EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 7.6, Problem 12E
Interpretation Introduction

Interpretation:

The orthogonality relations are to be derived, and h(θ)cos=12ak is to be deduced. Also, the formulas for bk and a0 are to be derived.

Concept Introduction:

The expression of the Fourier series for h(θ) is

h(θ) = k=0akcos+k=0bksin

Where h(θ) is the defined function, and a0, ak,bk are Fourier series coefficients which can be defined as:

a0=10h(θ)ak=1π0h(θ)cosdθ, k1ak=10h(θ)sindθ, k1

f(x)={20πf(x)dxiff(x)iseven0iff(x)isodd

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