Transforms and its Applications: UNIT 3: Fourier Series
Fourier Series: Half Range Series
Fourier Series: Example Important Solved Problems with formula, steps, derivation, answer and Exercise Problems based on Half Range Series.
HALF‒RANGE
SERIES
(a) HALF‒RANGE SINE
SERIES
(b) HALF‒RANGE COSINE
SERIES
Sine series:
To expand f(x) as a sine series in
(0, π) or (0,l), we extend the
function reflecting it in the origin, so that f(x) = −f(x).
f(x) = g(x) in (0, π) or
(0,1) is extended to f (x) = −g (−x)
in (‒π, 0) or (‒l, 0).
Cosine
series: To expand f(x) as a cosine series in (0, π) or (0,l), we extend the function reflecting it in the y‒axis, so that f (−x) = f(x).
f(x) = g(x) in (0,π) or
(0,l) is extended to f(x) = g(‒x) in (‒π, 0) or (‒1, 0).
Example 3: Write the formula for Fourier
constants to expand f(x) as a sine
series in (0, π).
Solution:
Example 2: Write the formula for Fourier
constants to expand f(x) as a sine
series in (0, l).
Solution:
Example 3: Write the formula for Fourier
constants to expand f(x) as a cosine
series in (0, π).
Solution:
Example 4: Write the formula for Fourier
constants to expand f(x) as a cosine
series in (0, l).
Solution:
Transforms and its Applications: UNIT 3: Fourier Series : Tag: Engineering mathematics, Maths : - Fourier Series: Half Range Series
Transforms and its Applications: UNIT 3: Fourier Series
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