Typesetting Math Using MathJax.ipynb
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TextLexer
Aron Ahmadia
|
r8567 | { | |
"metadata": { | |||
"name": "Typesetting Math Using MathJax" | |||
}, | |||
"nbformat": 3, | |||
"nbformat_minor": 0, | |||
"worksheets": [ | |||
{ | |||
"cells": [ | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"The Markdown parser included in IPython is MathJax-aware. This means that you can freely mix in mathematical expressions using the [MathJax subset of Tex and LaTeX](http://docs.mathjax.org/en/latest/tex.html#tex-support). [Some examples from the MathJax site](http://www.mathjax.org/demos/tex-samples/) are reproduced below, as well as the Markdown+TeX source." | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"# Motivating Examples\n", | |||
"\n", | |||
"---\n", | |||
"\n", | |||
"## The Lorenz Equations\n", | |||
"### Source\n", | |||
"```\\begin{aligned}\n", | |||
"\\dot{x} & = \\sigma(y-x) \\\\\n", | |||
"\\dot{y} & = \\rho x - y - xz \\\\\n", | |||
"\\dot{z} & = -\\beta z + xy\n", | |||
"\\end{aligned}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{aligned}\n", | |||
"\\dot{x} & = \\sigma(y-x) \\\\\n", | |||
"\\dot{y} & = \\rho x - y - xz \\\\\n", | |||
"\\dot{z} & = -\\beta z + xy\n", | |||
"\\end{aligned}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"## The Cauchy-Schwarz Inequality\n", | |||
"### Source\n", | |||
"```\\begin{equation*}\n", | |||
"\\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)\n", | |||
"\\end{equation*}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{equation*}\n", | |||
"\\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)\n", | |||
"\\end{equation*}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"## A Cross Product Formula\n", | |||
"### Source\n", | |||
"```\\begin{equation*}\n", | |||
"\\mathbf{V}_1 \\times \\mathbf{V}_2 = \\begin{vmatrix}\n", | |||
"\\mathbf{i} & \\mathbf{j} & \\mathbf{k} \\\\\n", | |||
"\\frac{\\partial X}{\\partial u} & \\frac{\\partial Y}{\\partial u} & 0 \\\\\n", | |||
"\\frac{\\partial X}{\\partial v} & \\frac{\\partial Y}{\\partial v} & 0\n", | |||
"\\end{vmatrix} \n", | |||
"\\end{equation*}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{equation*}\n", | |||
"\\mathbf{V}_1 \\times \\mathbf{V}_2 = \\begin{vmatrix}\n", | |||
"\\mathbf{i} & \\mathbf{j} & \\mathbf{k} \\\\\n", | |||
"\\frac{\\partial X}{\\partial u} & \\frac{\\partial Y}{\\partial u} & 0 \\\\\n", | |||
"\\frac{\\partial X}{\\partial v} & \\frac{\\partial Y}{\\partial v} & 0\n", | |||
"\\end{vmatrix} \n", | |||
"\\end{equation*}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"## The probability of getting \\(k\\) heads when flipping \\(n\\) coins is\n", | |||
"### Source\n", | |||
"```\\begin{equation*}\n", | |||
"P(E) = {n \\choose k} p^k (1-p)^{ n-k} \n", | |||
"\\end{equation*}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{equation*}\n", | |||
"P(E) = {n \\choose k} p^k (1-p)^{ n-k} \n", | |||
"\\end{equation*}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"## An Identity of Ramanujan\n", | |||
"### Source\n", | |||
"```\\begin{equation*}\n", | |||
"\\frac{1}{\\Bigl(\\sqrt{\\phi \\sqrt{5}}-\\phi\\Bigr) e^{\\frac25 \\pi}} =\n", | |||
"1+\\frac{e^{-2\\pi}} {1+\\frac{e^{-4\\pi}} {1+\\frac{e^{-6\\pi}}\n", | |||
"{1+\\frac{e^{-8\\pi}} {1+\\ldots} } } } \n", | |||
"\\end{equation*}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{equation*}\n", | |||
"\\frac{1}{\\Bigl(\\sqrt{\\phi \\sqrt{5}}-\\phi\\Bigr) e^{\\frac25 \\pi}} =\n", | |||
"1+\\frac{e^{-2\\pi}} {1+\\frac{e^{-4\\pi}} {1+\\frac{e^{-6\\pi}}\n", | |||
"{1+\\frac{e^{-8\\pi}} {1+\\ldots} } } } \n", | |||
"\\end{equation*}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"## A Rogers-Ramanujan Identity\n", | |||
"### Source\n", | |||
"```\\begin{equation*}\n", | |||
