1.)Determine whether the Fourier series of the following functions converge uniformly or not. a. f(x) = ex, - 1 < x < 1 b. f(x) = sinh(x), - π< x < π Answer: a)The periodic function is not continuous at ± etc., so convergence cannot be uniform. b. Like a, the periodic function has jumps at ±π etc.
1.)Determine whether the Fourier series of the following functions converge uniformly or not. a. f(x) = ex, - 1 < x < 1 b. f(x) = sinh(x), - π< x < π Answer: a)The periodic function is not continuous at ± etc., so convergence cannot be uniform. b. Like a, the periodic function has jumps at ±π etc.
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
1.)Determine whether the Fourier series of the following functions converge uniformly or not.
a. f(x) = ex, - 1 < x < 1
b. f(x) = sinh(x), - π< x < π
Answer:
a)The periodic function is not continuous at ± etc., so convergence cannot be uniform.
b. Like a, the periodic function has jumps at ±π etc.
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