Real life application of Differential Equations, Laplace Transform in CSE

Real life application of Differential Equations, Laplace Transform in CSE

1. Real Life Applications of
Differential Equations,
Laplace Transform and
Fourier Transform in CSE
Md Al Imran
211-15-3986
Daffodil International University

2. What?
•Laplace Transform
In mathematics, a differential equation
is an equation that relates one or more
unknown functions and their
derivatives.
•Differential Equation
The Laplace transform of a function
f(t), defined for all real numbers t ≥ 0, is
the function F(s), which is a unilateral
transform defined by

3. What?
A Fourier transform (FT) is a
mathematical transform that
decomposes functions depending on
space or time into functions
depending on spatial frequency or
temporal frequency.
•Fourier transform

4. Applications
ofDifferential
Equations,Lapl
-ace Transform
andFourier
Transform in
CSE
TheLaplaceTransformisawidelyused
integraltransforminmathematicswithmany
applicationsinscienceandengineering.The
LaplaceTransformcanbeinterpretedasa
transformationfromtimedomainwhere
inputsandoutputsarefunctionsoftimeto
thefrequencydomainwhereinputsand
outputsarefunctionsofcomplexangular
frequency.LaplaceTransformmethodshave
akeyroletoplayinthemodernapproachto
theanalysisanddesignofComputerScience
andEngineering.

5. Applications
ofDifferential
Equations,Lapl
-ace Transform
andFourier
Transform in
CSE
Fouriertransformisusedinawiderangeof
applicationssuchasimageanalysis,image
filtering,imagereconstructionandimage
compression.TheFourierTransformisan
importantimageprocessingtoolwhichis
usedtodecomposeanimageintoitssine
andcosinecomponents.

6. Reference
•https://en.wikipedia.org/wiki/Differential_equation
•https://en.wikipedia.org/wiki/Laplace_transform
•https://en.wikipedia.org/wiki/Fourier_transform
•https://www.irjet.net/archives/V5/i5/IRJET-V5I5593.pdf
•http://www.ijirset.com/upload/2018/november/46_Applications%20
of%20Fourier%20transform%20in%20Engineering%20Field%20_1_.pdf