noa
/
functionnal


			
				
					
						
						
							123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208
							<!doctype html>
<html lang="en">

	<head>
		<meta charset="utf-8">

		<title>reveal.js - Math Plugin</title>

		<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">

		<link rel="stylesheet" href="../../css/reveal.css">
		<link rel="stylesheet" href="../../css/theme/night.css" id="theme">
	</head>

	<body>

		<div class="reveal">

			<div class="slides">

				<section>
					<h2>reveal.js Math Plugin</h2>
					<p>A thin wrapper for MathJax</p>
				</section>

				<section>
					<h3>The Lorenz Equations</h3>

					\[\begin{aligned}
					\dot{x} &amp; = \sigma(y-x) \\
					\dot{y} &amp; = \rho x - y - xz \\
					\dot{z} &amp; = -\beta z + xy
					\end{aligned} \]
				</section>

				<section>
					<h3>The Cauchy-Schwarz Inequality</h3>

					<script type="math/tex; mode=display">
						\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
					</script>
				</section>

				<section>
					<h3>A Cross Product Formula</h3>

					\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
					\mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
					\frac{\partial X}{\partial u} &amp;  \frac{\partial Y}{\partial u} &amp; 0 \\
					\frac{\partial X}{\partial v} &amp;  \frac{\partial Y}{\partial v} &amp; 0
					\end{vmatrix}  \]
				</section>

				<section>
					<h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>

					\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]
				</section>

				<section>
					<h3>An Identity of Ramanujan</h3>

					\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
					1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
					{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
				</section>

				<section>
					<h3>A Rogers-Ramanujan Identity</h3>

					\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
					\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
				</section>

				<section>
					<h3>Maxwell&#8217;s Equations</h3>

					\[  \begin{aligned}
					\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
					\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
					\nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
					\]
				</section>

				<section>
					<h3>TeX Macros</h3>

					Here is a common vector space:
					\[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
					used in functional analysis.
				</section>

				<section>
					<section>
						<h3>The Lorenz Equations</h3>

						<div class="fragment">
							\[\begin{aligned}
							\dot{x} &amp; = \sigma(y-x) \\
							\dot{y} &amp; = \rho x - y - xz \\
							\dot{z} &amp; = -\beta z + xy
							\end{aligned} \]
						</div>
					</section>

					<section>
						<h3>The Cauchy-Schwarz Inequality</h3>

						<div class="fragment">
							\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
						</div>
					</section>

					<section>
						<h3>A Cross Product Formula</h3>

						<div class="fragment">
							\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
							\mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
							\frac{\partial X}{\partial u} &amp;  \frac{\partial Y}{\partial u} &amp; 0 \\
							\frac{\partial X}{\partial v} &amp;  \frac{\partial Y}{\partial v} &amp; 0
							\end{vmatrix}  \]
						</div>
					</section>

					<section>
						<h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>

						<div class="fragment">
							\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]
						</div>
					</section>

					<section>
						<h3>An Identity of Ramanujan</h3>

						<div class="fragment">
							\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
							1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
							{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
						</div>
					</section>

					<section>
						<h3>A Rogers-Ramanujan Identity</h3>

						<div class="fragment">
							\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
							\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
						</div>
					</section>

					<section>
						<h3>Maxwell&#8217;s Equations</h3>

						<div class="fragment">
							\[  \begin{aligned}
							\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
							\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
							\nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
							\]
						</div>
					</section>

					<section>
						<h3>TeX Macros</h3>

						Here is a common vector space:
						\[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
						used in functional analysis.
					</section>
				</section>

			</div>

		</div>

		<script src="../../lib/js/head.min.js"></script>
		<script src="../../js/reveal.js"></script>

		<script>

			Reveal.initialize({
				history: true,
				transition: 'linear',

				math: {
					// mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
					config: 'TeX-AMS_HTML-full',
					TeX: {
						Macros: {
							R: '\\mathbb{R}',
							set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ]
						}
					}
				},

				dependencies: [
					{ src: '../../lib/js/classList.js' },
					{ src: '../../plugin/math/math.js', async: true }
				]
			});

		</script>

	</body>
</html>