. Consider the function f(x) defined on the interval (-2,2] where 0, f(x) = 2, 1, -2≤x≤-1 -1 < x≤1 1
. Consider the function f(x) defined on the interval (-2,2] where 0, f(x) = 2, 1, -2≤x≤-1 -1 < x≤1 1
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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Question
![Math 422: Additional Problems for Problem Set 1
AP-1. Consider the function f(x) defined on the interval [-2, 2] where
f(x) =
0,
2₁
1,
-2≤x≤-1
-1 < x≤1
1 < x≤2
(a) Sketch the graph of the f(x) over the interval [-2,2]
(b) Sketch the graph of the periodic extension of f(x) over the interval [-6, 6] (i.e., 3 full periods)
(c) Sketch the graph of the Fourier series for f(x) over the interval [-6, 6] (i.e., 3 full periods)
Σ(-2)=
(d) State the values to which the Fourier sine series converges at the points: x= -2, x=-1, x=0, x= 1 and 2 = 2.
Σ(−1) =
Σ(0) =
Σ(1) =
Σ(2) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1b35bbd-9a7b-4095-9828-537a6266d726%2F6c7ac3d0-8d40-4462-b787-52dc6d862935%2Fwoqg0g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Math 422: Additional Problems for Problem Set 1
AP-1. Consider the function f(x) defined on the interval [-2, 2] where
f(x) =
0,
2₁
1,
-2≤x≤-1
-1 < x≤1
1 < x≤2
(a) Sketch the graph of the f(x) over the interval [-2,2]
(b) Sketch the graph of the periodic extension of f(x) over the interval [-6, 6] (i.e., 3 full periods)
(c) Sketch the graph of the Fourier series for f(x) over the interval [-6, 6] (i.e., 3 full periods)
Σ(-2)=
(d) State the values to which the Fourier sine series converges at the points: x= -2, x=-1, x=0, x= 1 and 2 = 2.
Σ(−1) =
Σ(0) =
Σ(1) =
Σ(2) =
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