math.html 5.6 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198
  1. <!doctype html>
  2. <html lang="en">
  3. <head>
  4. <meta charset="utf-8">
  5. <title>reveal.js - The HTML Presentation Framework</title>
  6. <meta name="description" content="A framework for easily creating beautiful presentations using HTML">
  7. <meta name="author" content="Hakim El Hattab">
  8. <meta name="apple-mobile-web-app-capable" content="yes" />
  9. <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" />
  10. <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
  11. <link rel="stylesheet" href="../css/reveal.min.css">
  12. <link rel="stylesheet" href="../css/theme/night.css" id="theme">
  13. <!-- For syntax highlighting -->
  14. <link rel="stylesheet" href="../lib/css/zenburn.css">
  15. <!--[if lt IE 9]>
  16. <script src="lib/js/html5shiv.js"></script>
  17. <![endif]-->
  18. </head>
  19. <body>
  20. <div class="reveal">
  21. <div class="slides">
  22. <section>
  23. <h2>reveal.js Math Plugin</h2>
  24. <p>A thin wrapper for MathJax</p>
  25. </section>
  26. <section>
  27. <h3>The Lorenz Equations</h3>
  28. \[\begin{aligned}
  29. \dot{x} &amp; = \sigma(y-x) \\
  30. \dot{y} &amp; = \rho x - y - xz \\
  31. \dot{z} &amp; = -\beta z + xy
  32. \end{aligned} \]
  33. </section>
  34. <section>
  35. <h3>The Cauchy-Schwarz Inequality</h3>
  36. <script type="math/tex; mode=display">
  37. \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)
  38. </script>
  39. </section>
  40. <section>
  41. <h3>A Cross Product Formula</h3>
  42. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  43. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  44. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  45. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  46. \end{vmatrix} \]
  47. </section>
  48. <section>
  49. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  50. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  51. </section>
  52. <section>
  53. <h3>An Identity of Ramanujan</h3>
  54. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  55. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  56. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  57. </section>
  58. <section>
  59. <h3>A Rogers-Ramanujan Identity</h3>
  60. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  61. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  62. </section>
  63. <section>
  64. <h3>Maxwell&#8217;s Equations</h3>
  65. \[ \begin{aligned}
  66. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  67. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  68. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  69. \]
  70. </section>
  71. <section>
  72. <section>
  73. <h3>The Lorenz Equations</h3>
  74. <div class="fragment">
  75. \[\begin{aligned}
  76. \dot{x} &amp; = \sigma(y-x) \\
  77. \dot{y} &amp; = \rho x - y - xz \\
  78. \dot{z} &amp; = -\beta z + xy
  79. \end{aligned} \]
  80. </div>
  81. </section>
  82. <section>
  83. <h3>The Cauchy-Schwarz Inequality</h3>
  84. <div class="fragment">
  85. \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
  86. </div>
  87. </section>
  88. <section>
  89. <h3>A Cross Product Formula</h3>
  90. <div class="fragment">
  91. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  92. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  93. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  94. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  95. \end{vmatrix} \]
  96. </div>
  97. </section>
  98. <section>
  99. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  100. <div class="fragment">
  101. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  102. </div>
  103. </section>
  104. <section>
  105. <h3>An Identity of Ramanujan</h3>
  106. <div class="fragment">
  107. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  108. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  109. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  110. </div>
  111. </section>
  112. <section>
  113. <h3>A Rogers-Ramanujan Identity</h3>
  114. <div class="fragment">
  115. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  116. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  117. </div>
  118. </section>
  119. <section>
  120. <h3>Maxwell&#8217;s Equations</h3>
  121. <div class="fragment">
  122. \[ \begin{aligned}
  123. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  124. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  125. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  126. \]
  127. </div>
  128. </section>
  129. </section>
  130. </div>
  131. </div>
  132. <script src="../lib/js/head.min.js"></script>
  133. <script src="../js/reveal.min.js"></script>
  134. <script>
  135. Reveal.initialize({
  136. history: true,
  137. transition: 'linear',
  138. math: {
  139. // mathjax: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js',
  140. dialect: 'TeX-AMS_HTML-full'
  141. },
  142. dependencies: [
  143. { src: '../lib/js/classList.js' },
  144. { src: '../plugin/math/math.js', async: true }
  145. ]
  146. });
  147. </script>
  148. </body>
  149. </html>