Math 405 - Complex Analysis - Fall 2018

General Information:

Meeting Time:MWF 9 - 9:50
Location: Small Physics Lab 235
Instructor:Ryan Vinroot
Office: Jones 100D
Office Hours: M 3:30-5, W 2-3:30, Th 10:30-12 (and by appointment)
Textbook:Complex Variables and Applications (9th Edition) by James Ward Brown and Ruel V. Churchill
Class Participation - 5%, Midterm - 30%, Homework - 35%, Final Exam - 30%. The grading scale will be the standard 10 percentage point scale, so that a final score of 93 or higher is an A, 90-92 is an A-, 87-89 is a B+, 83-86 is a B, 80-82 is a B-, 77-79 is a C+, 73-76 is a C, 70-72 is a C-, etc.
Attendance & Lecture Policy:It is expected that you attend all lectures, with exceptions minimized. It is greatly appreciated when you are on time. Please do your best to stay awake and attentive during lecture, please do not email or text during lecture, and keep all cell phones/hand held devices/tablets/laptops put away during lecture. While it is understandable that you may miss a lecture here and there, or be sleepy in class once in awhile, repeated absences, late arrivals, naps, or general non-attentiveness will negatively affect your class participation score.
Prerequisites: Math 311 Elementary Analysis. It is extremely important to have a thorough knowledge of the topics from Math 214 Foundations of Mathematics, and to have a firm grasp of the main concepts from Math 311.
Course Summary: Complex analysis is the study of functions and Calculus of a complex variable. We will study and develop many of the most important notions from Calculus 1 and 2, as well as Elementary Analysis, including limits, derivatives, integrals, and power series. While proofs will not be the primary focus of the course, we will give proofs (or outlines of proofs) of most of the Theorems we develop and use. You will be expected to prove some things as well, but the main focus will be on the concepts and computations. We will cover the majority of Chapters 1-5 in the textbook, and will cover various sections in Chapters 6-8 as time allows.

Dates & Course Announcements:

Midterm and Final Exams:

There will be one midterm (details will be determined later). The final exam will be timed. The midterm and the final will each count as 30% of your final grade. The final exam will be on Mon, Dec 10, from 9 AM until 12 Noon.

Exam Calendar (Tentative):
Exam Date Time/Due Location
Midterm Mon, Nov 5 In class Small 235
Final Exam Mon, Dec 10 9 AM - 12 Noon Small 235
  • All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
  • Important Dates and Class Holidays:
    • Fri, Sep 7: ADD/DROP DEADLINE
    • Sat, Oct 13 - Tues, Oct 16: NO CLASS (Fall Break)
    • Fri, Oct 26: WITHDRAW DEADLINE
    • Mon, Nov 5: MIDTERM (IN CLASS)
    • Wed, Nov 21 - Sun, Nov 25: NO CLASS (Thanksgiving Break)
    • Mon, Dec 10, 9:00 AM - 12 Noon: FINAL EXAM
  • (8/29) My office hours during the first short week of classes will be: Wed Aug 29 10-11, Thurs Aug 30 9-11 and 3-4, Fri Aug 31 10-11:30 and 1-2.
  • (9/3) My office hours this week will be: Mon (Sept 3) 3-4:30, Wed 10-11 and 2-3, Thurs 10:30-12.
  • (9/10) My regular weekly office hours this semester have been set as follows: Mon 3:30-5, Wed 2-3:30, Thurs 10:30-12.
    If none of those times work, you can always email me and we can try to find another time.
  • (10/8) Please note that HW #6 is due the Friday after Fall Break.
  • (10/8) I will continue on Wed Oct 9 at 8:30 am the proof of Clairaut's theorem in an optional half lecture.
  • (10/29) The midterm is set to be in class next Mon, Nov 5. The material covered is: Chapter 1 (Sec. 1-12), Chapter 2 (Sec. 13-27, Statement of Theorem in Sec. 28), Chapter 3 (Sec. 30-40), Chapter 4 (Sec. 41-45), and Chapter 8 (Sec. 96, 97, 103). Here are some problems corresponding to the sections covered which might be good to work on when studying:
    Chapter 1: pgs. 13-14 #3, 6, pg. 16 #7, 9, pg. 24 #5, pg. 31 #4, 5, pg. 35 #4
    Chapter 2: pgs. 43-44 #1, 3, 6, pgs. 54-55 #1, 13, pg. 61 #1, 2, 6, pgs. 70-71 #1(a,b), 3, 4, pgs. 76-77 #1(c,d), 4, 5
    Chapter 3: pg. 89 #1, 2, 4, pg. 95 #1, 2, pg. 99 #3, pg. 103 #1, 2, pg. 108 #9, 10, pg. 111 #7, 8 , pg. 114 #1, 2
    Chapter 4: pgs. 119-120 #2, 5, pgs. 123-124 #1, 5, pgs. 132-133 #1, 2, 6
    Chapter 8: pg. 301 #3, 4, 5, pg. 306 #7, pgs. 325 #2, 3
  • (11/2) I will have extra office hours today, 10-10:45, and 3:45-4:59. For Monday, you can start the midterm as early as 8:30. If you cannot make it early, you may continue to work on the midterm until 10:20. If you have commitments before and after class, please let me know and we will work something out.
  • (11/7) First, please note that there is a HW due next Monday in class. Second, as I mentioned in class today, everyone can turn in corrections to the midterm to me by next Friday, Nov 16, by 5 PM, for up to 1/2 of your lost points back. You must do your corrections (for any part of a problem on which you lost points) on clean sheets of paper (LaTex is fine), and attach them to your original exam. I must have all of this in my hands (don't email them, because they must be attached to your original midterm) by 5 pm next Friday for you to receive any credit, and no late papers will be accepted. You can give them to me in class at your convenience, or you can bring them to my office.
  • (11/15) HW9 is due next Mon, Nov 19, in class. However, if you turn it in the next day (Tues) OR the Monday after Thanksgiving, I will only count it one day late. That is, Tues or the Mon after Thanksgiving I am treating as the SAME DAY in terms of the late HW penalty/policy.
  • (12/3) The final is on Mon, Dec 10, 9 AM-12 Noon, in our regular classroom Small 235. The sections covered are those that were covered on the midterm along with the following: Chapter 4, Sec. 46-58 except for 51, Chapter 5, Sec Sec. 60-68, and Chapter 6, Sec. 74-77. Below are suggested problems from sections which have been covered since the midterm. For all sections covered, you should also go over old homework problems, and for sections covered on the midterm, you can work on any problems which you have not yet done. Here is a list of practice problems, starting with the most recent material:
    Chapter 6: pgs. 237-238 #1(a,c,d), 2(a,c), 3, 4, 5, 6
    Chapter 5: pgs. 205-206 #1-5, pgs. 195-197 #1-10, pgs. 185-186 #1, 2, 4
    Chapter 4: pgs. 170-172 #1, 2, 7, pgs. 159-161 #1(a,b,d), 2-5, pg. 147 #1, 2, 4, pgs. 138-139 #1, 2, 3, 6.
  • (12/7) Just a few more words about the final exam. First, I will have an office hour on Sun, Dec 9, 5:30-6:30 pm. If you haven't picked up your last HW, then you can do that then. Second, the final exam will have a first page of T/F questions, a second page of some "short answer/short calculation" questions, and then 8 problems that are more like the midterm style questions. About 60% of the exam will be on material covered since the midterm. It will be approximately twice as long as the midterm, maybe 2.25 times as long. But, it will be roughly the same style, but with T/F questions.


