MATH3401: Complex Analysis

Lectures

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Lecture Material Semester 1, 2021



  • The original Möbius transformation video shown in class on 05/03/21, made by Doug Arnold and Jonathon Rogness of the University of Minnesota, can be found here.

  • Carlos, our 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 resource from Carlos include one on conformal mapping 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, 8th March:
    Maryam Mirzakhani;
    Cathleen Morawetz.



  • Screenies of lectures



    Revision session, 09 June.

    Revision session, 04 June.



    Lecture 37, 28 May, html.

    Lecture 37, 28 May, pdf.

    Lecture 36, 28 May, html.

    Lecture 36, 28 May, pdf.

    Lecture 35, 26 May, html.

    Lecture 35, 26 May, pdf.

    Lecture 34, 24 May, html.

    Lecture 34, 24 May, pdf.




    Lecture 33, 21 May, html.

    Lecture 33, 21 May, pdf.

    Lecture 32, 19 May, html.

    Lecture 32, 19 May, pdf.

    Lecture 31, 17 May, html.

    Lecture 31, 17 May, pdf.




    Lecture 30, 14 May, html.

    Lecture 30, 14 May, pdf.

    Lecture 29, 12 May, html.

    Lecture 29, 12 May, pdf.

    Lecture 28, 10 May, html.

    Lecture 28, 10 May, pdf.




    Lecture 27, 7 May, html.

    Lecture 27, 7 May, pdf.

    Lecture 26, 5 May, html.

    Lecture 26, 5 May, pdf.

    Link to Université de Liège soap bubble video.

    Link to Popflock's Queen Dido information.

    Lecture 25, 4 May, html.

    Lecture 25, 4 May, pdf.




    Lecture 24, 30 Apr., html.

    Lecture 24, 30 Apr., pdf.

    Lecture 23, 28 Apr., html.

    Lecture 23, 28 Apr., pdf.




    Lecture 22, 23 Apr., html.

    Lecture 22, 23 Apr., pdf.

    Lecture 21, 21 Apr., html.

    Lecture 21, 21 Apr., pdf.

    Lecture 20, 19 Apr., html.

    Lecture 20, 19 Apr., pdf.




    Lecture 19, 16 Apr., html.

    Lecture 19, 16 Apr., pdf.

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

    Lecture 18, 12 Apr., html.

    Lecture 18, 12 Apr., pdf.




    Mid-semester review, 31 Mar., pdf.

    Lecture 17, 31 Mar., html.

    Lecture 17, 31 Mar., pdf.

    Lecture 16, 29 Mar., html.

    Lecture 16, 29 Mar., pdf.




    Lecture 15, 26 Mar., html.

    Lecture 15, 26 Mar., pdf.

    Lecture 14, 24 Mar., html.

    Lecture 14, 24 Mar., pdf.

    Lecture 13, 22 Mar., html.

    Lecture 13, 22 Mar., pdf.




    Lecture 12, 19 Mar., html.

    Lecture 12, 19 Mar., pdf.

    Lecture 11, 17 Mar., html.

    Lecture 11, 17 Mar., pdf.

    Lecture 10, 15 Mar., html.

    Lecture 10, 15 Mar., pdf.




    Lecture 9, 12 Mar., html.

    Lecture 9, 12 Mar., pdf.

    Lecture 8, 10 Mar., html.

    Lecture 8, 10 Mar., pdf.

    Lecture 7, 8 Mar., html.

    Lecture 7, 8 Mar., pdf.





    Lecture 6, 5 Mar., html.

    Lecture 6, 5 Mar., pdf.

    Lecture 5, 3 Mar., html.

    Lecture 5, 3 Mar., pdf.

    Geogebra Applet for displaying nth roots, from Carlos, your supertutor.

    Lecture 4, 1 Mar., html.

    Lecture 4, 1 Mar., pdf.




    Lecture 3, 26 Feb., html.

    Lecture 3, 26 Feb., pdf.

    Lecture 2, 24 Feb, html.

    Lecture 2, 24 Feb., pdf.

    Handout on fields, sequences for lecture 2.

    Link to 3Blue1Brown's Riemann Zeta video.

    Lecture 1, 22 Feb, html.

    Lecture 1, 22 Feb., pdf.




    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 MATH2000 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 Web Page.