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@@ -93,6 +93,79 @@
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\]
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</section>
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+ <section>
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+ <section>
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+ <h3>The Lorenz Equations</h3>
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+
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+ <div class="fragment">
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+ \[\begin{aligned}
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+ \dot{x} & = \sigma(y-x) \\
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+ \dot{y} & = \rho x - y - xz \\
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+ \dot{z} & = -\beta z + xy
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+ \end{aligned} \]
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+ </div>
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+ </section>
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+
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+ <section>
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+ <h3>The Cauchy-Schwarz Inequality</h3>
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+
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+ <div class="fragment">
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+ \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
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+ </div>
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+ </section>
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+
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+ <section>
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+ <h3>A Cross Product Formula</h3>
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+
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+ <div class="fragment">
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+ \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
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+ \mathbf{i} & \mathbf{j} & \mathbf{k} \\
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+ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
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+ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
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+ \end{vmatrix} \]
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+ </div>
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+ </section>
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+
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+ <section>
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+ <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
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+
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+ <div class="fragment">
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+ \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
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+ </div>
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+ </section>
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+
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+ <section>
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+ <h3>An Identity of Ramanujan</h3>
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+
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+ <div class="fragment">
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+ \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
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+ 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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+ {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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+ </div>
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+ </section>
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+
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+ <section>
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+ <h3>A Rogers-Ramanujan Identity</h3>
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+
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+ <div class="fragment">
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+ \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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+ \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
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+ </div>
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+ </section>
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+
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+ <section>
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+ <h3>Maxwell’s Equations</h3>
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+
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+ <div class="fragment">
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+ \[ \begin{aligned}
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+ \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
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+ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
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+ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
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+ \]
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+ </div>
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+ </section>
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+ </section>
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+
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</div>
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</div>
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@@ -103,9 +176,11 @@
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<script>
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Reveal.initialize({
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+ history: true,
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transition: 'linear',
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math: {
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+ // host: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js',
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mode: 'TeX-AMS_HTML-full'
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},
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