Chapter 12 - Fourier Series

Question 1

Fourier series of f (x)

Answer 1

S (x)= (a0/2) + sum (1 to inf) of (an cosnx + bn sinnx)

Question 2

A0

Answer 2

(1/pi) * integral (-pi to pi) f (x) dx

Question 3

An

Answer 3

1/pi * integral (-pi to pi) f(x) cosnx dx

Question 4

Bn

Answer 4

1/pi * integral (-pi to pi) f(x) sinnx dx

Question 5

What does it mean if S (x) is periodic, with fundamental period 2pi?

Answer 5

S (x + 2k*pi) = s (x) for all x in r and any integer k

Question 6

Even function

Answer 6

F (-x) = f (x) for all x

Question 7

Odd function

Answer 7

F (-x) = -f (x) for all x

Question 8

What does f (x) equal when f (x) is even?

Answer 8

(A0/2) + sum (1 to inf) of (an*cosnx)

Question 9

What does f (x) equal when f (x) is odd?

Answer 9

Sum (1 to inf) of (bn*sinnx)

Question 10

Dirichlet conditions

Answer 10

F (x) must be single-valued and continuous, except for at a finite number of points at which it has finite discontinuities.

F (x) must only have a finite numver of maxima and minima on the interval