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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Chapter2: Second-order Linear Odes
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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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