1. RAYAT SHIKSHAN SANSTHA’S S.M.JOSHI COLLEGE HADAPSAR, PUNE-411028.
PRESANTATION BY
Prof . DESAI S.S
Mathematics department
Subject –Laplace Transform

2. LAPLACE TRANSFORMS
INTRODUCTION

3. Definition
Transforms -- a mathematical conversion from one way of thinking to another to make a problem easier to solve
problem in original way of thinking
solution in original way of thinking
transform
solution
in transform
way of
thinking
inverse
transform
2. Transforms

4. problem in time domain solution in time domain Laplace transform
s domain
inverse
Laplace
transform
Other transforms
Fourier
z-transform
wavelets
2. Transforms

5. Laplace transformation
time domain
linear
differential
equation
time
domain
solution
Laplace transform
inverse Laplace
transform
Laplace
transformed
equation
Laplace
solution
algebra
Laplace domain or
complex frequency domain
4. Laplace transforms

6. Basic Tool For Continuous Time: Laplace Transform
Convert time-domain functions and operations into frequency-domain
f(t) ® F(s) (tR, sC)
Linear differential equations (LDE) ® algebraic expression in Complex plane
Graphical solution for key LDE characteristics
Discrete systems use the analogous z-transform
Jlh: First red bullet needs to be fixed?

7. The Complex Plane (review)
Imaginary axis (j)
Real axis
(complex) conjugate

8. Laplace Transforms of Common Functions
Name
f(t)
F(s)
Impulse 1
Step
Ramp
Jlh: function for impulse needs to be fixed
Exponential
Sine

9. Laplace Transform Properties

10. THANK YOU