Program Explanation Given information: The function is F ( s ) = s 3 ( s − 4 ) 4 . Explanation: The given function is F ( s ) = s 3 ( s − 4 ) 4 . Apply inverse Laplace transform to the function F ( s ) = s 3 ( s − 4 ) 4 . L − 1 { F ( s ) } = L − 1 { s 3 ( s − 4 ) 4 } = L − 1 { s 3 ( s − 2 ) ( s + 2 ) ( s 2 + 4 ) } Apply partial fraction method to solve the above expression, s 3 ( s − 4 ) 4 = A ( s − 4 ) 4 + B ( s − 4 ) 3 + C ( s − 4 ) 2 + D ( s − 4 ) ........... (1) Multiply the equation by denominator as, s 3 ( s − 4 ) 4 ( s − 4 ) 4 = A ( s − 4 ) 4 ( s − 4 ) 4 + B ( s − 4 ) 4 ( s − 4 ) 3 + C ( s − 4 ) 4 ( s − 4 ) 2 + D ( s − 4 ) 4 ( s − 4 ) s 3 = A + B ( s − 4 ) + C ( s − 4 ) 2 + D ( s − 4 ) 3 Substitute 4 for s in above equation ( 4 ) 3 = A + B ( 4 − 4 ) + C ( 4 − 4 ) 2 + D ( 4 − 4 ) 3 64 = A Differentiate the above equation. 3 s 2 = B + 2 C ( s − 4 ) + 3 D ( s − 4 ) ........... (2) Differentiate the above equation. 6 s = 2 C + 6 D ( s − 4 )

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

Chapter 7.3, Problem 18P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=s3( s−4)4 by using partial fraction.

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Chapter 7.3, Problem 17P

Chapter 7.3, Problem 19P

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Chapter 7 Solutions

EBK DIFFERENTIAL EQUATIONS

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F ( s ) = s 3 ( s − 4 ) 4 by using partial fraction.

Solution Summary: The author explains how to obtain the inverse Laplace transformation of the functions by using partial tion.

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of the functions F(s)=s3( s−4)4 by using partial fraction.

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Chapter 7 Solutions