## Fourier Series Definition in Hindi Part 2 |Introduction of Fourier Series Periodic Function

This video Lecture of fourier series explanation helps students to understand the best Idea of Solving the Fourier series by Smart way. This course video is for those students who are not regular in the class due to there own reasons.

Fourier series Lecture in Hindi PART 2 by Jk Smart Classes

in this video, we explain Fourier series easy explanation following concept 1.Fourier Series Definition 2.Fourier Series Periodic Function

1. **FOURIER SERIES** Timestamps 1:35 A Fourier series of a periodic function consists of a sum of sine and cosine terms. Sines and cosines are the most fundamental periodic functions.

The Fourier series is named after the French Physicist Jacques Fourier. Fourier series has its application in problems pertaining to Wave Equation, Heat conduction, acoustics, etc

**2. PERIODIC FUNCTIONS:**– Start from timestamps in this video 4:10 A periodic function has a basic shape which is repeated over and over again. The fundamental range is the time (or sometimes distance) over which the basic shape is defined. The length of the fundamental range called the period.

A general periodic function f(x) of period T satisfies the condition f(x+T) = f(x)

Here f(x) is a real-valued function and T is a positive real number. The function f(x) = sinx is periodic of period 2p since Sin(x+2np) = sinx, n=1,2,3

Today we are going to discuss Fourier series which is important for engineering students and BSC students and other government and competitive exams first-grade school lecturer or second-grade teacher or any else or for higher education like NET, JEE, etc.

We will discuss what is the Fourier series? and how we solve them we will solve some numerical based on that so what is Fourier series so, students, we have some new words here what is a periodic function? it is that function that repeats itself after a particular interval.

for example, these all are periodic functions if we see the series of sin x it is of this type so as you can see after a particular interval the series repeats itself these are the sin waves it is repeating itself .

similarly, if we see the graph of cos and tan after a particular interval function repeats let me tell you we study in engineering or higher mathematics we can represent series algebraically by Taylor’s theorem and Maclaurin’s theorem the series of sin x is here we have represented sin algebraically in the same way.

if we have a function that is algebraic, like all these functions can be represented in series in terms of trigonometric functions like x can be represented in terms of trigonometric functions and that is the concept of Fourier series here we will learn, how can we represent algebraic functions in sin and cosine terms now

you will have a question that sir algebraic functions are not periodic then how can we represent it we can represent the algebraic function too in periodic functions here we will have to define that it is repeating after a particular interval of time.

so we will discuss the concept in questions so students in order to calculate Fourier series the formula we have is this is the formula we have for Fourier series.

if you have to calculate the Fourier series between -l to l then we will use this formula here the value of a0 is the formula for an is and the value for bn is so,

students, we have the following values we will solve an, a0 and substitute there and then we get the Fourier series and the interval if -l to l if you are asked to find the Fourier series between -2 to 2 between -pi to pi whatever the interval.

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