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Semester: MAA4402 Functions Complex Var.

Complex Analysis

Nostalgic?   See 2021t, 2017g, 1999g,
Nostalgic?, see Spring 1999. or Spring 2017.
We are sorry, but the number you have dialed is imaginary. Please rotate your phone by 90 degrees and try again.
-David Grabiner

.   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 ChecklistThe checklist (pdf) which gives pointers on competant mathematical writing. 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.)
  1. Learn the Math-Greek alphabet.
  2. In my PlexNotes, read pages 1-4, memorize abbreviations in Appendix: Notation (pp.24-25, currently), and review Binomial coefficients in Appendix B: Binomials.
  3. 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.
  4. Get the basics of 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 +={1,2,3,4,...} for the set of positive integers; the posints.
  5. Refresh your memory on your Calc 2. Taylor series material (absolute/conditional convergence, radius of convergence, Taylor polynomial and error term, etc.)

Plex resources

Web resources

Our textbook is Complex Variables and Applications, 9th edition.
Author: Brown, Churchill ISBN: 978-0-07-338317-0
Year: 2014 Publisher: McGraw-Hill

Photo of text cover

Quantifiers and (“for all”  and  “there exists”) are like nitroglycerin, in that one little mis-step leads to the whole thing blowing up in your face.

There is no partial credit when it comes to Explosives and Quantifiers.

-JLF King

The various Math czars who help out:

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

Aut2021: MAA4402 8436(15961) Functions Complex Var. MWF6 LIT223
Aut2021: MAA5404 8442(15579) Intro Complex Var. MWF6 LIT223

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

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


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 (6th 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.

[Image: Coffee cup] 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

[Image: Steaming coffee cup] Exams and Projects (Complex Analysis)

StudyGuides ExamText When(1999) Alpha Study Exam Alpha Feb15Mon., 17:20-19:05, LIT125 Beta Study Exam Beta Mar29Mon., 17:15-19:05, LIT125 Gamma Study Exam Gamma Apr26Mon., 5:30PM-7:30PM, LIT203 Solutions to Gamma

Horizontal rule

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____End: Complex Analysis Page