Complex Analysis [curr]

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).

Computer	Time	B-Probs	Humor	Telepathy	Whiteboard
Austin	Arjun	Bridget	Anneka & Faythe	?	?

End-of-semester Plex IOP (Individual Optional Project)

...was due, slid u n d e r room 402 Little Hall my office door (Little Hall 402, Northeast corner) , no later than 2PM, Thursday, 25April2024

The IOP must be carefully typed, but diagrams may be hand-drawn.

For the typesetting, one possibility is the (free) mathematics-typesetting language LaTeX .

At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist (pdf, 3pages) to earn full credit.

Plex resources

Facts for Fibonacci-like Sequences (pdf). In particular, the pamphlet derives the representation formula for f_n by means of a contour integral.

The Fibonacci Speedup (txt) shows how to use repeated squaring and modular arithmetic to rapidly compute the last two digits of the 1024^th Fibonacci number.
PlexNotes (pdf) with several examples of contour integration. [Sunday, 14Apr2024]
Available also is an exposition of Taylor's Thm on R.
Front-page news in the Huffington Post, our (yay!, essayless) Class-U was well-received.
Our 2024g Plex syllabus.
w:Gamma function and w:Particular Gamma-values.
See also jk: gamma and Gamma (pdf), as well as w:Euler-Mascheroni (pronunciation).
Application: Computing the Volume of the n-ball (pdf).
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.
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).
Conveniently, in one location: All 8 Plex quizzes (pdf).
The handsomely typeset Class-T had everyone bubbling with delight.
The heart-warming Class-S.
Last year's (2023) Robert Long Essay Competition (RLEC) essay titles.
An example of the Map+Computation approach to solving Plex problems (Two Page technique)
UF pays a fee so that students can use the professional version of Overleaf, a free LaTeX typesetter.
Fnc ln(|z|) is harmonic. Then P.13 and P.64 of PlexNotes.
When do limits commute? The (YT) radius-1 circle has circumference 8, don't-cha-know.
The useful w:Jordan's lemma to an integral along a semicircle goes to zero, as the radius goes to infinity.

Web resources

An app for computing the residue of a fnc at an isolated singularity. IIUCorrectly, this is a contributed app, not written by the Wolfram company. Caveat user.] (The app apparently only works at poles, not at essential-singularities, even if the Larent-Series (LS) is known.)
The Wolfram|Alpha implements general computation. (Sometimes the correct input syntax is a challenge.)
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.

Assignment for first week of class.

Email me (squashATuflDOTedu, Prof. King) right away, if you will have a DRC letter giving extra time on exams. [As I have back-to-back classes -in different buildings- I'll need to discuss with you how to give extra time.]

It is helpful if you are free 8th (the period immediately after our class) so that I can give you extra time.
To help you self-evaluate, take up to 80ish minutes to solve as many problem as you can, on this test of high-school mathematics, with a touch of calculus (pdf).
Memorize the useful Math-Greek alphabet (pdf).
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 FiCA text, read pages 1-17 and post [jointly, with another student] at least 2 HW problems from that section. Alternatively, you may read ahead and post solutions from the next section.
Exams from previous SeLo incarnations. In particular, look at the microquizzes for several previous incarnations of Plex.
This will help you decide if my teaching-style is the right style for you.
If you wish to be in a Plex class photo, please prepare a name-card (the writing must be LARGE and DARK) for Wednesday's class, Wednesday, 17Jan.

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.)

Complex Analysis (Plex)

End-of-semester Plex IOP (Individual Optional Project)

Plex resources

Web resources