[past] Complex Analysis

. Our Teaching Page has important information for my students. (It has the Notes, Exams and Links from all of my previous courses.)
The Teaching Page has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Further information is at our class-archive URL (I email this private URL directly to students).

Assignment for first week of class. (See below, for the materials referred to.)

Learn the Math-Greek alphabet.
In my PlexNotes, read pages 1-4, memorize abbreviations in Appendix: Notation (pp.24-25, currently), and review Binomial coefficients in Appendix B: Binomials.
In our text B&C [Brown & Churchill], read pages 1-39 and write-up (but do not hand-in) at least 3 HW problems from those pages.
Get the basics of w:Set-builder notation (up through “Equivalent predicates...”). Important: For us, the (double-bar N) symbol ℕ={0,1,2,...}; i.e zero is a natural number, a natnum.
We use ℤ₊={1,2,3,4,...} for the set of positive integers; the posints.
Refresh your memory on your Calc 2. Taylor series material (absolute/conditional convergence, radius of convergence, Taylor polynomial and error term, etc.)

Plex resources

The useful Math-Greek alphabet (pdf).
PlexNotes (pdf). with several examples of contour integration.
Available also is an exposition of Taylor's Thm on R.
Conveniently, in one locations: All 0 DfyQ quizzes so far (pdf) [Date]
The useful w:Jordan's lemma to an integral along a semicircle goes to zero, as the radius goes to infinity.
Plex syllabus.
An example of the Map+Computation approach to solving Plex problems (Two Page technique)
Page 3 of Fibonacci sequences pamphlet (pdf) now has the f_n representation formula derived with a contour integral. Cool!
Here are HW problems, mostly from FiCA. for you to post solns to our Plex Archive; I recommend the free LaTeX typesetting system.

HW soln example: Two ways of computing a Laurent series of a rational function.
UF pays a fee so that students can use the professional version of Overleaf, a free LaTeX typesetter.
w:Gamma function and jk: gamma and Gamma (pdf), as well as w:Euler-Mascheroni.
An application is computing Volume of the n-ball (pdf).
Fnc ln(|z|) is harmonic. Then P.13 and P.64 of PlexNotes.
When do limits commute? The radius-1 circle has circumference 8, don't-cha-know.
See w:Holomorphic function. and w:Analytic function.
An interesting example is: On the reals, a C-infinity function which is not everywhere-analytic (pdf).
The useful w:Jordan's lemma to an integral along a semicircle goes to zero, as the radius goes to infinity.

Web resources

A First Course in Complex Analysis [hyperlinked PDF] and AFCiCA [PDF identical to paperback] are made freely available by the authors, Matthias Beck, Gerald Marchesi, Dennis Pixton & Lucas Sabalka. It is from Prof. Beck's website.
An online Complex-numbers calculator. [I haven't played with it much, so cannot vouch for accuracy. Note that extending logarithm to the Complex plane involves choices, as complex log() is multi-valued; be cautious with the log() symbol on this calculator.]
An Integral Calculator that allows “infinity ” and “-infinity ” to be typed as the Limits-of-Integration.
A C-infinity function which is not everywhere analytic (pdf).

Time	Computer	Blackboard	ES-Probs	Phone-list
Yasmeen	?	?	?	?

MAA4402 2838 (13781) Functions Complex Var MWF6 [12:50-13:40]
MAA5404 0988 (22626) Intro Complex Var MWF6 [12:50-13:40]
Spr2023: LittleHall 221(NW)

The various Math czars who help out:

Computer	Time	Blackboard	EP-Probs
Lily / Anna	Tyler	everyone	?

Fantastic and Unexpected: Our 2023g Plex IOP was available a day early.
Our nifty Class-C announced the Math Festival organized by Prof. Bartosova.
Conveniently, in one location: All 11 + BonusA + BonusB + BonusC Plex quizzes so far (pdf). [Friday, 14Apr2023]
Online is Practice-B and More Practice-B problems. to help you prepare for the exam by Posting solns and giving polite useful feedback on solns posted by your colleagues..

The highly residual Class-B is now online.
Our Plex 2023g syllabus. with Exam Dates.
The highly-anticipated Plex Class-A [now with all solns] brought shouts of acclaim from admirers worldwide, who praised its clean two-tone format, as well as its Robert Long Prize freebie question.

Aut2021: MAA4402 8436(15961) Functions Complex Var. MWF6 LIT223

Aut2021: MAA5404 8442(15579) Intro Complex Var. MWF6 LIT223

Conveniently, in one location, all 15 Plex quizzes this semester (pdf).
Our exciting Class-V took place on Wednesday, 06Oct2021, in class.
Folks enjoyed that it was staggeringly similar to the previously posted Practice problems PDF, and that three of those problems were solved in class.
The nifty Class-W (pdf), elicited shouts of enthusiasm. Admirers remarked on its minimalistic two-tone format, and marveled at the essay question's similarity to a proof done in class, and in PlexNotes. A Triumph!, declared all the major newspapers... and NPR!

