To determine To write: The Fourier series of the given function comparing it with the appropriate function. Explanation Definition used: Fourier series with period 2 L : The Fourier series of the function with period 2 L is given as: f ( x ) = a 0 + a 1 cos ( π x L ) + a 2 cos ( 2 π x L ) + ⋅ ⋅ ⋅ + a n cos ( n π x L ) + ⋅ ⋅ ⋅ + b 1 sin ( π x L ) + b 2 sin ( 2 π x L ) + ⋅ ⋅ ⋅ + b n sin ( n π x L ) + ⋅ ⋅ ⋅ The n th coefficients are given as a 0 = 1 2 L ∫ − L L f ( x ) d x a n = 1 L ∫ − L L f ( x ) cos ( n π x L ) d x b n = 1 L ∫ − L L f ( x ) sin ( n π x L ) d x Result used: For the function f ( x ) = { 0 , − π ≤ x < − π 2 , π 2 ≤ x < π 1 , − π 2 ≤ x < π 2 , the Fourier series is 1 2 − 2 π [ cos x − 1 3 cos 3 x + 1 5 cos 5 x − ⋅ ⋅ ⋅ ] . For the function f ( x ) = { − 1 , − π ≤ x < 0 1 , 0 ≤ x < π , the Fourier series is 4 π [ sin x + 1 3 sin 3 x + 1 5 sin 5 x − ⋅ ⋅ ⋅ ] . Calculation: It is given that the function is f ( x ) = { − 2 , − 4 ≤ x < 0 0 , 0 ≤ x < 4 . Write the function f ( x ) as f ( x ) = 1 + f 1 ( x ) where f 1 ( x ) = { − 1 , − π ≤ x < 0 1 , 0 ≤ x < π . The Fourier series for f 1 ( x ) is 4 π [ sin x + 1 3 sin 3 x + 1 5 sin 5 x − ⋅ ⋅ ⋅ ] that is no cosine terms and no constant term

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 30.7, Problem 3E

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To write: The Fourier series of the given function comparing it with the appropriate function.

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Chapter 30.7, Problem 2E

Chapter 30.7, Problem 4E

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Chapter 30 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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