Fourier Series-Mathematics

Fourier series 1. Fourier series with period 2L 2. Fourier series of even and odd function 3. Fourier sine and cosine

What you'll learn

Fourier series

Fourier series-Over the period 2L

Even and odd function

Sine and cosine series

Requirements

Basic of integration

Description

Fourier series 1. Fourier series with period 2L 2. Fourier series of even and odd function 3. Fourier sine and cosine A Fourier series represents a periodic function as an infinite sum of sines and cosines. It is widely used in signal processing, engineering, physics, and mathematics to analyze periodic functions.The integrals determine how much of each sine and cosine wave contributes to reconstructing f(x).Applications of Fourier SeriesSignal Processing – Used to analyze and reconstruct signals.Electrical Engineering – Helps in circuit analysis and AC waveforms.Physics – Used in heat transfer, quantum mechanics, and wave equations.Vibration Analysis – Helps analyze mechanical systems.Fourier Series for Even and Odd FunctionsWhen working with Fourier series, recognizing whether a function is even or odd simplifies calculations by determining which terms in the series will be present. Effect on Fourier SeriesSince even functions are symmetric about the y-axis, their Fourier series contain only cosine terms (no sine terms).Key TakeawaysEven function → Only cosine termsOdd function → Only sine termsMixed function → Both sine & cosine termsFourier Sine and Cosine SeriesThe Fourier sine and cosine series are special cases of the Fourier series when a function is either odd or even on a given interval.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 Lecture 2

Lecture 3 Lecture 3

Lecture 4 Lecture 4

Lecture 5 Lecture 5

Lecture 6 Lecture 6

Lecture 7 Lecture 7

Section 2: Fourier series of Even and Odd function

Lecture 8 Lecture 8

Lecture 9 Lecture 9

Lecture 10 Lecture 10

Lecture 11 Lecture 11

Lecture 12 Lecture 13

Lecture 13 Lecture 14

Lecture 14 Lecture 15

Lecture 15 Lecture 16

Lecture 16 Lecture 17

Lecture 17 Lecture 18

Section 3: Fourier sine and cosine series

Lecture 18 Lecture 19

Lecture 19 Lecture 20

Lecture 20 Lecture 21

Lecture 21 Lecture 22

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