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Application of Complex Inversion Integral Formula (Bromwich)

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Laplace Transform
Application of Complex Inversion Integral Formula (Bromwich's Integral Formula)

Problem:- Find the Laplace Transform of the function F(t) = (1 - e^(-at))/a
Prove by the method of contour integration that F(t) is itself the Laplace Transform of the function arrived at.

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Solution Summary

This solution is comprised of a detailed explanation for finding the Laplace Transform of the function: F(t) = (1 - e^(-at))/a by using complex inversion integral formula or, Bromwich's integral formula.
It contains step-by-step explanation to apply the complex inversion integral formula for finding the Laplace Transform of the function F(t) = (1 - e^(-at))/a. Solution also contains detailed step-by-step explanation for using the method of contour integration.

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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