Introduction

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In Wikiversity, you can create a quiz to test your understanding of the learning content. The options for creating a quiz to check your knowledge are explained on the Wikiversity help page "Quiz".

Example Quiz

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1 Calculate the integral   with   as the integration path?Enter the real part and imaginary part up to two decimal places (also e.g. 4.21 for the real and imaginary parts separately).

Answer:

 

 

2 Enter you the Residue   the Function   in the Poitt   an. (Error tolerance 5% for the Real- and Imaginary)

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3 Enter the Residue   of the function   at the point  . Enter the values with a decimal point (e.g., 4.21) for the real and imaginary parts separately (error tolerance 5% for real and imaginary parts).

Answer:

 

 

4 Enter the Residue   of the function   at the point  . Enter the values with a decimal point (e.g., 4.21) for the real and imaginary parts separately (error tolerance 5% for real and imaginary parts).

Answer:

 

 

5 Enter the residue   of the function   at the point  . Enter the values with a decimal point (e.g., 4.21) for the real and imaginary parts separately (error tolerance 5% for real and imaginary parts).

Answer:

 

 

6 Which of the following properties are holomorphic criteria for a function  ?

  can be locally developed into a power series for each  .
The partial derivatives for the real part and imaginary part of   exist.
The function is complex differentiable at a single point  .
The function is complex differentiable at every point  .
The function is infinitely complex differentiable at every point  .
The real and imaginary parts satisfy the Cauchy-Riemann equations and are at least once continuously real-differentiable.
The function can be developed into a complex power series.
The function is continuous, and the line integral of the function over any closed contractible path is zero.
The function values inside a disk can be determined from the function values on the boundary using the Cauchy integral formula.
  is real differentiable, and it holds that
 
where   is the Cauchy-Riemann operator defined by  .
The real part function   and the imaginary part function   with   are real integrable.


See Also

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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/Quiz

  • Date: 01/14/2024