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  1. <!doctype html>
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  4. <meta charset="utf-8">
  5. <title>reveal.js - Math Plugin</title>
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  10. <body>
  11. <div class="reveal">
  12. <div class="slides">
  13. <section>
  14. <h2>reveal.js Math Plugin</h2>
  15. <p>A thin wrapper for MathJax</p>
  16. </section>
  17. <section>
  18. <h3>The Lorenz Equations</h3>
  19. \[\begin{aligned}
  20. \dot{x} &amp; = \sigma(y-x) \\
  21. \dot{y} &amp; = \rho x - y - xz \\
  22. \dot{z} &amp; = -\beta z + xy
  23. \end{aligned} \]
  24. </section>
  25. <section>
  26. <h3>The Cauchy-Schwarz Inequality</h3>
  27. <script type="math/tex; mode=display">
  28. \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)
  29. </script>
  30. </section>
  31. <section>
  32. <h3>A Cross Product Formula</h3>
  33. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  34. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  35. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  36. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  37. \end{vmatrix} \]
  38. </section>
  39. <section>
  40. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  41. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  42. </section>
  43. <section>
  44. <h3>An Identity of Ramanujan</h3>
  45. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  46. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  47. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  48. </section>
  49. <section>
  50. <h3>A Rogers-Ramanujan Identity</h3>
  51. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  52. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  53. </section>
  54. <section>
  55. <h3>Maxwell&#8217;s Equations</h3>
  56. \[ \begin{aligned}
  57. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  58. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  59. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  60. \]
  61. </section>
  62. <section>
  63. <section>
  64. <h3>The Lorenz Equations</h3>
  65. <div class="fragment">
  66. \[\begin{aligned}
  67. \dot{x} &amp; = \sigma(y-x) \\
  68. \dot{y} &amp; = \rho x - y - xz \\
  69. \dot{z} &amp; = -\beta z + xy
  70. \end{aligned} \]
  71. </div>
  72. </section>
  73. <section>
  74. <h3>The Cauchy-Schwarz Inequality</h3>
  75. <div class="fragment">
  76. \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
  77. </div>
  78. </section>
  79. <section>
  80. <h3>A Cross Product Formula</h3>
  81. <div class="fragment">
  82. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  83. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  84. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  85. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  86. \end{vmatrix} \]
  87. </div>
  88. </section>
  89. <section>
  90. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  91. <div class="fragment">
  92. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  93. </div>
  94. </section>
  95. <section>
  96. <h3>An Identity of Ramanujan</h3>
  97. <div class="fragment">
  98. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  99. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  100. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  101. </div>
  102. </section>
  103. <section>
  104. <h3>A Rogers-Ramanujan Identity</h3>
  105. <div class="fragment">
  106. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  107. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  108. </div>
  109. </section>
  110. <section>
  111. <h3>Maxwell&#8217;s Equations</h3>
  112. <div class="fragment">
  113. \[ \begin{aligned}
  114. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  115. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  116. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  117. \]
  118. </div>
  119. </section>
  120. </section>
  121. </div>
  122. </div>
  123. <script src="../../lib/js/head.min.js"></script>
  124. <script src="../../js/reveal.js"></script>
  125. <script>
  126. Reveal.initialize({
  127. history: true,
  128. transition: 'linear',
  129. math: {
  130. // mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
  131. config: 'TeX-AMS_HTML-full'
  132. },
  133. dependencies: [
  134. { src: '../../lib/js/classList.js' },
  135. { src: '../../plugin/math/math.js', async: true }
  136. ]
  137. });
  138. </script>
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