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Linear Algebra and Learning from Data

Exercise 4.1.7

Answers

Since $\int_{- π}^{π} \cos (nx) dx = 0$ for any $n$ , and $\int_{- π}^{π} \cos (nx) \cos (mx) dx = 0$ , when $n \neq m$ , we have

$2 π a_{0} = \int_{- π}^{π} f (x) dx = π$ , we have $a_{0} = \frac{1}{2}$
$\int_{- π}^{π} \cos (x) f (x) dx = \int_{- π ∕ 2}^{π ∕ 2} \cos (x) dx = 2$ , $\int_{- π}^{π} a_{1} \cos^{2} (x) dx = a_{1} π$ , so $a_{1} = \frac{π}{2}$

niuers

2020-03-20 00:00

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