Math 4010 & 5160 Section 101 Homepage
News & Announcements
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VIDEO LINKS MAY BE BROKEN!
---> AppState migrated from Panopto to Kalura in Spring 2021. I had a bunch of old recording
done in Panopto that got migrated. I fixed links in the Spring 2020 Complex Variables
class. I had recorded more for that class because of Covid.
---> See Spring 2020 Version for working video.
Final Project Topics -- Dibs which have been offically called upon:
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- [4/30] Cory = Physics!
- [4/30] John & Samwise = The Zeta Function & A Proof of the Riemann Hypothesis
- [4/30] Lexi & Chelsey = Periodic Functions
- Christa & Kelly = Conformal Mappings & the Schwartz Lemma
- Angela = Complex numbers and their relation to nuclear reactions
- Hannah = The Jumping Theorem for Cauchy Integrals
- Zack = Fluid Dynamics
- Charlotte = The Gamma Function
- Stephen & Carter = Mobius Transforms & Geometry & ?Dihmimrunjigfrumistan?
- Leah = Prime Number Theorem
- Abbie = Fourier Series
- Richard = Complex Logarithm Stuff
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05/07: I just submitted grades. I posted your final grade component (participation/presentation/handout)
on AsULearn. I also posted your cumulative course average with the your course letter grade posted
as a comment on the final course average.
For those who still have some of my books, feel free to continue borrowing for a while. When you
finish with them, drop them off at my office (Sandy or Robin can open my office door) or leave them
in my mailbox if there's room.
If you ever have any questions - mathematical or otherwise - and you think I might be of help, don't
hesitate to stop by my office or send me an email. I'm happy to help if I can!
I hope you all have a great summer!
04/25: New Video: Gamelin VIII.2 (pages 229-230) & Fisher 3.1 (pages 177-179) = Rouche's Theorem
Gamelin VIII.4 (pages 232-234) & Fisher 3.2 (pages 191-192) = Open Mapping & Inverse Function Theorems
Gamelin VIII.2 (19 mins)
Gamelin VIII.4 (35 mins)
04/23: Test #2 Clarifications
Gamelin VIII.1 (pages 224-228) & Fisher 3.1 (175-177)
Class part 1 (32 mins) [crash] Class part 2 (29 mins) [crash] Class part 3 (15 mins)
04/18: Test #2 is due Wednesday, April 25th.
New Video: Gamelin VII.4 (pages 206-207) & Fisher 2.6 (pages 162-166) = Integrals and Branch Points
Gamelin VII.5 (pages 209-211) = Fractional Residues
Gamelin VII.6 (pages 212-215) = Cauchy Principal Values
Gamelin VII.7 (pages 216-218) & Fisher 2.6 (pages 157-161) = Jordan's Lemma & Sine Integral
Gamlien VII.8 (pages 219-222) = Exterior Domains & Residues at Infinity [SKIP]
Gamelin VII.4 (45 mins)
Gamelin VII.5 (25 mins)
Gamelin VII.6 (20 mins)
Gamelin VII.7 (20 mins)
04/16: Discussing Homework #7 Related Examples
Class part 1 (23 mins) [crash] Class part 2 (5 mins) [crash] Class part 3 (48 mins) [crash]
04/10 Homework #7 (.pdf) [Source: (.tex)] due Tuesday, April 10th.
