Class notes EMA51001 (maths)

Course Code: EMA51002
Course Name: Analytical Mathematics
Module-IV LAPLACE AND INVERSE LAPLACE TRANSFORM
PART-A-2-Marks CO BTL
1 Define Laplace transform 4 1
2 Find 𝐿(sin 4𝑡)
3 Find 𝐿(𝑡 + 2)2 4 2

4 Find 𝐿(𝑒 𝑡 sin 2𝑡) 4 2
5 1 4 2
Find 𝐿−1 (𝑠−7)

6 1 4 2
Find 𝐿−1 ((𝑠+3)2 )

7 Write the Laplace transform of second derivative. 4 1
8 State Convolution theorem on Laplace Transform. 4 1
9 Find 𝐿(sin 3𝑡 cos 2𝑡) 4 2

10 Find the Laplace transform of cos 𝑎𝑡 2

PART-B-6-Marks CO BTL
4𝑡 4 3
1 Find 𝐿(𝑒 sin 2𝑡 sin 𝑡)

2 Find 𝐿(cos 2𝑡 + 𝑡) 4 3

3 Find 𝐿(𝑒 −2𝑡 𝑐𝑜𝑠 3𝑡) 4

4 Find 𝐿−1 ( 1 + 1
+
3
+
6𝑠
) 3
𝑠2 𝑠−4 𝑠2 −4 𝑠2 +9


5 𝑠+2 4 3
Find 𝐿−1 ((𝑠+4)2 )

6 1 4 3
Find 𝐿−1 (𝑠2 (𝑠+4))

7 1 3
Find 𝐿−1 ((𝑠+1)(𝑠+2))

8 Find final value theorem for 2 + 3 𝑐𝑜𝑠 𝑡 4 3

9 Verify final value theorem for 1 − 𝑒 −3𝑡 3

10 𝑠+2 4 3
Find the inverse Laplace transform of ((𝑠2 +4𝑠+5)2 )