math.html 5.9 KB

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  1. <!doctype html>
  2. <html lang="en">
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  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">
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  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. \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
  37. </section>
  38. <section>
  39. <h3>A Cross Product Formula</h3>
  40. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  41. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  42. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  43. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  44. \end{vmatrix} \]
  45. </section>
  46. <section>
  47. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  48. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  49. </section>
  50. <section>
  51. <h3>An Identity of Ramanujan</h3>
  52. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  53. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  54. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  55. </section>
  56. <section>
  57. <h3>A Rogers-Ramanujan Identity</h3>
  58. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  59. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  60. </section>
  61. <section>
  62. <h3>Maxwell&#8217;s Equations</h3>
  63. \[ \begin{aligned}
  64. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  65. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  66. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  67. \]
  68. </section>
  69. <section>
  70. <section>
  71. <h3>The Lorenz Equations</h3>
  72. <div class="fragment">
  73. \[\begin{aligned}
  74. \dot{x} &amp; = \sigma(y-x) \\
  75. \dot{y} &amp; = \rho x - y - xz \\
  76. \dot{z} &amp; = -\beta z + xy
  77. \end{aligned} \]
  78. </div>
  79. </section>
  80. <section>
  81. <h3>The Cauchy-Schwarz Inequality</h3>
  82. <div class="fragment">
  83. \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
  84. </div>
  85. </section>
  86. <section>
  87. <h3>A Cross Product Formula</h3>
  88. <div class="fragment">
  89. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  90. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  91. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  92. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  93. \end{vmatrix} \]
  94. </div>
  95. </section>
  96. <section>
  97. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  98. <div class="fragment">
  99. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  100. </div>
  101. </section>
  102. <section>
  103. <h3>An Identity of Ramanujan</h3>
  104. <div class="fragment">
  105. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  106. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  107. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  108. </div>
  109. </section>
  110. <section>
  111. <h3>A Rogers-Ramanujan Identity</h3>
  112. <div class="fragment">
  113. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  114. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  115. </div>
  116. </section>
  117. <section>
  118. <h3>Maxwell&#8217;s Equations</h3>
  119. <div class="fragment">
  120. \[ \begin{aligned}
  121. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  122. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  123. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  124. \]
  125. </div>
  126. </section>
  127. </section>
  128. </div>
  129. </div>
  130. <script src="../lib/js/head.min.js"></script>
  131. <script src="../js/reveal.min.js"></script>
  132. <script>
  133. Reveal.initialize({
  134. history: true,
  135. transition: 'linear',
  136. math: {
  137. // host: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js',
  138. mode: 'TeX-AMS_HTML-full'
  139. },
  140. dependencies: [
  141. { src: '../lib/js/classList.js', condition: function() { return !document.body.classList; } },
  142. { src: '../plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
  143. { src: '../plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
  144. { src: '../plugin/highlight/highlight.js', async: true, callback: function() { hljs.initHighlightingOnLoad(); } },
  145. { src: '../plugin/math/math.js', async: true }
  146. ]
  147. });
  148. </script>
  149. </body>
  150. </html>