The aftermath of Bell's tablet PC lectures

These are the lecture notes and videos of Bell's
tablet PC lectures.

• Lecture 1 on 08-19 and the video Introduction
• Lecture 2 on 08-21 and the video The Cauchy-Riemann equations (proof of the remainder estimate)
• Lecture 3 on 08-23 and the video The C-R equations, converse and the complex exponential
• Lecture 4 on 08-26 and the video Power series
• Lecture 5 on 08-28 and the video Complex integration
• Lecture 6 on 08-30 and the video Goursat's lemma
• Lecture 7 on 09-04 and the video Cauchy theorem on a convex open set
• Lecture 8 on 09-06 and the video Liouville's theorem and the Fundamental Theorem of Algebra
• Lecture 9 on 09-09 and the video Analytic functions are given locally by convergent power series
• Lecture 10 on 09-11 and the video Zeroes of analytic functions and the Identity theorem
• Lecture 11 on 09-13 and the video The Maximum principle
• Lecture 12 on 09-16 and the video Harmonic functions and harmonic conjugates
• Lecture 13 on 09-18 and the video Complex logarithms, isolated singularities
• Lecture 14 on 09-20 and the video Isolated singularities, pt at infinity, Riemann removable singularity thm
• Lecture 15 on 09-23 and the video Singularities at infinity, partial fractions, Schwarz lemma
• Lecture 16 on 09-25 and the video Schwarz lemma, log and roots on convex sets, Argument principle
• Lecture 17 on 09-27 and the video Open mapping theorem and consequences
• Review for Exam 1 on 09-30 and the video
• Exam 1 was in class on 10-02. Here is the exam and solutions
• Lecture 18 on 10-04 and the video The Inverse function theorem and Local mapping theorem
• Lecture 19 on 10-09 and the video Conformal mapping, zeroes of harmonic functions
• Lecture 20 on 10-11 and the video Automorphism group of the unit disc, why "Argument" principle
• Lecture 21 on 10-14 and the video Fun with the Baby residue theorem on toy regions
• Lecture 22 on 10-16 and the video Applications of the residue theorem
• Lecture 23 on 10-18 and the video More residue theorem examples
• Lecture 24 on 10-21 and the video Linear fractional transformations
• Lecture 25 on 10-23 and the video LFTs, Jukovsky map, conformal mapping
• Lecture 26 on 10-25 and the video Schwarz reflection principle
• Lecture 27 on 10-28 and the video Laurent expansions
• Lecture 28 on 10-30 and the video More about Laurent expansions, residue at an essential singularity
• Lecture 29 on 11-01 and the video Rouché's theorem and Hurwicz's theorems
• Lecture 30 on 11-04 and the video Homotopy, simply connected domains, THE Cauchy theorem
• Lecture 31 on 11-06 and the video Montel's theorem
• Lecture 32 on 11-08 and the video Proof of the Riemann Mapping Theorem
• Lecture 33 on 11-11 and the video The Riemann Map
• Lecture 34 on 11-13 and the video Harmonic functions, averaging property, Poisson kernel
• Lecture 35 on 11-15 and the video Dirichlet problem, Schwarz's theorem
• Lecture 36 on 11-18 and the video Applications of the Poisson integral formula, Riemann removable singularity theorem
• Lecture 37 on 11-20 and the video Weak averaging property and reflection principle for harmonic functions
• Lecture 38 on 11-22 and the video The General Cauchy theorem and integral formula
• Lecture 39 on 11-25 and the video Proof of the General Cauchy theorem and integral formula
• Exam 2 was due on November 18. Here is the exam and solutions (see also the video for Lecture 39)
• Lecture 40 on 12-02 and the video The General Residue theorem and Rouché theorem
• Lecture 41 on 12-04 and the video The Mittag-Leffler and Weierstrass theorems
• Optional lecture about Infinite products and the video
• Review on 12-06 and the video

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