Avsnittsöversikt
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Material:
- Cauchy's theorem
- Cauchy's integral formula
- Cauchy estimates for derivatives
- Mean value property (for holomorphic functions)
- Liouville's theorem
Suggested reading and exercises:
Read sections 4.5 - 4.6 in the course book and work on the following exercises:
- 4.5: 3(a, c, e), 4, 6, 15.
- 4.6: 3, 4, 11.
(optional) Just for fun, if you want to see what can go wrong with Green's theorem, see Fesq's article giving a Counterexample to Green's formula.
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Cauchy's integral formula explained in a video by Martin Tamm from a previous version of the course.
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A proof of the Cauchy-Goursat theorem can be found, for instance in the fourth chapter of the book:
Since it is not easy to access the book from our library, I include my notes here for those interested.Churchill, Ruel V.; Brown, James W.Complex variables and applications. McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg