Exercise on Complex Analysis
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Task (Differentiability, 5 Points)
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Examine the following functions on for partial and complex differentiability! Specify the points where differentiability exists.
- ,
- ,
- ,
- ,
Task (Wirtinger, 5 Points)
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Determine the partial derivatives with respect to and for the functions from the first task at the points where they exist.
Task (Working with Polynomials, 5 Points)
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Solution to Exercise 3
We consider a polynomial , given by
with and . Show that can also be expressed as a polynomial in and by specifying the coefficients in
.
Task (Chain Rule, 5 Points)
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Solution to Exercise 4
Let be continuously differentiable. Prove that
and
hold.
Translation and Version Control
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This page was translated based on the following Wikiversity source page and uses the concept of Translation and Version Control for a transparent language fork in a Wikiversity:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Übungen/2._Zettel