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Half Range Fourier Sine and Cosine Series - Part 1 | Examples & Solutions | Engineering Mathematics

In this video, we will discuss the concept of half-range series and its application in Fourier series. We will start by defining what a half-range series is and its significance in engineering mathematics. A half-range series is a Fourier series that is defined only on half of the interval of its periodic function. In other words, the Fourier series is truncated and only the coefficients for the positive values of x are considered. The half-range series expansion can be expressed in terms of only sine or cosine terms, or a combination of both. We will explore the half-range expansion Fourier series and its formula, which can be used to determine the Fourier coefficients of a half-range function. We will also examine the concept of the sine half-range Fourier series and how it differs from the cosine half-range Fourier series. Furthermore, we will solve some example problems involving half-range Fourier series, including finding the half-range Fourier sine and cosine series for a given periodic function. We will also discuss some common questions and problems related to half-range series and how they can be solved. One such example problem involves finding the half-range cosine series of sinx. We will also look at some other practical examples of half-range Fourier series and its application in engineering mathematics. By the end of this video, you will have a clear understanding of what a half-range series is and how it can be used in Fourier series. You will also have the skills to solve example problems involving half-range Fourier series and be able to tackle any half-range series questions that come your way. So, let's dive in and explore the world of half-range series in Fourier analysis! [ 📐 Watch Next ] [21MAT31] Half Range Fourier Sine and Cosine Series Part 1 -    • Half Range Fourier Sine and Cosine Se...   Part 2 -    • Half Range Fourier Sine and Cosine Se...   Part 3 -    • Half Range Fourier Sine and Cosine Se...   Part 4 -    • Half Range Fourier Sine and Cosine Se...   Part 5 -    • Half Range Fourier Sine and Cosine Se...   Part 6 -    • Half Range Fourier Sine and Cosine Se...   Part 7 -    • Half Range Fourier Sine and Cosine Se...   Part 8 -    • Half Range Fourier Sine and Cosine Se...   [ 📐 Playlists ] [21MAT31] - Engineering Mathematics 3 Module 1 -    • Laplace Transforms [21MAT31] Module 1   Module 2 -    • Fourier Series   Module 3 -    • Fourier Transform & Z Transform   Module 4 -    • Numerical Solution of PDE [21mat31] -...   Module 5 -    • Numerical Solution of 2nd Order ODEs ...   #vtu #21mat31 #module2 #engineeringmathematics3 #fourierseries #fourierseriesproblems #mathematicstutor