. Consider the function f(x) defined on the interval (-2,2] where 0, f(x) = 2, 1, -2≤x≤-1 -1 < x≤1 1

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Chapter2: Second-order Linear Odes
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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) =
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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