb. 3

III.3, III.4, & I.2: Exponential, Trig, and inverse functions

Sonya & Dan

Joan

II.6: 24, 28, 32, 37, 44, 45, 51, 53

Mon. Feb. 10

(III.5) & IV.1 & IV.2 & (IV.3): Paths and Line integrals.

Tim & James

Dan

IV.4: 1, 4, 7, 9, 12, 18, 27, 28. (Also some PODASIPS.)

Mon. Feb. 17

V.1 & V.2: The Local Cauchy Theorem

Joan & Sonya

Tim

V.8: 1--4,7--12.

Mon. Feb. 24

V.3 & V.4: Applications of the Local Cauchy Theorems

Terrill & Tim

James

V.8: 18, 19, 22, 29, 33, 50, 52, 56, 58, 59.

Mon. Mar. 3

V.5, V.6, & V.7: The Global Cauchy Theorems

Dan & James

Terrill

V.8: 61, 62, 63, 70, 71, 73, 75, 76, 82, 83.

Mon. Mar. 10

Break

Mon. Mar. 17

VII.1, VII.2, VII.3, & VII.4: Sequences and Series of complex functions

Terrill & Sonya

Sonya

VII.5: 39, 43, 49, 59, 60, 64, 65, 74,75,76.

Mon. Mar. 24

VIII.1 & VIII.2: Zeroes and Singularities

Dan & Tim

Joan

VIII.5: 1, 2, 8, 9, 10, 13, 14, 18, 24, 28, 29, 39.

Mon. Mar. 31

VIII.3 & VIII.4: the residue theorem and the Extended plane.

Joan & James

Dan

VIII.5: 44--46, 56, 59, 60, 65, 74, 81, 85, and 86.

Mon. Apr. 7

IX.1 & IX.2: Conformal mappings and Moembius Transformations

Dan & Sonya

Tim

IX.6: 2, 10, 23, 24, 30, 33, 41, 52, 57, and 62.

Mon. Apr. 14

IX.3: The Riemann mapping theorem

Terrill & James

James

IX.6: 62--70, 27, 41,42, and 57.

Mon. Apr. 21

X.1: The Mittag-Leffler Theorem

Joan & Tim

Terrill

X.4: 1--7, 10, 12, 17.

Mon. Apr. 28

X.3: Analytic continuation

Hunter

X.4: 36, 38, 39, 42, 46.