Determine whether the Fourier series of the following functions converges uniformly or not. Sketch each function a) f(x) = sin(x) + |sin(x)|, - π < x < π solve using power and series (Fourier) Note:any solution that does not use power and series calculations (convergence) will be considered wrong Answers: a)This periodic function is continuous, and its derivative is continuous, except for jumps in ± π, etc. Convergence is uniform.
Determine whether the Fourier series of the following functions converges uniformly or not. Sketch each function a) f(x) = sin(x) + |sin(x)|, - π < x < π solve using power and series (Fourier) Note:any solution that does not use power and series calculations (convergence) will be considered wrong Answers: a)This periodic function is continuous, and its derivative is continuous, except for jumps in ± π, etc. Convergence is uniform.
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
Determine whether the Fourier series of the following functions converges uniformly or not. Sketch each function
a) f(x) = sin(x) + |sin(x)|, - π < x < π
solve using power and series (Fourier)
Note:any solution that does not use power and series calculations (convergence) will be considered wrong
Answers:
a)This periodic function is continuous, and its derivative is continuous, except for jumps in ± π, etc. Convergence is uniform.
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