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  1. <!doctype html>
  2. <html lang="en">
  3. <head>
  4. <meta charset="utf-8">
  5. <title>reveal.js - Math Plugin</title>
  6. <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
  7. <link rel="stylesheet" href="../../css/reveal.css">
  8. <link rel="stylesheet" href="../../css/theme/night.css" id="theme">
  9. </head>
  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. <h3>TeX Macros</h3>
  64. Here is a common vector space:
  65. \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
  66. used in functional analysis.
  67. </section>
  68. <section>
  69. <section>
  70. <h3>The Lorenz Equations</h3>
  71. <div class="fragment">
  72. \[\begin{aligned}
  73. \dot{x} &amp; = \sigma(y-x) \\
  74. \dot{y} &amp; = \rho x - y - xz \\
  75. \dot{z} &amp; = -\beta z + xy
  76. \end{aligned} \]
  77. </div>
  78. </section>
  79. <section>
  80. <h3>The Cauchy-Schwarz Inequality</h3>
  81. <div class="fragment">
  82. \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
  83. </div>
  84. </section>
  85. <section>
  86. <h3>A Cross Product Formula</h3>
  87. <div class="fragment">
  88. \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
  89. \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  90. \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
  91. \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
  92. \end{vmatrix} \]
  93. </div>
  94. </section>
  95. <section>
  96. <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
  97. <div class="fragment">
  98. \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
  99. </div>
  100. </section>
  101. <section>
  102. <h3>An Identity of Ramanujan</h3>
  103. <div class="fragment">
  104. \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
  105. 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
  106. {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
  107. </div>
  108. </section>
  109. <section>
  110. <h3>A Rogers-Ramanujan Identity</h3>
  111. <div class="fragment">
  112. \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
  113. \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
  114. </div>
  115. </section>
  116. <section>
  117. <h3>Maxwell&#8217;s Equations</h3>
  118. <div class="fragment">
  119. \[ \begin{aligned}
  120. \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  121. \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  122. \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  123. \]
  124. </div>
  125. </section>
  126. <section>
  127. <h3>TeX Macros</h3>
  128. Here is a common vector space:
  129. \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
  130. used in functional analysis.
  131. </section>
  132. </section>
  133. </div>
  134. </div>
  135. <script src="../../js/reveal.js"></script>
  136. <script>
  137. Reveal.initialize({
  138. history: true,
  139. transition: 'linear',
  140. math: {
  141. // mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
  142. config: 'TeX-AMS_HTML-full',
  143. TeX: {
  144. Macros: {
  145. R: '\\mathbb{R}',
  146. set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ]
  147. }
  148. }
  149. },
  150. dependencies: [
  151. { src: '../../plugin/math/math.js', async: true }
  152. ]
  153. });
  154. </script>
  155. </body>
  156. </html>