advanced engineering math (problems w/ solutions)

5/24/2018 Advanced Engineering Math (Problems w/ Solutions)

1/16

LAPLACE TRANSFORM BY DI RECT INTEGRATION:

Problem 01

Find the Laplace transform of when .

Solution 01

Thus,

answer

Problem 02

Find the Laplace transform of .

Solution 02

Thus,

answer

Problem 03


Solution 03


2/16

For

Using integration by parts: . Let

Using integration by parts again. Let

Thus,

Therefore,

answer

LI NEARI TY PROPERTY | LAPLACE TRANSFORM:

Problem 04


Solution 04

answer

Problem 05By using the linearity property, show that


3/16

Solution 05

But

Thus,

From thetable of Laplace transform,

and

Hence,

okay

FI RST SHIF TING PROPERTY OF LAPLACE TRANSFORM:

Problem 06Find the Laplace transform of .

Solution 06

Thus,

answer

Problem 07


Solution 07
http://www.mathalino.com/reviewer/advance-engineering-mathematics/table-laplace-transforms-elementary-functionshttp://www.mathalino.com/reviewer/advance-engineering-mathematics/table-laplace-transforms-elementary-functions


4/16

Thus,

answer

Problem 08


Solution 08

Thus,

answer

Problem 09


Solution 09

Thus,

answer

SECOND SHI FTI NG PROPERTY OF LAPLACE TRANSFORM :

Problem 10

Find the Laplace transform of

Solution 10

and

Thus,

answer


5/16

Problem 11


Solution 11

and

Thus,

answer

MULTIPLI CATION BY POWER OF t:

Problem 12


Solution 12

answer

Problem 13


Solution 13

answer

Problem 14



6/16

Solution 14

answer

DIVISION BY t| LAPLACE TRANSFORM:

Problem 15


Solution 15

Let

Hence,


7/16

Thus,

answer

Problem 16


Solution 16

Since

and

Then,


8/16

answer

Problem 17


Solution 17

Since

and

Then,


9/16

answer

Problem 18


Solution 18

Since

Then,


10/16

answer

LAPLACE TRANSFORM OF DERI VATIVES:

Problem 19

Find the Laplace transform of using the transform ofderivatives.

Solution 19

..........

..........

..........

answer

Problem 20


Solution 20

..........

answer

Problem 21


Solution 21

..........

answer


11/16

Problem 22

Find the Laplace transform of using the transform of

derivatives.

Solution 22

..........

..........

answer

LAPLACE TRANSFORM OF INTEGRALS:

Problem 23

Find the Laplace transform of if .

Solution 23

Since,

Then,

answer

Problem 24


Solution 24

Hence,


12/16

answer

Problem 25


Solution 25

Fromdivision by t:

answer

EVALUATION OF INTEGRALS:

Problem 26

Evaluate

Solution 26

Since

and
http://www.mathalino.com/reviewer/advance-engineering-mathematics/division-t-laplace-transformhttp://www.mathalino.com/reviewer/advance-engineering-mathematics/division-t-laplace-transform


13/16

Then,

Therefore,

answer

Problem 27

Find the value of .

Solution 27

Therefore,

Therefore,

answer

Problem 28

Find the value of

Solution 28

By "first shifting property" of Laplace transformation:

From "multiplication by power of t":


14/16

Therefore,

answer

Problem 29

Evaluate .

Solution 29

Byfirst shifting property:

Thus,

answer

I NVERSE LAPLACE TRANSFORM:

Problem 30

Find the inverse transform of .

Solution 30

answer

Problem 31


Solution 31
http://www.mathalino.com/reviewer/advance-engineering-mathematics/first-shifting-property-laplace-transformhttp://www.mathalino.com/reviewer/advance-engineering-mathematics/first-shifting-property-laplace-transform


15/16

answer

Problem 32


Solution 32

answer

Problem 33

Perform the indicated operation:

Solution 33

For

set

set

Thus,

answer

Problem 34

Find the inverse transform of

Solution 34

Factor the denominator by factor theorem

is a factor

is a factor

is a factor


16/16

Thus,

For

Set

Set

Set

Therefore,

answer

advanced engineering math (problems w/ solutions)

Documents

t laplace transform

thetable of laplace

transform ofderivatives

linearity property

power of t

forusing integration

letusing integration

di rect integration