Laplace Transforms: Example Important Solved Problems with formula, steps, derivation and answer based on Initial and Final Value Theorems
INITIAL AND FINAL VALUE
THEOREMS

Proof:
We know that,
L[f
'(t)] = sL[f(t)] ‒ f(0) = s F(s) ‒ f(0)


*Note:
The author wishes to thank Dr. B. Jothiram, formerly Asst. Prof. and H.O.D.
Maths (Retd.) Govt. College of Engineering, Salem who has suggested to him the
block diagram.

Example 2: Verify the initial and final value
theorem for the function f(t) = 1 + e‒1(sin
t + cos t)
Solution:

Hence,
Initial value theorem verified.
Final
value theorem states that

L.H.S
= R.H.S
Hence,
Final value theorem verified.
Example 3: Verify the initial and final value
theorems for f(t) = 3 e‒2t
Solution:
f(t) = 3 e‒2t

L.H.S = R.H.S
Hence,
Initial value theorem verified.
Final
value theorem

L.H.S. = R.H.S.
Hence,
Final value theorem verified.
Example 4 Using the initial value theorem,
find

Solution:
Initial
value theorem states that

Transforms and its Applications: UNIT 1: Laplace Transforms : Tag: Engineering mathematics, Maths : Laplace Transforms - Initial and Final Value Theorems
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