Inverse Laplace Transform in Materials Engineering Department
Learn about the concept of inverse Laplace transform in the field of Materials Engineering Department. Understand the definition, properties, transform pairs, and the application of inverse Laplace transform through partial fraction expansion. Dive into numerical methods and data analysis in engineering.
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The Inverse of Laplace Transform University of Technology Materials Engineering Dept. Ceramics & Construction Materials By
Definition If the Laplace transform of the function f(t) is F(s) L{f(t)}= F(S) The original function f(t) is called the inverse transform and will be denoted by L-1{F(s)} f (t) = L 1 F(s)
1 F(s) = f (t) =e 2t L s +2 Laplace Transform s is complex variable t is a real variable L-1 f(t) is a real function F(s) is a complex valued function Inverse LaplaceTransform Time Domain Frequency Domain
Linearity Property L 1 F(s)+G(s) = L 1 F(s) + L 1 G(s) First Shifting Property
Inverse Laplace by Partial Fraction Expansion We willconsider threecases * distict poles repeatedpoles complexpoles * *
1. Chapra, Steven C., and Raymond P. Canale. Numerical methods for engineers. Vol. 2. New York: McGraw-Hill, 2012, p230. 2. Collins, George. "Fundamental numerical methods and data analysis. Fundamental Numerical Methods and Data Analysis, by George Collins, II. (1990). 3.Dr. Kadhum Muttar, University of Technology ,Materials Engineering Dept.
