Mathematics for Applied Sciences (Osnabrück 2011-2012)/Part I/Exercise sheet 26



Warm-up-exercises

Determine the partial fraction decomposition of

 



Determine the coefficients in the partial fraction decomposition of the Example by replacing   with some numbers.



Determine the complex and the real partial fraction decomposition of

 



Determine the complex partial fraction decomposition of

 



Determine the complex and the real partial fraction decomposition of

 



Determine the complex and the real partial fraction decomposition of

 



Determine the complex and the real partial fraction decomposition of

 



Determine an antiderivative (primitive function) of the function

 



Determine an antiderivative (primitive function) of the function

 



Determine an antiderivative (primitive function) of the function

 



Determine an antiderivative of the function

 

through partial fraction decomposition.



We consider the function

 

a) Determine the real partial fraction decomposition of  .

b) Determine an antiderivative of   for  .



Find a representation of the rational number   as a sum of rational numbers, such that every denominator is a power of a prime number.





Hand-in-exercises

Write the rational function

 

in the new variables  . Compute the antiderivative through the real partial fraction decomposition and through the substitutio .



Determine the complex and the real partial fraction decomposition of

 



Determine the complex and the real partial fraction decomposition of

 



Determine an antiderivative (primitive function) of the function

 



Determine an antiderivative (primitive function) of the function

 



Determine an antiderivative (primitive function) of the function