Information
Instructor | Jean-Baptiste (JB) Campesato |
campesat [@t) math.toronto.edu | |
Start the subject with "MAT334:" | |
Schedule | Monday, 10am to 11am |
Wednesday, 10am to 11am | |
Friday, 10am to 11am | |
Online via Zoom (Credentials sent through Quercus) | |
Office Hours (via Zoom) | Monday, 11am to 12pm |
Friday, 11am to 12pm | |
Course Information | On Quercus |
Practice problems | On Quercus |
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Hide all lectures |
Friday, September 11 - Show | |
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Files |
Slides My notes (pp. 1-2) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
The complex plane ℂ
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Textbook section | Section 1.1 |
Monday, September 14 - Show | |
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Files |
Slides My notes (pp. 3-6) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
The complex plane ℂ (continuation)
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Textbook Section | Section 1.1 |
Wednesday, September 16 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Geometry in the complex plane
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Textbook Section | Section 1.2 |
Friday, September 18 - Show | |
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Slides My notes More on the Riemann sphere: slides - handout (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Topology of ℂ
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Textbook Section | 1.3 |
Monday, September 21 - Show | |
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Files |
Slides My notes More on the Riemann sphere: slides - handout A question asked several times in office hour (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Functions, sequences, series
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Textbook Section | 1.4 |
Wednesday, September 23 - Show | |
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Files |
Slides - Handout My notes (pp. 1-4) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Functions, sequences, series (continuation)
Usual functions
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Textbook Section | 1.5 |
Friday, September 25 - Show | |
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Files |
Slides - Handout My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Usual functions (continuation)
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Textbook Section | 1.5 |
Monday, September 28 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Usual functions (continuation)Using slides from last Friday.
Line integrals and Green's theorem
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Textbook Section | 1.6 |
Wednesday, September 30 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Line integrals and Green's theorem (continuation)
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Textbook Section | 1.6 |
Friday, October 2 - Show | |
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Files |
Slides (slides 1-6) My notes (pp. 1-3) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Holomorphic/Analytic functions
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Textbook Section | 2.1 |
Monday, October 5 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Holomorphic/Analytic functions (continuation)
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Textbook Section | 2.1 |
Wednesday, October 7 - Show | |
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Files |
Slides (pp. 1-11) My notes (pp. 1-2) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Holomorphic/Analytic functions (continuation)Using slides from last lecture.
Power series
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Textbook Section | 2.2 |
Friday, October 9 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Power series (continuation)
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Textbook Section | 2.2 |
Wednesday, October 14 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Cauchy's integral formula
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Textbook Section | 2.3 |
Friday, October 16 - Show | |
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Files |
Slides - Handout (slides 1-5) My notes (§1) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Cauchy's integral formula (continuation)Using slides from last Wednesday.
Consequences of Cauchy's integral formulaHolomorphic functions are analytic
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Textbook Section | 2.4 |
Monday, October 19 - Show | |
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Files |
Slides - Handout (slides 6-10) My notes (pp. 2-4) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Consequences of Cauchy's integral formula (continuation)Continuation of analytic functionsOrder of a zero |
Textbook Section | 2.4 |
Wednesday, October 21 - Show | |
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Files |
Slides - Handout (slides 11-18) My notes (pp. 4-7) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Consequences of Cauchy's integral formula (continuation)Morera's theoremThe characterizations of holomorphicity/analyticity we encountered this term!Liouville's theoremApplication: the Fundamental Theorem of Algebra.Analytic logarithmElementary proof of the multiplication theorem for power series |
Textbook Section | 2.4 |
Friday, October 23 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Isolated singularities
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Textbook Section | 2.5 |
Monday, October 26 - Show | |
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Files |
Isolated singularities: Slides My notes Laurent series: Slides - Handout My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Isolated singularities
Laurent series and residues
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Textbook Section | 2.5 |
Wednesday, October 28 - Show | |
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Files |
Slides - Handout My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Laurent series and residues
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Textbook Section | 2.5 |
Friday, October 30 - Show | |
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Files |
Slides - Handout My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Cauchy's residue theorem
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Textbook Section | 2.6 |
Monday, November 2 - Show | |
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Files |
Slides - Handout My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Cauchy's residue theorem (continuation)
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Textbook Section | 2.6 |
Wednesday, November 4 - Show | |
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Files |
Slides (slides 1-4) My notes (pp. 1-2) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Zeroes of analytic functions
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Textbook Section | 3.1 |
Friday, November 6 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Zeroes of analytic functions (continuation)
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Textbook Section | 3.1 |
Monday, November 16 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Zeroes of analytic functions (continuation)
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Textbook Section | 3.1 |
Wednesday, November 18 - Show | |
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Files |
Slides (slides 1-5) My notes (pp. 1-2) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
The Maximum Modulus Principle and the Mean Value Property
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Textbook Section | 3.2 |
Friday, November 20 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
The Maximum Modulus Principle and the Mean Value Property (continuation)
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Textbook Section | 3.2 |
Monday, November 23 - Show | |
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Files |
Slides (1-5) My notes (pp. 1-2) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Linear fractional transformations
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Textbook Section | 3.3 |
Wednesday, November 25 - Show | |
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Files |
Slides (6-9) My notes (pp. 2-3) (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Linear fractional transformations (continuation)
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Textbook Section | 3.3 |
Friday, November 27 - Show | |
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Files |
Linear fractional transformations: Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Linear fractional transformations (continuation)
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Textbook Sections | 3.3 |
Monday, November 30 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Conformal mappings
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Textbook Section | 3.4 |
Wednesday, December 2 - Show | |
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Files |
Conformal mappings: Slides My notes The Riemann mapping theorem: Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
Conformal mappings (continuation)
The Riemann mapping theorem
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Textbook Section | 3.4, 3.5 |
Friday, December 4 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
The Riemann mapping theorem (continuation) |
Textbook Section | 3.5 |
Monday, December 7 - Show | |
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Files |
Slides My notes (there are probably some typos and/or mistakes: just send me an e-mail if you think that something is wrong) |
Content |
The Schwarz-Christoffel formula |
Textbook Section | 3.5 |
Wednesday, December 9 and Thursday, December 10 (Thanksgiving Monday make up) - Show | |
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Content |
Reviews
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