META-INF.resources.js.revealjs.2.6.1.test.examples.math.html Maven / Gradle / Ivy

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		reveal.js - Math Plugin

		

		
		
	

	

		

			

				
					reveal.js Math Plugin
					A thin wrapper for MathJax
				

				
					The Lorenz Equations

					\[\begin{aligned}
					\dot{x} & = \sigma(y-x) \\
					\dot{y} & = \rho x - y - xz \\
					\dot{z} & = -\beta z + xy
					\end{aligned} \]
				

				
					The Cauchy-Schwarz Inequality

					 $\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$ 
				

				
					A Cross Product Formula

					\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
					\mathbf{i} & \mathbf{j} & \mathbf{k} \\
					\frac{\partial X}{\partial u} &  \frac{\partial Y}{\partial u} & 0 \\
					\frac{\partial X}{\partial v} &  \frac{\partial Y}{\partial v} & 0
					\end{vmatrix}  \]
				

				
					The probability of getting \(k\) heads when flipping \(n\) coins is

					\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]
				

				
					An Identity of Ramanujan

					\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
					1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
					{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
				

				
					A Rogers-Ramanujan Identity

					\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
					\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
				

				
					Maxwell’s Equations

					\[  \begin{aligned}
					\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
					\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
					\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
					\]
				

				
					
						The Lorenz Equations

						
							\[\begin{aligned}
							\dot{x} & = \sigma(y-x) \\
							\dot{y} & = \rho x - y - xz \\
							\dot{z} & = -\beta z + xy
							\end{aligned} \]
						
					

					
						The Cauchy-Schwarz Inequality

						
							\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
						
					

					
						A Cross Product Formula

						
							\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
							\mathbf{i} & \mathbf{j} & \mathbf{k} \\
							\frac{\partial X}{\partial u} &  \frac{\partial Y}{\partial u} & 0 \\
							\frac{\partial X}{\partial v} &  \frac{\partial Y}{\partial v} & 0
							\end{vmatrix}  \]
						
					

					
						The probability of getting \(k\) heads when flipping \(n\) coins is

						
							\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]
						
					

					
						An Identity of Ramanujan

						
							\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
							1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
							{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
						
					

					
						A Rogers-Ramanujan Identity

						
							\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
							\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
						
					

					
						Maxwell’s Equations

						
							\[  \begin{aligned}
							\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
							\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
							\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
							\]