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3. Fourier Series (a) Sketch the function 1 + x² for the entire domain -∞ < x < ∞. (b) Determine if 1 + x² is an even/odd function. 1 (c) Consider 1+x² in the domain −1 ≤ x ≤ 1. Compute the first four non-zero terms (including the constant term) in the Fourier series representation of the function in −1 ≤ x ≤ 1. (d) Use MATLAB to plot your result for (c) along with a plot of 1+x² on the same graph over 1≤ x ≤ 1. (e) Plot the same two curves again but over -2≤ x ≤ 2. (You should find that the Fourier series representation matches well with the function in the domain −1 ≤ x ≤ 1 but not outside this domain.)

3. Fourier Series (a) Sketch the function 1 + x² for the entire domain -∞ < x < ∞. (b) Determine if 1 + x² is an even/odd function. 1 (c) Consider 1+x² in the domain −1 ≤ x ≤ 1. Compute the first four non-zero terms (including the constant term) in the Fourier series representation of the function in −1 ≤ x ≤ 1. (d) Use MATLAB to plot your result for (c) along with a plot of 1+x² on the same graph over 1≤ x ≤ 1. (e) Plot the same two curves again but over -2≤ x ≤ 2. (You should find that the Fourier series representation matches well with the function in the domain −1 ≤ x ≤ 1 but not outside this domain.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Fourier Series (a) Sketch the function 1 + x² for the entire domain -∞ < x < ∞. (b) Determine if 1 + x² is an even/odd function. 1 (c) Consider 1+x² in the domain −1 ≤ x ≤ 1. Compute the first four non-zero terms (including the constant term) in the Fourier series representation of the function in −1 ≤ x ≤ 1. (d) Use MATLAB to plot your result for (c) along with a plot of 1+x² on the same graph over 1≤ x ≤ 1. (e) Plot the same two curves again but over -2≤ x ≤ 2. (You should find that the Fourier series representation matches well with the function in the domain −1 ≤ x ≤ 1 but not outside this domain.)
Transcribed Image Text:3. Fourier Series (a) Sketch the function 1 + x² for the entire domain -∞ < x < ∞. (b) Determine if 1 + x² is an even/odd function. 1 (c) Consider 1+x² in the domain −1 ≤ x ≤ 1. Compute the first four non-zero terms (including the constant term) in the Fourier series representation of the function in −1 ≤ x ≤ 1. (d) Use MATLAB to plot your result for (c) along with a plot of 1+x² on the same graph over 1≤ x ≤ 1. (e) Plot the same two curves again but over -2≤ x ≤ 2. (You should find that the Fourier series representation matches well with the function in the domain −1 ≤ x ≤ 1 but not outside this domain.)
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