Unit – 4
Laplace transformation
PERIODIC FUNCTIONS:
Let f (t) be a periodic function with Period T, then
Example1: Find the Laplace transform of the waveform
Solution: 
Example2: Find the Laplace transform of the function (Half wave rectifier)
Solution:
Example3: Find the Laplace transform of the periodic function (saw tooth wave)
Solution: 
Now we obtain f (t) when F (s) is given, then we say that inverse Laplace transform of F (s) is f (t).
Where,
is called the inverse Laplace transform operator.
From the application point of view, the inverse Laplace transform is very useful.
IMPORTANT FORMULAE:
4. 
5. 
6. 
7. 
8. 
9. 
10.
11.
12.
13.
14.
15.
16.
17.
MULTIPLICATION by s: 
DIVISION by s:
Example1: Find the inverse Laplace Transform of
Solution:
Example2: Find the inverse Laplace Transform of
Solution:
Example3: Find the inverse Laplace Transform of function by MULTIPLICATION by s
Solution:
Example4: Find the inverse Laplace Transform of function by Division by s
Solution:
Example1: Evaluate 
Solution: 
Example2: Evaluate 
Solution: 
Example3: Evaluate 
Solution: 
Text Book:
1) Calculus: Gorakh Prasad
2) Advance Engineering Mathematics – E. Kreyszig, John Wiley & Sons Inc.
