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newton-rapson.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Calculating root using NR Method</title>
<link rel="stylesheet" href="css/style_newton-sim.css">
<script src='https://cdn.plot.ly/plotly-2.4.2.min.js'></script>
</head>
<body oncontextmenu="return false">
<header>
<div class="logo"><img class="logo" src="images/andc_logo.jpg"></div>
<h1>VLab@ANDC</h1>
<ul class="navigation">
<li><a href="index.html">Home</a></li>
<li><a href="index.html#labs_section">Labs</a></li>
<li><a href="index.html#team">Team</a></li>
<li><a href="index.html#contact">Contact Us</a></li>
<li><a href="https://www.andcollege.du.ac.in/" target="_blank" rel="noopener noreferrer">College Website</a>
</li>
</ul>
</header>
<div class="heading">
<div class="heading--1">
<h1>Newton-Rapson-Method</h1>
</div>
<select name="eqation-type" id="select-eqn">
<option value="select">Select</option>
<option value="Algebraic-equation" class="alg-eqn">Algebraic equation</option>
<option value="Transcendental-equation" class="trsn-eqn">Transcendental equation</option>
</select>
<div class="heading--2 algebraic--equation1">
<h1> For finding the roots of linear, quadratic and third degree polynomial.
</div>
</h1>
<div class="heading--2 transedental--equation1">
<h1> For finding the roots of transcendental equation.
</h1>
</div>
</div>
<div class="algebraic--equation2">
<div class="explanation">
Given a function f(x) on floating number x and an initial guess for root, find root of function in interval.
Here f(x) represents algebraic or transcendental equation.
For simplicity, derivative of function is also provided.
<b> Example:</b> <br>
<div class="example">
<b>Input:</b> <br> A function of x (for example x<sup>3</sup> +4x<sup>2</sup> + 8.), <br>
derivative function of x (3x<sup>2</sup> +8x)
and an initial guess x<sub>0</sub> = -1 <br>
<b>Output:</b> <br> The value of root is : -4.412
or any other value close to root.
</div>
</div>
<form class="newton-method">
<p class="equation-detail">f(x)= a x<sup>3</sup> +b x<sup>2</sup>+c x<sup>1</sup> + d :</p>
<p class="equation-detail">Enter the coefficients of the equation:</p>
<input type="text" placeholder="a" class="cube--equation cube-coefficient">x<sup>3</sup>+
<input type="text" placeholder="b" class="cube--equation square-coefficient">x<sup>2</sup>+
<input type="text" placeholder="c" class="cube--equation linear-coefficient">x<sup>1</sup>+
<input type="text" placeholder="d" class="cube--equation coefficient"><br>
<label for="iterations">Enter the number of iterations: </label>
<input type="text" placeholder="i" class="cube--equation iterations"><br>
<label for="intervals">Enter the initial guess: </label>x<sub>0</sub> =
<input type="text" placeholder="x" class="cube--equation interval--A"> <br>
<label for="rootGenerate">For generating root: </label>
<button class="btn--cls root--finder">Click here</button>
<div class="result">
<span class="validRange">Result: </span><span class="eqnResult"></span>
</div>
<button id="file--download" class="btn--cls">File Download</button><br>
<label for="gtext">Graph:</label>
<div id="graph">
</div>
</form>
</div>
<div class="transedental--equation2">
<div class="explanation">
Given a function f(x) on floating number x and an initial guess for root, find root of function in interval.
Here f(x) represents transcendental equation.
For simplicity, derivative of function is also provided.
<b> Example:</b> <br>
<div class="example">
<b>Input:</b> <br> A function of x (for example= x<sup>2</sup> -2sinx), <br>
derivative function of x = 2(x-cosx)
and an initial guess x<sub>0</sub> = 2 <br>
<b>Output:</b> <br> The value of root is : 1.405
or any other value close to root.
</div> <br>
In optics, the <b>Fraunhofer diffraction</b> equation is used to model the diffraction of waves when the
diffraction pattern is viewed at a long distance from the diffracting object (in the far-field region), and
also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created
near the object (in the near field region) is given by the Fresnel diffraction equation. <br>
<img src="images/fraunDiff.png" alt="Fraunhofer-diffraction" width="600" height="300" class="fraunImg">
<img src="images/singleSlit.gif" alt="Fraunhofer-diffraction" width="500" height="200" class="fraunImg"> <br>
By using the intensity equation I/I<sub>0</sub>= (sinx/x)<sup>2</sup>,maxima or minima is calculated
accordingly. Here the value of x is founded by solving the equation (x-tanx) and finding its different
roots.
</div>
<form class="newton-method-tran">
<p class="equation-detail">f(x)= x-tanx</p>
<label for="intervals">Enter the initial guess: </label>x<sub>0</sub> =
<input type="text" placeholder="x" class="cube--equation interval--trans"> <br>
<label for="iterations">Enter the number of iterations: </label>
<input type="text" placeholder="i" class="cube--equation iterationsTrans"> <br>
<label for="rootGenerate">For generating root: </label>
<button class="btn--cls root--finder-tran">Click here</button>
<div class="result">
<span class="validRange">Result: Root of the eqation is </span><span class="eqnResultTran"></span>
</div>
**Enter the value of roots in ascending order.
<table>
<tr>
<th>Value of Root</th>
<th>Value of intensity I/I<sub>0</sub></th>
</tr>
<tr>
<th><input type="root1" class="cube--equationTr root1"></th>
<th class="inten1"></th>
</tr>
<tr>
<th><input type="root2" class="cube--equationTr root2"></th>
<th class="inten2"></th>
</tr>
<tr>
<th><input type="root3" class="cube--equationTr root3"></th>
<th class="inten3"></th>
</tr>
<tr>
<th><input type="root4" class="cube--equationTr root4"></th>
<th class="inten4"></th>
</tr>
</table>
<button class="graph--tran btn--cls">Check graph</button>
<button id="file--download--tran" class="btn--cls">File Download</button><br>
<label for="gtext">Graph:</label>
<div id="graph--1">
</div>
</form>
</div>
<script src="js/newton-rap-sim.js"></script>
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</body>
</html>