Students added points to their Class-W score by typing up solutions to W-bonus. (The Bonus was due Monday, 08Nov2021.)
Class-X (pdf), went off without a hitch.

A panoply of nice Residue and Contour-integral problems led admirers to praise the straight-forwardness of the problems, and the simple yet elegant layout on the page.
The highly-anticipated IOP-Z was due Thursday, 09Dec2021
Plex 2021t syllabus.

Spr2017: MAA4402 2838 Elem.Complex.Var MWF6 LIT203

Spr2017: MAA5404 16A3 Intro.Complex.Var MWF6 LIT203

End-of-Semester Games Party (click for larger & different)

Complex Complex class 2017Spring, Games Party

Look Ma! All 7 Plex quizzes so far (pdf).
On Wedn., 01Feb2017, we had the pleasant Class-A, with its popular two-tone format.
Voila! A few Practice Class-B problems. Wedn., 01Mar2017, unveiled Class-B, with its initial question about Plane English.
Available are some sample questions for Class-C. Integral to our understanding of complex analysis, was Class-C.
The thought-provoking IOP-D was due 2PM, Thur., 20Apr2017.
Our Plex syllabus with exam-dates.

The various Math czars who help out:

Time	Computer	Blackboard	ES-Probs	Phone-list
Everyone...	Leah & Harry	Christopher P.	?	Mauricio

Spr1999: MAA4402 2838...Elem.Complex.Var..MWF5..LIT203

Spr1999: MAA5404 2840..Intro.Complex.Var..MWF5..LIT203

26May2000

I was chairman of the Complex Analysis Ph.D Exam committee this past year. (Other members were Prof.s Rao, Shen and Walsh.) Here is a copy of the Ph.D exam of 25May2000 (pdf).

Our textbook is Complex Variables and Applications (6^th edition).

Author:

Churchill, Brown.

My intention is to treat the subject from a geometric point of view, and to give a number of applications both within and outside of mathematics. Plex 1999g syllabus is available.

Homework and reading, so far…

Periodically, I update our list of E-problems. (E stands for Extra.)

Below, I list problems from our textbook. I use P and Pgs to abbreviate Page(s) and Sec to abbr. Section(s). Problems with an asterisk are either more important, or are problems that I am more likely to ask you to solve at the blackboard.

Please hand-in problems listed as GRADED. I will put comments on them and hand them back to you. These are not counted towards your course grade other than indirectly.

You should write up solutions for the other homework problems, but you should only hand them in if you are in doubt about the correctness of your solution.

DateDue HaveRead DoTheseProblems ________________________________________________________________ 08Jan P05: 4-6,11,(12,14)*. P11: 4,9,10,11 11Jan Pgs.1-23 P11: 12,13,(14,16,18)*. 13Jan Pgs.23-33 15Jan Pgs.33-45 P17: 2,5,9,(10,13,16)*. 20Jan Pgs.45-57 P22: 4,6,(7,8)*. P25: 1-10. 22Jan Pgs.57-63 P31: 4-8. Start reading/reviewing the basic facts on CONVERGENCE OF A SERIES e.g, the Ratio, Root, Comparison and Alternating Series tests; geometric series, absolute and conditional convergence (etc.) and TAYLOR SERIES (Power Series) e.g, radius and interval of convergence, multiplication of power series (etc.). One good reference for this is Calculus, by Tom Apostle. Also, most any book entitled Advanced Calculus will have a treatment of Power Series which is suitable for our needs. 29Jan Pgs.63-71 P42: 1,3,(4,7,10-12)*. P47: 4,(6-8)*. P54: 1-6. Extra Class, Feb01Mon., periods 10-11, in LIT 125. 05Feb Pgs.71-85 P62: 2,5,7*,9,10,(11,14,15)*. P67: 3,6,10,11,12,13,15. P74: 2,6,11,14. Extra Class, Feb08Mon., periods 10-11, in LIT 125. 08Feb Sec. 29-32 12Feb Pgs.85-109 03Mar GRADED: E8 and P93:1,2,5,12. Spring Break, March 6-14. Class CANCELED, Mar15Mon. 17Mar Sec. 38-41. DRILL:P102:3,4,7,16. P128:3,4. 19Mar GRADED: P103:13,15,18. P121:9. P129:5 [Consider the difference of the integrands, then use the Quotient Rule for differentiation]. E8. 24Mar GRADED: E9, using Cauchy's Inequality. 26Mar P62: 7. Contrast the book's method with the solution that I showed in class. 14Apr Hand in E11. End Homework

Exams and Projects (Complex Analysis)

(1999) Alpha Study (pdf) Exam Alpha (pdf) Feb15Mon., 17:20-19:05, LIT125 Beta Study (txt) Exam Beta (pdf) Mar29Mon., 17:15-19:05, LIT125 Gamma Study (txt) Exam Gamma (pdf) Apr26Mon., 5:30PM-7:30PM, LIT203

Author:	Brown, Churchill	ISBN:	978-0-07-338317-0
Year:	2014	Publisher:	McGraw-Hill