Math 5160 Section 101 Homepage
News & Announcements
ASSIGNMENTS:
Homework #5 [Source: (.tex)] is due Wednesday, March 18th 25th.
Homework #6 [Source: (.tex)] is due Wednesday, April 1st.
Note: Problems #1-#4 cover material from Chapter IV. Problem #4 - You should assume that second partials are continuous.
Problem #5 is a "basic" complex analysis fact. Background is covered in V.1.
Homeworks #7 & #8 [Source: (.tex)] are due Wednesdays, April 8th & 15th.
Note: Homework #7 = Problems #1-#6 are drawn from Chapter V.
Homework #8 = Problems #7-#9 are drawn from Chapter VI.1 & VI.2.
Video: Additional Examples (70 mins) related to Homeworks 7 & 8
Test #2 - EMAILED - Due Friday, April 24th.
Video: Test #2 Related Examples (25 mins)
Final Projects - Guidelines and Due Dates [Source: (.tex)]
- Proposals are due Friday, April 24th and Presentations/Handouts are due by noon, Wednesday, May 6th.
CLASS TOPICS & VIDEOS:
Gamelin IV.1 (pages 102-106) and Fisher 1.6 (pages 56-65) = contour intergrals and ML-estimate
Gamelin IV.2 (pages 107-109) and Fisher 2.3 (pages 106-110) [parts] = FTC
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 [started]
Gamelin IV.5 (pages 117-119) and Fisher 2.4 (pages 130-131, problem 2.4 #18) = Cauchy estimates and Liouville's theorem
Gamelin IV.6 (pages 119-122) and Fisher 2.4 (pages 129-130) = Morera's theorem [started]
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
Video:
Gamelin IV.1 (40 mins)
Gamelin IV.2 (30 mins)
Gamelin IV.3 (13 mins)
Gamelin IV.4 (37 mins)
Gamelin IV.5 [No video]
Gamelin IV.6 [No video]
Gamelin IV.7 (22 mins)
Gamelin IV.8 (18 mins)
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.3 (pages 138-143) and Fisher 2.2 (pages 93-100) = Power Series
Gamelin V.4 (pages 144-147) and Fisher 2.2 (pages 123-128) = Analytic function are locally power series
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
Video:
Gamelin V.1 (30 mins)
Gamelin V.2 (55 mins)
Gamelin V.3 (62 mins)
Gamelin V.4 (36 mins)
Gamelin V.5 (18 mins)
Gamelin V.6 (22 mins)
Gamelin V.7 (27 mins)
Gamelin V.8 (20 mins)
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
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)
Video:
Gamelin VI: Motivational Example (20 mins)
Gamelin VI.1 (45 mins)
Gamelin VI.2 (48 mins)
Gamelin VI.3 (15 mins)
Gamelin VI.4 (21 mins)
Gamelin VI.5 & 6 [sketch] (8 mins)
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.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.1 (45 mins)
Gamelin VII.2 (20 mins)
Gamelin VII.3 (15 mins)
Gamelin VII.4 (45 mins)
Gamelin VII.5 (25 mins)
Gamelin VII.6 (20 mins)
Gamelin VII.7 (20 mins)
Gamelin VIII.1 (pages 224-228) & Fisher 3.1 (175-177) = The Argument Principle
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.1 (42 mins)
Gamelin VIII.2 (19 mins)
Gamelin VIII.4 (35 mins)
Older notes...
03/27--04/01 Let's cover the remainder of Gamelin chapter V on Friday (3/27), Monday (3/30), and Wendesday (4/1):
Gamelin V.4 (pages 144-147) and Fisher 2.2 (pages 123-128) = Analytic function are locally power series
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
Videos:
Gamelin V.4 (36 mins)
Gamelin V.5 (18 mins)
Gamelin V.6 (22 mins)
Gamelin V.7 (27 mins)
Gamelin V.8 (20 mins)
03/25 Homework #6 [Source: (.tex)] is due Wednesday, April 1st.
Homeworks #7 & #8 [Source: (.tex)] are due Wednesdays, April 8th & 15th.
Gamelin V.2 (pages 133-137) = Sequences and Series of Functions also Pointwise, Uniform, and Normal Convergence
Gamelin V.3 (pages 138-143) and Fisher 2.2 (pages 93-100) = Power Series
Videos from Spring 2018:
Gamelin V.2 (55 mins)
Gamelin V.3 (62 mins)
03/23 We will meet via Zoom and then (and as a backup plan)...
Gamelin IV.8 (pages 124-128) [skimmed] = Complex Notation & Synopsis of Pompeiu's Formula
Gamelin V.1 (pages 130-132) and Fisher 1.4 (pages 37-41) = Series Basics
Videos from Spring 2018:
Gamelin IV.8 (18 mins)
Gamelin V.1 (30 mins)
Join my Zoom Meeting
03/16-03/20 [Spring Break Part 2: Brought to you by Coronavirus Hysteria.]
03/09-03/13 [Spring Break]
03/06 IV.6 [finished]
IV.7 (pages 123-124) and 2.3.1 (pages 119-123) = Goursat's theorem
Videos from Spring 2018:
Gamelin IV.7 (22 mins)
03/04 IV.5 (pages 117-119) and 2.4 (pages 130-131, problem 2.4 #18) = Cauchy estimates and Liouville's theorem
IV.6 (pages 119-122) and 2.4 (pages 129-130) = Morera's theorem [started]
03/02 IV.4 [finished]
02/28 IV.2 [finished]
IV.3 (pages 110-111) and 2.3 (pages 106-110) [parts] = Cauchy's Theorem
IV.4 (pages 113-116) and 2.3 (pages 111-116) = The Cauchy Integral Formula [started]
Videos from Spring 2018:
Gamelin IV.3 (13 mins)
Gamelin IV.4 (37 mins)
Homework #5 [Source: (.tex)] is due Wednesday, March 18th 25th.
