Avsnittsöversikt
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Material:
- more on the Cauchy-Riemann equations
- harmonic functions
- logarithm(s), exponential function, powers, trigonometric functions
- point at infinity, Riemann sphere, a.k.a extended complex numbers
Suggested reading and exercises:
Chapters 1, 2, 3 in the course book (you can skip sections 3.4 and 3.6, which discuss applications we will not explore). Work on the following exercises from the book:
- 3.2: 5(a, c, e), 6, 11, 13(a), 17(a, c)
- 3.3: 1, 3, 4, 5(b), 8
- 3.5: 1(a,c,d), 3, 8.
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This video from 3Blue1Brown contains some visuals that might help you understand complex numbers and stereographic projection, especially from 4:15 to 17:30. The rest of the video is just for fun if you want to learn about quaternions.
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This is part of a series of videos created by Martin Tamm when the course was taught previously. It discusses the Riemann sphere and stereographic projection.
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This is a video about elementary functions (exponentials, logarithms, square roots, etc) by Martin Tamm from a previous version of the course.
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MM5022_Lecture_03 Fil