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**MATHEMATICS 3340

COMPLEX VARIABLES WITH APPLICATIONS

University of Virginia, Fall 2017

**Course Location:** Clark G004

**Course Time:** TuTh 12:30-1:45

**Textbook:** *Fundamentals of Complex Analysis* (third edition), by Saff and Snider

**Instructor:** David Sherman

**Office:** 211 Kerchof Hall

**Office Hours:** Tu 2-3; Th 10:30-11:30 and 2-3; and by appointment

**Office Phone:** 924-7079

**Email:** dsherman@virginia.edu

**Course webpage:** http://people.virginia.edu/~des5e/F17,3340/base.html

**Prerequisites:** multivariable calculus

**Course content:** Complex analysis is the jewel of the undergraduate mathematics curriculum. Many things that are too nice to be true throughout mathematics -- they *are* true in complex analysis. For example: polynomials can be completely factored; functions are infinitely differentiable and even equal to power series; integrals that were impossible in your calculus course can be evaluated; many computations come down to pictures -- things like "how many times does this curve go around that point?"; there are many applications to real-world physical problems, in part because all the functions solve certain simple differential equations. We will start at the beginning of the text and end around Section 7.3, skipping many inessential sections along the way. The main mathematical topics are these: complex numbers, analytic functions, complex integration (Cauchy's theorem, residue theorem, etc.), Laurent series and singularities, and conformal mappings.

**Timetable:** A developing timetable for the course is kept at people.virginia.edu/~des5e/F17,3340/F17,3340,timetable.html.

**Exams:** There will be two evening midterms (September 27 and November 8, 7-8:30 PM in Monroe 122) and a final exam (December 11, 2-5), all conducted without calculators or notes of any kind. It is university policy that final exams cannot be taken early, and can only be taken late with paperwork from the dean.

**Homework:** We'll have frequent written assignments, announced in class and listed on the timetable. Typically these will be due to my mailbox (just to the left after entering Kerchof Hall) by 11 AM on Fridays; of course they may be submitted in class Thursdays. On each assignment several problems are carefully graded, and the remaining problems are quickly examined to see that a sincere effort was made. Scores are recorded at the top of the paper, as follows: (graded problems/points possible) + (completeness of remaining problems/points possible) = (total/points possible). The grader will be fairly picky so that students can identify all areas of confusion before the midterms.

**Classwork:** Sometimes during lecture, students will work problems in pairs or larger groups, enjoying a happy, conversational atmosphere with access to notes, books, an instructor, and each other. If you miss lecture, you cannot make up the classwork.

**Quizzes:** We may occasionally have quizzes during lecture -- whenever this happens, students will be apprised at least one course meeting prior.

**Grading:** Course grades will be based on numerical totals, calculated as follows: 20% each midterm, 35% final, and 25% [homework + classwork + quizzes]. I will assign letter grade numerical ranges for each midterm after it is scored.

**Learning disabilities:** Students who have a learning disability documented by LNEC may be entitled to special accommodations during exams. If this is the case, documentation from LNEC should be given to me at least a week before the exam.

**Important dates:**

Last day to add: September 5

Last day to drop: September 6

Reading holidays: September 30 - October 3

Exam 1: September 27

Exam 2: November 8

Last day to withdraw: October 17

Thanksgiving holidays: November 22-26

Last day of classes: December 5

Final exam: December 11, 2-5

**Random dicta:**

1) I hope you're not insulted by my stating two rules of common courtesy: please turn cell phones and laptops off during lecture, and please do not leave before the end of lecture unless you have discussed the reason with me before lecture starts.

2) You learn math by *doing it*. Remember that you can practice with odd-numbered problems from the book.

3) You may work with other students, as long as you write up solutions entirely in your own words. You are also allowed to use outside sources (books, webpages, wise Uncle Bob), but you must cite them on your paper.

4) It is a mistake to think you can solve any major problems just with potatoes.

5) Be an enthusiastic learner. Participate in class by asking and answering questions. Come talk to me in my office to iron out things you don't understand.

6) If circumstances arise which affect your performance in the course, you should inform me *before* they influence your grade.

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