The aftermath of Bell's tablet PC lectures
These are the lecture notes and videos of Bell's
tablet PC lectures.
- Lecture 1 on 08-21
and the
video
Introduction
- Lecture 2 on 08-23
and the
video,
The Cauchy-Riemann equations
(proof of the remainder estimate)
- Lecture 3 on 08-25
and the
video
C-R equations and the complex exponential
- Lecture 4 on 08-28
Complex power series
- Lecture 5 on 08-30
Complex integration
- Lecture 6 on 09-01
and the
video
Goursat's lemma
- Lecture 7 on 09-06
and the
video
Cauchy theorem on a convex open set
- Lecture 8 on 09-08
and the
video
Liouville's theorem and the Fundamental theorem of Algebra
- Lecture 9 on 09-11
and the
video
Analytic functions are given by power series
- Lecture 10 on 09-13
and the
video
Zeroes of analytic functions
- Lecture 11 on 09-15
and the
video
The Maximum principle
- Lecture 12 on 09-18
and the
video
Harmonic functions and harmonic conjugate
- Lecture 13 on 09-20
and the
video
Complex logarithms, isolated singularities, Riemann removable
singularity thm
- Lecture 14 on 09-22
and the
video
Isolated singularities, the pt at infinity, Picard theorems
- Lecture 15 on 09-25
and the
video
Singularities at infinity, partial fractions, Schwarz lemma
- Lecture 16 on 09-27
and the
video
Schwarz lemma, log and roots, Open mapping theorem
- Lecture 17 on 09-29
and the
video
Argument principle, complex inverse function theorem
- Lecture 18 on 10-02
and the
video
Inverse function theorem, Local mapping theorem
- Lecture 19 on 10-04
and the
video
Conformal mapping, zeroes of harmonic functions, MA 525
- Lecture 20 on 10-06
and the
video
Fun with the Baby residue theorem on Toy regions
- Lecture 21 on 10-11
and the (19 minute)
video
Applications of the Residue theorem
- Review on 10-13
and the
video
Solutions to some old exam questions
- Exam 1 on 10-16
and the
solutions
- Lecture 22 on 10-18
and the
video
More on the Residue theorem
- Lecture 23 on 10-20
and the
video
Why the "Argument principle"
- Lecture 24 on 10-23
and the
video
Consequences of the Schwarz lemma
- Lecture 25 on 10-25
and the
video
LFTs, Jukovsky map, conformal mapping
- Lecture 26 on 10-27
and the
video
Conformal mappings, Schwarz reflection
- Lecture 27 on 10-30
and the
video
Real analytic curves and Schwarz reflection, Laurent expansions
- Lecture 28 on 11-01
and the
video
Laurent expansions, residue at an essential singularity
- Lecture 29 on 11-03
and the
video
Rouché's theorem and Hurwicz's theorems
- Lecture 30 on 11-06
and the
video
Homotopy, simply connected domains, THE Cauchy theorem
- Lecture 31 on 11-08
and the
video
Simply connected domains, Montel's theorem
- Lecture 32 on 11-10
and the
video
Proof of Montel's theorem, prep for proof of Riemann Mapping Thm
- Lecture 33 on 11-13
and the
video
Proof of the Riemann Mapping Theorem
- Lecture 34 on 11-15
(no video) Harmonic functions, Poisson kernel
- Lecture 35 on 11-17
and the
video
Dirichlet problem, Schwarz's theorem
- Lecture 36 on 11-20
and the
video
Riemann removable singularity theorem for harmonic functions, Ave prop
implies harmonic
- Lecture 37 on 11-27
and the
video
Weak averaging property and the reflection principle for harmonic
functions
- Lecture 38 on 11-29
and the
video
The General Cauchy theorem
- Lecture 39 on 12-01
and the
video
The General residue theorem, argument principle, and Rouché's
theorem
- Lecture 40 on 12-04
and the
video
The Mittag-Leffler and Weierstrass theorems
- Lecture 41 on 12-06
and the
video
Mittag-Leffler, Weierstrass, infinite products
- Lecture 42 on 12-08
and solutions to Exam 2
and the
video
Review
Back to Bell's MA 530 Home page