Bernd Schröder

Introduction to Complex Analysis


Curriculum Vitae
Class Materials
Research Interests



The videos below are part of a remotely delivered course on introductory complex analysis, following Churchill and Brown's book. For the "license", click here.

For mathematics presentations in general, the pause button is your best friend. But I must emphasize this statement for classes that involve proofs, such as this one. Because material can be presented rapidly with slides, there is no slowing down as I write stuff by hand on the board. That means you really need to pause the videos frequently to make sure that you can digest the points that are being made. The best approach is to first read the book and then follow the presentations. (That actually goes for any mathematics class, including those presented face to face.) 

For best performance, the videos should be downloaded and then run locally.

  1. Introduction
    Video.   (19:57min, 21MB)               Slides.
  2. Complex Numbers
    Video.   (42:47min, 38MB)              Slides.
    Supplement: Proofs by Induction
    Video.   (14:04min, 13MB)              Slides.
  3. Exponential Form
    Video.   (27:01min, 21MB)              Slides.
  4. Complex Functions
    Video.   (18:48min, 18MB)              Slides.
  5. Limits and Continuity
    Video1.  (43:02min, 44MB)   Video2.  (45:44min, 53MB)          Slides.
  6. Differentiability
    Video.    (28:16min, 27MB)             Slides.
  7. Cauchy-Riemann Equations
    Video1.  (50:46min, 46MB)  Video2.  (19:24min, 19MB)               Slides.
  8. The Exponential and Logarithmic Functions
    Video.    (33:03min, 29MB)             Slides.
  9. Trigonometric and Hyperbolic Functions
    Video.    (28:21min, 24MB)             Slides.
  10. Definite Integrals
    Video.    (  8:47min,  9MB)             Slides.
  11. Contour Integrals
    Video.    (17:12min, 18MB)             Slides.
  12. Upper Bounds for Integrals
    Video.    (11:06min, 12MB)             Slides.
  13. Cauchy-Goursat Theorem
    Video1.   (39:03min, 41MB)    Video2.   (12:25min, 14MB)       Slides.
  14. Cauchy Integral Formula
    Video.    (35:17min, 36MB)             Slides.
  15. Series Expansion
    Video.    (35:13min, 31MB)             Slides.
  16. Laurent Expansion
    Video.    (26:34min, 24MB)             Slides.
  17. Power Series
    Video.    (56:16min, 54MB)             Slides.
  18. Residue Theorem
    Video.    (36:05min, 33MB)             Slides.
  19. Zeros and Poles
    Video.    (34:55min, 36MB)             Slides.
  20. Calculus of Residues
    Video1.   (48:53min, 51MB)    Video2.   (36:10min, 33MB)       Slides.
  21. More on Residues
    Video1.   (29:19min, 29MB)    Video2.   (40:27min, 39MB)   Slides.
  22. Moebius Transforms
    Video.     (52:50min, 48MB)            Slides.
  23. More Transforms
    Video.     (30:00min, 34MB)            Slides.
  24. Conformal Maps
    Video.     (18:55min, 19MB)            Slides.
  25. Harmonic Functions
    Video.     (35:47min, 37MB)            Slides.








Obviously, if I post something, I want people to use it. If you are a teacher, feel free to use the videos and the slides in classes. The goal is to get people to do better in mathematics.

One caveat: If you want to create an on-line course with the videos, note that I have already done so. Please consider sending your students to my course  :)

Slides for a presentation on on-line delivery (focused on Differential Equations)