aem : Fourier series of Even and Odd Function
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This document discusses Fourier series and their application to even and odd functions. It introduces Fourier series and their use in decomposing periodic functions into harmonic components. It then explains that for even functions, the Fourier coefficients bn are zero and an can be determined from the integral of the function times cosine from 0 to π. For odd functions, the Fourier coefficient a0 is zero and bn can be determined from the integral of the function times sine from 0 to π. The document concludes that Fourier series have important applications in civil engineering for solving vibration problems such as determining earthquake frequencies.
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aem : Fourier series of Even and Odd Function
- 1. Active Learning Assignment of Advanced Engineering Mathematics Topic: Fourier series of Even and Odd Function
- 2. * CONTENTS * Fourier Series. Even and Odd Function. Application of Fourier Series in Civil Engineering
- 3. FOURIER SERIES JOSEPH FOURIER (Founder of Fourier series)
- 4. Fourier Series Fourier series make use of the orthogonality relationships of the sine and cosine functions. FOURIER SERIES can be generally written as, Where, ……… (1.1) ……… (1.2) ……… (1.3)
- 5. BASIS FORMULAE OF FOURIER SERIES The Fourier series of a periodic function ƒ(x) with period 2п is defined as the trigonometric series with the coefficient a0, an and bn, known as FOURIER COEFFICIENTS, determined by formulae (1.1), (1.2) and (1.3). The individual terms in Fourier Series are known as HARMONICS.
- 6. Even Functions Definition: A function f(x) is said to be even if f(-x)=f(x). e.g. cosx are even function Graphically, an even function is symmetrical about y-axis.
- 7. Even Functions When function is even: When f(x) is an even function then f(x)sinx is an odd function. Thus an = a0= an = bn= Therefore f(x)=
- 10. Odd Functions Definition: A function f(x) is said to be even if f(-x)=-f(x). e.g. sin x, are odd functions. Graphically, an even function is symmetrical about the origion.
- 11. Odd Functions When function is odd: When f(x) is an odd function then f(x)cosnxis an odd function and f(x)sinx is an even function. a0==0 an = bn= Therefore f(x)=
- 14. Note:
- 15. Application in Civil Engineering The most useful application is solving vibration problems. Vibration are obviously important in many parts of civil engineering. We can find of frequency of earthquake.