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
of Differential
Equations, Lapl
-ace Transform
and Fourier
Transform in
CSE
The Laplace Transform is a widely used
integral transform in mathematics with many
applications in science and engineering. The
Laplace Transform can be interpreted as a
transformation from time domain where
inputs and outputs are functions of time to
the frequency domain where inputs and
outputs are functions of complex angular
frequency. Laplace Transform methods have
a key role to play in the modern approach to
the analysis and design of Computer Science
and Engineering.

5. Applications
of Differential
Equations, Lapl
-ace Transform
and Fourier
Transform in
CSE
Fourier transform is used in a wide range of
applications such as image analysis, image
filtering , image reconstruction and image
compression. The Fourier Transform is an
important image processing tool which is
used to decompose an image into its sine
and cosine components.

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