MATH3401/3901: Complex Analysis/ Advanced Complex Analysis

Lectures

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Lecture Material Semester 1, 2025


  • The original Möbius transformation video shown in class on 14/03/25, made by Doug Arnold and Jonathon Rogness of the University of Minnesota, can be found here.

    • Carlos Campuzano, our former supertutor, has written a number of nice programs for experimenting with Möbius transformations. One is available online here. The applet is written in GeoGebra, which is open source. You can download GeoGebra here: if you do so, you may like then to download Carlos's applet directly here.

  • Other resources from Carlos, including one on conformal mapping, are here;

  • one on domain colouring is here.

  • one on geometric series is here;

  • and one from Aaron Montag on Taylor series with domain colouring is here.

    • Some other relevant resources related to Carlos's project are available here.

    Videos from class, 14 March:
    Maryam Mirzakhani;
    Cathleen Morawetz.


    Screenies of lectures

    Lecture 31, 23 May

    Lecture 30, 22 May

    Link to Université de Liège soap bubble video.

    link to ThoughtCo's Queen Dido information.

    Lecture 29, 19 May

    Lecture 28, 16 May

    Lecture 27, 15 May

    Lecture 26, 12 May

    Lecture 26, 12 May, supplemental material on applications of conformal mappings.: not directly examinable, but still interesting.

    Lecture 26, 12 May, supplemental material on the Poisson Integral Formula.: not examinable, but still interesting.

    Lecture 25, 09 May

    Lecture 24, 08 May

    Lecture 23, 02 May

    Lecture 22, 01 May

    Lecture 21, 28 Apr.

    Lecture 20, 17 Apr.

    Link to 3Blue1Brown's Space-filling Curve video.

    Lecture 18, part 1, mid-sem review, 11 Apr.

    Lecture 18, part 2, 11 Apr.

    Lecture 17, 10 Apr.

    Lecture 16, 07 Apr.

    Lecture 15, 04 Apr., supplemental material on the Wirtinger Operator.: not examinable, but still interesting.

    Lecture 15, 04 Apr.

    Lecture 14, 03 Apr.

    Lecture 13, 31 Mar.

    Lecture 12, 28 Mar.

    Lecture 11, 27 Mar.

    Lecture 10, 24 Mar.

    Lecture 9, 21 Mar.

    Lecture 8, 20 Mar.

    Lecture 7, 17 Mar.

    Lecture 6, 14 Mar.

    Lecture 5, 13 Mar.

    Lecture 4, 03 Mar.

    Lecture 3, 28 Feb.

    Lecture 2, 27 Feb.

    Link to 3Blue1Brown's Riemann Zeta video.

    Handout on fields, sequences for lecture 2.

    Lecture 1, 24 Feb.



    Reference Material

    For reference, I've uploaded the MATH1051 workbook, both with solutions and without.

    Also, the MATH1052 Workbook is available here, and the completed chapter on partial derivatives is available here.

    The MATH2001/2901 Workbook is available here.

    Finally, notes from some of the material covered in MATH2400/MATH2401 are available here. Please be aware that these notes don't include proofs, a key part of those courses!


    MATH3401/3901 Web Page.