Program Explanation Given information: The extension of transforms of derivatives theorem is written as, L { f ′ ( t ) } = s L { f ( t ) } − f ( 0 + ) − ∑ n = 1 ∞ e − s t n j f ( t n ) The function f ( t ) is defined as shown below. f ( t ) = { 1 t ∈ [ a , b ] 0 t ∉ [ a , b ] Calculation: The given function f ( t ) is a piecewise constant function, therefore the derivative of given functionis zero. f ′ ( t ) = 0 Apply the Laplace transform and extension of transforms of derivative theorem on the above equation as, L { f ′ ( t ) } = L { 0 } s L { f ( t ) } − f ( 0 + ) − e − a s j f ( a ) − e −

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.

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Chapter 7.2, Problem 33P

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Program Description: Purpose of the problem is to derive the equation L{f(t)}=e−as−e−bss , if f(t)=1 on the interval [a,b] and f(t)=0 otherwise.

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Chapter 7.2, Problem 32P

Chapter 7.2, Problem 34P

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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 equation L { f ( t ) } = e − a s − e − b s s , if f ( t ) = 1 on the interval [ a , b ] and f ( t ) = 0 otherwise.

Solution Summary: The author explains that the function f(t) is a piecewise constant function, therefore the derivative of given functionis zero.

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Program Description: Purpose of the problem is to derive the equation L{f(t)}=e−as−e−bss , if f(t)=1 on the interval [a,b] and f(t)=0 otherwise.

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Chapter 7 Solutions