Inverse Laplace Transformation of arctan (s/2)

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SUMMARY

The discussion focuses on solving the Inverse Laplace Transformation of arctan(s/2). Participants highlight that the derivative of arctan(t) is 1/(t^2+1) and emphasize the relationship between differentiation in the time domain and multiplication by s in the Laplace domain. The classical method for computing the inverse Laplace transform involves the Bromwich integral, but the specific case of arctan(s/2) may lead to complex calculus and may not yield a solution expressible in simple standard functions.

PREREQUISITES
  • Understanding of Laplace transforms and their properties
  • Familiarity with differentiation and integration in calculus
  • Knowledge of special functions and their applications
  • Experience with the Bromwich integral method for inverse transforms
NEXT STEPS
  • Study the Bromwich integral method for inverse Laplace transforms
  • Explore advanced calculus techniques involving special functions
  • Research the properties of arctan and its derivatives
  • Consult extended Laplace transform tables for less common functions
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Students and professionals in mathematics, engineering, and physics who are working with Laplace transforms, particularly those dealing with complex functions and inverse transformations.

nileszoso
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The Title pretty much says it all. I'm trying to learn how to solve the Inverse Laplace Transformation of Arctan(s/2). An equation of this sort was not explicitly covered in class and I'm having difficulty figuring where to start to solve it. If anyone could give me a general idea that would point me in the right direction that would be greatly appreciated.

Thanks in advance
 
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The derivative of arctan(t)=1/(t^2+1). Differentiation in time-domain is the same as multiplication by s in Laplace-domain. See http://en.wikipedia.org/wiki/Laplace_transform for a table. You should be able to derive the correct answer from this.
 
Thank you! This helped, although I'm still not sure what exactly is meant by "Differentiation in time-domain is the same as multiplication by s in Laplace-domain. " But like I said this got my started on the way to solve the problem.
 
Hi nileszoso!

A classical method to compute the inverse Laplace transform is the use of the Bromwich integral. In the case of arctan(s/2) this leads to ardous calculus with special functions.
Moreover, the inverse Laplace Transform of arctan(s) doesn't appears in some extended tables. So, it is questionable whether there is really a solution which can be expressed with not too complicated combinations of standard functions.
Where this problem is coming from ?
 

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