MATH 411 - Honors Complex Variables (Fall 2016)
Time and Location
Time: MWF 3:00 - 3:50 pm Room:
CAB
377
Instructor
Dr. Arno Berger (CAB 683,
berger@ualberta.ca)
Office hours
W 4:15 - 6:00 pm, R 3:00 - 6:00 pm or by appointment.
General information
Please see this PDF
document for all relevant details concerning MATH
411. (An abbreviated version of this document will be
distributed in class.)
Course notes
Be prepared to take careful notes in class, as
no set textbook will be used.
The course will loosely follow the fine notes by
Drs. Runde and Bowman (PDF, 4.7MB) which you are very welcome to
use. Be aware, however, that notation and terminology
may differ from those used in class.
Material covered in class (Course Diary)
I plan to keep an up-to-date list of the topics, examples etc. covered in class.
Lecture #
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Date
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Material covered / special events
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Remarks/ additional material
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WELCOME TO MATH 411 !!
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1
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Fri 2 Sep
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The complex numbers: Algebraic foundations.
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Mon 5 Sep
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No class - Labour Day.
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2
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Wed 7 Sep
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Geometric properties.
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3
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Fri 9 Sep
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Sequences and series of complex numbers.
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4
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Mon 12 Sep
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A brief review of topological concepts. The extended
complex plane.
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5
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Wed 14 Sep
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Limits and continuity.
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6
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Fri 16 Sep
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Linear functions. Complex differentiability.
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Handout - Lemma II.6
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7
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Mon 19 Sep
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The Cauchy-Riemann equations.
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8
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Wed 21 Sep
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Power series: Examples.
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9
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Fri 23 Sep
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More on power series. Path integrals.
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10
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Mon 26 Sep
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The Cauchy Integral Theorem.
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11
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Wed 28 Sep
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Goursat's Lemma. More general paths.
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Handout - arbitrary paths
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12
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Fri 30 Sep
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The Cauchy Integral formula.
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Thursday office hours extended to 3:00 -
6:00 pm.
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13
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Mon 3 Oct
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Sequences of analytic functions. Weierstrass' Theorem.
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14
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Wed 5 Oct
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Morera's Theorem.
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15
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Fri 7 Oct
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Liouville's Theorem. Fundamental Theorem of
Algebra. Identity Theorem.
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Mon 10 Oct
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No class.
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Happy Thanksgiving! |
16
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Wed 12 Oct
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The Open Mapping Theorem and Maximum Modulus Principle.
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17
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Fri 14 Oct
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Zeros. Isolated singularities.
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18
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Mon 17 Oct
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The Casorati-Weierstrass Theorem.
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19
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Wed 19 Oct
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Laurent series.
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Fri 21 Oct
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MIDTERM TEST 1.
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Good luck!!
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20
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Mon 24 Oct
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More on Laurent series.
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21
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Wed 26 Oct
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Examples.
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22
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Fri 28 Oct
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The Index (or Winding Number).
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23
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Mon 31 Oct
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The General Cauchy Integral Theorem.
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24
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Wed 2 Nov
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Simply connected regions. Homotopy.
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25
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Fri 4 Nov
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Residues.
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Enjoy Reading Week. |
26
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Mon 14 Nov
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The Residue Theorem.
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27
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Wed 16 Nov
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Applications of the Residue Theorem.
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Handout - Sec. IV.2.
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28
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Fri 18 Nov
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More applications of the Residue Theorem.
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29
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Mon 21 Nov
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A few theoretical consequences of the Residue Theorem.
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30
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Wed 23 Nov
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Conformal mappings.
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Fri 25 Nov
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MIDTERM TEST 2.
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Good luck!!
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31
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Mon 28 Nov
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Groups of conformal automorphisms. Examples.
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32
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Wed 30 Nov
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Principles of (pre-)compactness.
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33
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Fri 2 Dec
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The Arzelà-Ascoli Theorem. Montel's Theorem.
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Handout - Arzelà-Ascoli Theorem.
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34
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Mon 5 Dec
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The Riemann Mapping Theorem.
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35
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Wed 7 Dec
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Proof of the Riemann Mapping Theorem. Concluding
remarks. |
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Good bye and good luck !!
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Tue 20 Dec
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Final exam !
Please see box on the left for details.
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Good luck !! |
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