Engineering mathematics 1 second unit

1. FOURIER SERIES
• FOURIER SERIES EXPANSION
• FOURIER CONSTANTS (𝒂𝟎 , 𝒂𝒏 , 𝒃𝒏)
• EVEN FUNCTION
• ODD FUNCTION
• HARMONIC ANALYSIS

2. Fourier Series Definition

3. EVEN FUNCTION
An function f(x) is said to be an even function in –π < x < π if f(-x)=-f(x) for all x.
Fourier Constants 𝑎0 , 𝑎𝑛 , 𝑏𝑛 are given by
𝑏𝑛 = 0

6. ODD FUNCTION
An function f(x) is said to be an even function in –π < x < π if f(-x)=f(x) for all x
𝑎0= 0
𝑎𝑛= 0

9. HARMONIC ANALYSIS
In many engineering and scientific problems, f(x) is not given directly, rather
set of discrete values of function are given in the form (𝑥𝑖,𝑦𝑖),i =1,2,3,….m
where ’s are equispaced. The process of obtaining f(x) in terms of Fourier
series from given set of values (𝑥𝑖,𝑦𝑖) , is known as practical harmonic
analysis.