(a) Compute the Fourier sine series expansion of f(x) = 3x - x² on [0, 3] (b) To what value does this series converge at x = 1? Explain.
(a) Compute the Fourier sine series expansion of f(x) = 3x - x² on [0, 3] (b) To what value does this series converge at x = 1? Explain.
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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![1. (a) Compute the Fourier sine series expansion of f(x) = 3x – x² on [0, 3].
(b) To what value does this series converge at x = 1? Explain.
2. Solve the initial-boundary value problem
ди
3 a?u
0 <x < 4n, t 0
ди
(0, t)
10 Əx?
ди
. (Απ, t) 0
t > 0
=
0,
0 < x < T
u(x, 0) = {
8,
0 < x < 4n
T < x < 4n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedb31c39-2ab0-43ac-a5ed-7ff74e15773e%2Feb4f2f19-404f-4b4a-b2a1-32e055a527e8%2F8jac34_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a) Compute the Fourier sine series expansion of f(x) = 3x – x² on [0, 3].
(b) To what value does this series converge at x = 1? Explain.
2. Solve the initial-boundary value problem
ди
3 a?u
0 <x < 4n, t 0
ди
(0, t)
10 Əx?
ди
. (Απ, t) 0
t > 0
=
0,
0 < x < T
u(x, 0) = {
8,
0 < x < 4n
T < x < 4n
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