Intro Complex Analysis, Lec 18, Branches of Arg, Harmonic Functions over Washers, Wedges and Walls

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Lecture 18. (0:00) Taking (single-valued) branches of multivalued functions. (0:35) Two-parameter plot of the "full graph" of the multivalued argument function arg(z) with ParametricPlot3D. (4:10) What does it mean to take a branch? There's a lot of flexibility. The branch cuts don't even have to be straight lines.(17:08) Examples of harmonic functions (satisfying Laplace's equation) over various domains. (24:11) These examples can help us solve Laplace's equation on washers, wedges, and walls, which can ultimately help us solve Laplace's equation on more general regions. (36:40) Project ideas and readings. (40:53) Introduction to power functions and inverse trigonometric functions.

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  1. Bill Kinney
  2. multivalued
  3. branch cut
  4. logarithm
  5. argument
  6. Laplace's equation
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