December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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12.2 Fourier Series
INTRODUCTION
We have just seen in the preceding section that if {ø0(x), ø1(x), ø2(x), …} is a set of real-valued functions that is orthogonal on an interval [a, b] and if f is a function defined on the same interval, then we can formally expand f in an orthogonal series c0ø0(x) + c1ø1(x) + c2ø2(x) + … . In this section we shall expand functions in terms of a special orthogonal set of trigonometric functions.
Trigonometric Series
In Problem 12 in Exercises 12.1, you were asked to show that the set of trigonometric functions
(1)
is orthogonal on the interval [–p, p]. This set will be of special importance later on in the solution ...
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