Fourier Series in Hindi Part 7 Compute Fourier Series Example and Solution of F(x)=x-x2 in -Pi to Pi |
JK ENGINEERING CLASSES (JK SMART CLASSES) introduced a full course of the most difficult subject name is ENGINEERING MATHEMATICS 3 (M-3)in the engineering field for all B.TECH TRADE(EE, CE, AE, ME, ECE and CSE, IT).
in this video, we discuss the How To Compute Even & Function of Fourier Series in Engineering Mathematics 3 in Hindi.
EVEN FUNCTION OF FOURIER SERIES
A function y = f(x) is said to be even, if f(-x) = f(x). The Graph Show That Even function is always symmetrical about the y-axis.
ODD FUNCTION OF FOURIER SERIES
A function y=f(x) is said to be odd, if f(-x) = – f(x). The graph Show That odd function is always symmetrical about the origin.
For example, the function f(x) = in [-1,1] is even as f(-x) = = f(x) and the function f(x) = x in [-1,1] is odd as f(-x) = -x = -f(x). The graphs of these functions are shown below :.
1. If f(x) is even and g(x) is odd, then
• h(x) = f(x) x g(x) is odd
• h(x) = f(x) x f(x) is even
• h(x) = g(x) x g(x) is even
1. F(x) = x2 cosx is Even Function, then x2cosx are even function. If F(X) is Even, Then bn=0 This is FOURIER COSINE SERIES ao and an is present.
2. G(x) = xsinx is Even, since x and sinx are odd functions .
3. h(x) = x2 sinx is odd since x2 is even function and sinx is odd function.If f(x) is odd, then ao=an=0 This is FOURIER SINE SERIES the only bn is present