New Video: Gamelin VII.1 (pages 195-198) and Fisher 2.5 (pages 137-141) & 2.6 (pages 153-154) = Residues
Gamelin VII.2 (pages 199-202) and Fisher 2.6 (pages 154-158) Real integrals via residues part 1
Gamelin VII.3 (pages 203-204) and Fisher 2.6 (pages 161-162) Real integrals via residues part 2
Gamelin VII.1 (45 mins)
Gamelin VII.2 (20 mins)
Gamelin VII.3 (15 mins)
04/09 Gamelin VI.3 (page 178) and Fisher (page 152 problems 25-27) = Isolated Singularity at Infinity
Gamelin VI.4 (pages 179-181) and Fisher 2.5 (pages 147-149) = Rational Functions & Partial Fractions
Gamelin VI.5 (pages 182-185), VI.6 (pages 186-191) and Fisher 4.3 (pages 296-297 problems 16-23) & Chapter 5 (sort of) = Periodic Functions and Fourier Series (sketch/skipped)
Gamelin VII.1 (pages 195-198) and Fisher 2.5 (pages 137-141), 2.6 (pages 153-154) = Residues
Class part 1 (2 mins) [crash] Class part 2 (30 mins) [crash] Class part 3 (45 mins) [crash] to be continued...
I plan to post the rest of VII.1 tomorrow afternoon (or whenever I have time to record).
04/05 New Video: Gamelin VI.1 (pages 165-170) and Fisher 2.5 (pages 135-149) = The Laurent Decomposition
Gamelin VI.2 (pages 165-170) and Fisher 2.5 (pages 135-149) = Isolated Singularities
Motivational Speech (20 mins)
Gamelin VI.1 (45 mins)
Gamelin VI.2 (48 mins)
03/29 New Video: Gamelin V.5 (pages 149-150) = Analytic at Infinity
Gamelin V.6 (pages 151-153) and Fisher 2.2 (pages 101-102) & 2.4 (pages 132-133) = Manipulating Power Series
Gamelin V.7 (pages 154-157) and Fisher 2.4 (page 128) & 3.1 (pages 171-172) = Zeros of Analytic Functions
Gamelin V.8 (pages 158-162) [sketch] = Analytic Continuation
Gamelin V.5 (15 mins)
Gamelin V.6 (22 mins)
Gamelin V.7 (27 mins)
Gamelin V.8 (20 mins)
03/21 Homework #6 (.pdf) [Source: (.tex)] due Wednesday, March 28th.
New Video: Gamelin V.1 (pages 130-132) and Fisher 1.4 (pages 37-41) = Series Basics
Gamelin V.2 (pages 133-137) = Sequences and Series of Functions also Pointwise, Uniform, and Normal Convergence
Gamelin V.1 (30 mins)
Gamelin V.2 (55 mins)
03/20 New Video: Gamelin IV.7 (pages 123-124) and Fisher 2.3.1 (pages 119-123) = Goursat's Theorem
Gamelin IV.8 (pages 124-128) [skimmed] = Complex Notation & Synopsis of Pompeiu's Formula
Gamelin IV.7 (22 mins)
Gamelin IV.8 (18 mins)
03/13 Homework #5 (.pdf) [Source: (.tex)] due Wednesday, March 21st.
03/12 Snow day! In lieu of face-to-face class, here are some videos. I hope to posted homework soon and get
test grade information posted.
New Video: Gamelin IV.1 (pages 102-106) and Fisher 1.6 (pages 56-65) = Contour Integrals
Gamelin IV.2 (pages 107-109) and Fisher 2.3 (pages 106-110) [parts] = FTC for Analytic Functions
Gamelin IV.3 (pages 110-111) and Fisher 2.3 (pages 106-110) [parts] = Cauchy's Theorem
Gamelin IV.4 (pages 113-116) and Fisher 2.3 (pages 111-116) = The Cauchy Integral Formula
Gamelin IV.1 (40 mins)
Gamelin IV.2 (30 mins)
Gamelin IV.3 (13 mins)
Gamelin IV.4 (37 mins)
02/23 New Video: Gamelin III.3 (pages 83-84) and Fisher 4.1 (pages 245-247) = Harmonic Conjugates
Gamelin III.4 (pages 85-86) and Fisher 4.1 (pages 248-249) = Mean Value Property
Gamelin III.5 (pages 87-88) and Fisher 3.2 (pages 191-194) plus 4.1 (pages 248-249) = Maximum Modulus Principal
Gamelin III.3 (20 mins)
Gamelin III.4 (20 mins)
Gamelin III.5 (30 mins)
02/21 New Video: Gamelin III.2 part 2 (pages 76-82) covering closed forms, simple connectedness, and the connection
between exact and closed.
