Inverse laplace method for equation .

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SUMMARY

The discussion focuses on the inverse Laplace transform of the function 1/s(s-2). The method of partial fractions is utilized to decompose the function into simpler components, specifically A/s + B/(s-2). Participants emphasize the importance of determining the constants A and B by multiplying both sides of the equation by s(s-2) and substituting simple values for s to derive two equations. This technique is rooted in the principles established by mathematician Leonhard Euler.

PREREQUISITES
  • Understanding of Laplace transforms
  • Familiarity with partial fraction decomposition
  • Basic algebraic manipulation skills
  • Knowledge of the properties of linear equations
NEXT STEPS
  • Study the application of the inverse Laplace transform in engineering contexts
  • Learn advanced techniques for solving partial fractions
  • Explore the historical contributions of Leonhard Euler to mathematical methods
  • Investigate the use of Laplace transforms in differential equations
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Students and professionals in mathematics, engineering, and physics who are looking to deepen their understanding of Laplace transforms and their applications in solving differential equations.

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inverse laplace method for equation ...

Just doing some revision but I am a little stuck on how to find the inverse laplace of 1/s(s-2)
 
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You can find it using partial fractions.
 
1/s(s-2)= A/s+ B/(s-2) for appropriate A and B- that's the "partial fractions" the eminent LeonhardEuler mentioned. One good way to solve for A and B is to multiply both sides by s(s-2) and then plug in simple values for s to get two equations for A and B.
 

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