02/26 IV.1 (pages 102-106) and 1.6 (pages 56-65) = contour intergrals and ML-estimate
IV.2 (pages 107-109) and 2.3 (pages 106-110) [parts] = FTC
Videos from Spring 2018:
Gamelin IV.1 (40 mins)
Gamelin IV.2 (30 mins)
02/24 III.4 (pages 85-86) and 4.1 (pages 248-249) = mean value property of harm. func.
III.5 (pages 87-88) and also 3.2 (pages 191-194), 4.1 (pages 248-249) = maximum modulus for harm. func.
Videos from Spring 2018:
Gamelin III.3 (20 mins)
Gamelin III.4 (20 mins)
Gamelin III.5 (30 mins)
02/21 Test #1 covering Chapters I and II of Gamelin.
One side of one page of note allowed for the in class portion.
Take home portion due Monday (Feb. 24th).
02/19 III.2 [finished] = closedness
III.3 (pages 83-84) = harmonic conjugates
Videos from Spring 2018:
Gamelin III.2 (part 2) (45 mins)
02/17 III.2 (pages 76-82) = exact iff path independent
As decided on 2/14, Test #1 is this Friday (2/21).
Test #1 will cover Gamelin chapters I and II.
You may have one page (one sided) of notes.
02/14 II.7 = Mobius transforms [finished]
III.1 (pages 70-75) and 1.6 (pages 56-73) = line integrals & Green's theorem (Calc. 3 review)
02/12 II.7 continued.
Homework #4 [Source: (.tex)] is due Wednesday, February 19th.
02/10 II.5 harmonic examples [finished]
II.6 (pages 58-61) and 3.4 (pages 208-218) = conformal mappings
II.7 (pages 63-67) and 3.3 (pages 196-203) = Mobius transforms
= fractional linear transformations [started]
A Maple sheet to supplement II.6 and II.7: Conformal mappings and Mobius transforms (.mw) [Printed: (.pdf)]
Videos from Spring 2018 (we just started the second video's material):
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)
02/07 Some clean up and plotting.
II.5 (pages 54-57) and 2.1 (pages 81-84), 4.1 (pages 245-247) = harmonic functions
Complex Arithmetic and Basic Plotting: Maple Plots (.mw) [Printed: (.pdf)]
02/05 II.3 (pages 46-50) and 2.1 (pages 79-81) = analytic functions
II.4 (pages 51-53) = inverse function theorem & differentiating inverses
Videos from Spring 2018:
Gamelin II.2-II.3 (parts of) & II.4 (55 mins)
Note: I noticed a small error in the example showing f'(1+2i) D.N.E.
This is fixed in our handout below.
Complex Differentiability [Source: (.tex)]
02/04 I'm not sure where this came from originally...but enjoy:
02/03 II.2 (pages 42-46) and 2.1 (pages 77-79) = complex differentiability & Cauchy-Riemann equations
(See Complex Diff handout)
Homework #3 [Source: (.tex)] is due Wednesday, February 12th.
01/31 II.1 analysis basics [finished]
Began differentiation
A Calculus 3 Handout: Differentiability (.pdf) [Source: (.tex)]
01/29 II.1 (pages 33-39) and 1.3 (pages 22-28) plus parts of 1.4 (pages 30-37) = basic analysis/topology [started]
A quick tour of basic analysis definitions/theorems: Gamelin II.1 (90 mins)
(sequences, limits, continuity, open/closed, connectedness, compact, and some multivariate limits).
01/27 I.7 powers [finished]
I.8 (pages 29-31) and 1.5 (pages 48-53) = trig & inverse trig functions
01/24 I.6 logs [finished]
I.7 (pages 24-27) = powers [started]
Homework #2 [Source: (.tex)] is due Monday, February 3rd.
Videos from Spring 2018:
Gamelin I.5 and I.6 (35 mins)
Gamelin I.7 (30 mins)
01/22 I.4 (pages 15-18) = square & square roots
I.5 (pages 19-21) and 1.5 (pages 43-45) = exponential function
I.6 (pages 21-23) and 1.5 (pages 45-48) = logs [started]
01/17 I.2 (pages 5-9) and 1.1-2 (pages 5-20) = polar form stuff
I.3 (pages 11-13) = extended complex plane / Riemann sphere
Homework #1 [Source: (.tex)] is due Friday, January 24th.
01/15 I.1 (pages 1-4) and 1.1 (pages 1-4) = complex number basics
plus a touch of polar representation stuff.
01/13 Characterizing the Reals [Source: (.tex)]
01/08 Syllabus, Suggested Homework, and Tentative Schedule pages posted.
AsULearn switched on.
01/09 Course Data
MAT 5160 Section 101
COMPLEX VARIABLES
Meeting Times MWF 10:00am-10:50am in WA 308
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. $6 used $11 new
Complex Analysis by Theodore W. Gamelin
ISBN: 978-0-387-95069-3 (See AddAll.com for a comparison of prices) Approx. $43 new or $30 used
-- Bookfinder.com had better used prices.
Sometimes BookFinder.com or AllBookStores.com will find better deals.
Any questions about this class?
Send me an email at cookwj@appstate.edu