Program Explanation Given information: Transforms of derivatives theorem states that L { f ′ ( t ) } = s L { f ( t ) } − f ( 0 ) if the function f ( t ) is piecewise continuous. Similarly for second derivative of the function L { f ″ ( t ) } = s 2 L { f ( t ) } − s f ( 0 ) − f ′ ( 0 ) . Calculation: Consider function f ( t ) as t cos k t and obtain the first and second derivative of the function as follows: f ( t ) = t cos k t f ′ ( t ) = cos k t − k t sin k t f ″ ( t ) = − k sin k t − k sin k t − k 2 t cos k t = − 2 k sin k t − k 2 f ( t ) Now, apply the derivative transform theorem as, L { f ″ ( t ) } = L { − 2 k sin k t − k 2 f ( t ) } s 2 L { f ( t ) } − s f ( 0 ) − f ′ ( 0 ) = − 2 k L { sin k t } − k

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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.

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Chapter 7.2, Problem 28P

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Program Description: Purpose of the problem is to derive the formula that L{tcoskt}=s2−k2( s 2 + k 2 )2 .

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Chapter 7.2, Problem 27P

Chapter 7.2, Problem 29P

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Chapter 7 Solutions

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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 the problem is to derive the formula that L { t cos k t } = s 2 − k 2 ( s 2 + k 2 ) 2 .

Solution Summary: The author explains the purpose of the problem, which is to derive the formula that Llefttmathrmcoskt

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Program Description: Purpose of the problem is to derive the formula that L{tcoskt}=s2−k2( s 2 + k 2 )2 .

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Chapter 7 Solutions