Homework problems will be a very important part of the course, and there will be homework assigned almost every week. Proofs and computations should be written carefully and neatly, with attention paid to the completeness of your argument and clarity of your steps. Individual homework assignments should be written up by yourself, although some collaboration while working on the homework is OK. You should not, under any circumstances, attempt to look up solutions or hints to problems online. I will consider this plagiarism (an honor offense).

Homework is due at the beginning of class on the due date of the assignment, and if you like you may email me a pdf of your homework (only) if you LaTex it. Homework that is turned in or in my email inbox after 10 minutes past the beginning of the class is considered late. Everyone will get one free pass for a one-day late HW without penalty (by 5 pm the day after it is due). Late penalties are:
10% off if it is turned in after the beginning of class, but it is in my hands (on my door), or in my email inbox as a pdf by 5 pm on the day it is due.
20% off if it is turned in by 5 pm the next weekday after the due date.
20% more off for each (week)day late, turned in by 5 pm, thereafter.
Everything is easier, of course, if you turn in the homework on time!

Homework scores will each be out of 50 points. Your lowest homework score of the semester will be dropped.
Assignment Problems Due Date
1pg. 8 #8, pg. 13 #5, pg. 17 #14, 15 Mon, Sept 3
2pg. 25 #11, pg. 31 #7, pg. 35 #8, 10, pg. 44 #5, 8 Mon, Sept 10
3pg. 301 #2, pgs. 54-55 #2, 5, 9, 10 Mon, Sept 24
4pgs. 61-62 #4, 9, pgs. 70-72 #1(c,d), 5, 6, 8 Mon, Oct 1
5pgs. 76-77 #1(a,b), 2, 7, pg. 79 #1, pg. 90 #13, pg. 325 #4 Mon, Oct 8
6pg. 90 #6, 7, pg. 96 #7, pg. 99 #1, pg. 103 #6, pg. 107 #2 Fri, Oct 19
7pg. 114 #3, pg. 119 #3, 4, pg. 124 #2, pgs. 133-134 #9, 10 Mon, Oct 29
8pg. 139 #4, 5, pg. 147 #3, 5, pg. 159 #1(c,e,f), pg. 161 #6 Mon, Nov 12
9pg. 161 #7, pgs. 170-171 #3, 4, 5, 9, pg. 185 #3 Mon, Nov 19
10pg. 186 #9, pg. 197 #11, pg. 206 #6, 7, pg. 237 #1(b,e), 2(b,d) Mon, Dec 3

Math Major Writing Requirement (Math 300):

If you are a math major, and you would like to complete your major writing requirement through a writing assignment in this class, please let me know in the first week of class. This writing assignment will not count towards your grade in this class, but will rather just serve as your Major Writing Requirement (Math 300). You should only do this if all of the following hold: (1) you are not doing an honors thesis in Mathematics, (2) you are not doing your COLL 400 requirement in Mathematics, and (3) you are a senior. If you decide to do this, you must write your paper on a topic in Complex Analysis (or a closely related subject) approved by me, and you must keep to a schedule of turning in drafts we agree on at the beginning of the semester in order to get credit.

Student Accessibility Services:

William & Mary accommodates students with disabilities in accordance with federal laws and university policy. Any student who feels they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis should contact Student Accessibility Services staff at 757-221-2512 or at to determine if accommodations are warranted and to obtain an official letter of accommodation. For more information, please visit the SAS webpage.