Fourier Series Examples #10 Half Range Fourier Cosine Series Examples and Solutions in Hindi|PTU|GTU

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 & ODD FUNCTION OF FOURIER SERIES IN HINDI

EVEN FUNCTION
A function y = f(x) is said to be even, if f(-x) = f(x). The graph of the even function is always symmetrical about the y-axis.

ODD FUNCTION
A function y=f(x) is said to be odd, if f(-x) = – f(x). The graph of the 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
For example,
1. h(x) = x2 cosx is even, since both x2 and cosx are even functions
2. h(x) = xsinx is even, since x and sinx are odd functions
3. h(x) = x2 sinx is odd, since x2 is even and sinx is odd.

2. If f(x) is even, then bn=0 This is FOURIER COSINE SERIES ao and an is present
3. If f(x) is odd, then ao=an=0 This is FOURIER SINE SERIES only bn is present