Gamelin III.2 (part 2) (45 mins)
02/15 Homework #4 (.pdf) [Source: (.tex)] due Thursday, February 22nd.
Test #1 on Monday, February 26th.
You may have a side of one standard size piece of paper of notes.
There will be an in-class portion on Monday. Grad students will have a take home portion.
Undergrads might have a take home problem or two.
02/14 New Video: Conformal maps and linear fractional transformations
Gamelin II.6 (pages 58-61) & II.7 (pages 63-67) and
Fisher 3.4 (pages 208-218) & 3.3 (pages 196-203)
Gamelin II.6 (30 mins) [You can enlarge the board view - sorry it recorded the computer screen too!]
Gamelin II.6 (clean up) and II.7 (60 mins)
A Maple sheet to supplement II.6 and II.7: Conformal mappings and Mobius transforms (.mw) [Printed: (.pdf)]
02/07 Example from class: Complex Arithmetic and Basic Plotting (.mw) in Maple.
New video: Finishing up complex differentibility and Cauchy-Riemann equations (examples)
and Gamelin II.4 on inverses.
Gamelin II.2-3 (clean up) & II.4 (55 mins)
02/06 Homework #3 (.pdf) [Source: (.tex)] due Tuesday, February 13th.
02/05 A Calculus 3 Handout: Differentiability (.pdf) [Source: (.tex)]
01/30 New video: Analysis background material (sequences, limits, continuity, open/closed,
connectedness, compact, and some multivariate limits.
Gamelin II.1 (90 mins)
01/29 Homework #2 (.pdf) [Source: (.tex)] due Tuesday, February 6th.
01/26 I just posted videos covering...
Complex exponentiation: Gamelin I.5 (pages 19-21) & Fisher 1.5 (pages 43-45),
Logarithms: Gamelin I.6 (pages 21-23) & Fisher 1.5 (pages 45-48), and
Power (multi)functions and phase factors: Gamelin I.7 (pages 24-27).
Gamelin I.5 and I.6 (35 mins)
Gamelin I.7 (30 mins)
We will shorten Monday's class accordingly.
01/22 (Updated) Homework #1 (.pdf) [Source: (.tex)] due Tuesday, January 30th.
We will briefly discuss this handout in class: Characterizing the Reals [Source: (.tex)]
Don't take it too seriously.
01/17 Suggested reading for Monday's class:
Gamelin Chapter I (pages 1-32)
Fisher Sections 1.1-1.3 (pages 1-30)
We will almost certainly not cover all of Gamelin's first chapter, but
looking/reading ahead is not a bad thing.
01/10 Syllabi (Math 4010 and Math 5160) and Suggested Homework pages posted.
To do: Sketch a schedule and fix AsULearn.
01/09 Course Data
MAT 4010 & 5160 Section 101
COMPLEX VARIABLES
Meeting Times M 5:00pm-7:30pm in WA 308
[Our meeting time may change!]
Course Title & Description:
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MAT 5160 - Complex Variables (3 credits)
An introduction to the study of complex variables to include such
topics as line integrals, the Cauchy theorem, the Cauchy integral
formula, Morera's theorem, and the Laurent series.
Prerequisite: MAT 3220 (Real Analysis) or permission of the instructor
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Textbooks:
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Complex Variables (2nd edition) by Stephen D. Fisher
ISBN: 978-0-486-40679-4 (See AddAll.com for a comparison of prices) Approx. $10 used $17 new
Complex Analysis by Theodore W. Gamelin
ISBN: 978-0-387-95069-3 (See AddAll.com for a comparison of prices) Approx. $35 new
Sometimes BookFinder.com or AllBookStores.com will find better deals.
Any questions about this class?
Send me an email at cookwj@appstate.edu