"1 + \\frac{q^2}{(1-q)}+\\frac{q^6}{(1-q)(1-q^2)}+\\cdots =\n", | |||
"\\prod_{j=0}^{\\infty}\\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},\n", | |||
"\\quad\\quad \\text{for $|q|<1$}. \n", | |||
"\\end{equation*}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{equation*}\n", | |||
"1 + \\frac{q^2}{(1-q)}+\\frac{q^6}{(1-q)(1-q^2)}+\\cdots =\n", | |||
"\\prod_{j=0}^{\\infty}\\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},\n", | |||
"\\quad\\quad \\text{for $|q|<1$}. \n", | |||
"\\end{equation*}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"## Maxwell's Equations\n", | |||
"### Source\n", | |||
"```\\begin{aligned}\n", | |||
"\\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 \\\\\n", | |||
"\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n", | |||
"\\nabla \\cdot \\vec{\\mathbf{B}} & = 0 \n", | |||
"\\end{aligned}\n", | |||
"```\n", | |||
"### Display\n", | |||
"\\begin{aligned}\n", | |||
"\\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 \\\\\n", | |||
"\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n", | |||
"\\nabla \\cdot \\vec{\\mathbf{B}} & = 0 \n", | |||
"\\end{aligned}" | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"# Equation Numbering and References\n", | |||
"\n", | |||
"---\n", | |||
"\n", | |||
Aron Ahmadia
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r8660 | "Equation numbering and referencing will be available in a future version of IPython." | |
Aron Ahmadia
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r8567 | ] | |
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"# Inline Typesetting (Mixing Markdown and TeX)\n", | |||
"\n", | |||
"---\n", | |||
"\n", | |||
"While display equations look good for a page of samples, the ability to mix math and *formatted* **text** in a paragraph is also important.\n", | |||
"\n", | |||
"## Source\n", | |||
"``` This expression $\\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a **[Markdown-formatted](http://daringfireball.net/projects/markdown/)** sentence. \n", | |||
"```\n", | |||
"## Display\n", | |||
"This expression $\\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a **[Markdown-formatted](http://daringfireball.net/projects/markdown/)** sentence. " | |||
] | |||
}, | |||
{ | |||
"cell_type": "markdown", | |||
"metadata": {}, | |||
"source": [ | |||
"# Other Syntax\n", | |||
"\n", | |||
"---\n", | |||
"\n", | |||
"You will notice in other places on the web that `$$` are needed explicitly to begin and end MathJax typesetting. This is **not** required if you will be using TeX environments, but the IPython notebook will accept this syntax on legacy notebooks. \n", | |||
"\n", | |||
"### Source\n", | |||
"```$$\n", | |||
"\\begin{array}{c}\n", | |||
"y_1 \\\\\\\n", | |||
"y_2 \\mathtt{t}_i \\\\\\\n", | |||
"z_{3,4}\n", | |||
"\\end{array}\n", | |||
"$$\n", | |||
"```\n", | |||
"\n", | |||
"```\n", | |||
"$$\n", | |||
"\\begin{array}{c}\n", | |||
"y_1 \\cr\n", | |||
"y_2 \\mathtt{t}_i \\cr\n", | |||
"y_{3}\n", | |||
"\\end{array}\n", | |||
"$$\n", | |||
"```\n", | |||
"\n", | |||
"```\n", | |||
"$$\\begin{eqnarray} \n", | |||
"x' &=& &x \\sin\\phi &+& z \\cos\\phi \\\\\n", | |||
"z' &=& - &x \\cos\\phi &+& z \\sin\\phi \\\\\n", | |||
"\\end{eqnarray}$$\n", | |||
"```\n", | |||
"\n", | |||
"```\n", | |||
"$$\n", | |||
"x=4\n", | |||
"$$\n", | |||
"```\n", | |||
"\n", | |||
"### Display\n", | |||
"$$\n", | |||
"\\begin{array}{c}\n", | |||
"y_1 \\\\\\\n", | |||
"y_2 \\mathtt{t}_i \\\\\\\n", | |||
"z_{3,4}\n", | |||
"\\end{array}\n", | |||
"$$\n", | |||
"\n", | |||
"$$\n", | |||
"\\begin{array}{c}\n", | |||
"y_1 \\cr\n", | |||
"y_2 \\mathtt{t}_i \\cr\n", | |||
"y_{3}\n", | |||
"\\end{array}\n", | |||
"$$\n", | |||
"\n", | |||
"$$\\begin{eqnarray} \n", | |||
"x' &=& &x \\sin\\phi &+& z \\cos\\phi \\\\\n", | |||
"z' &=& - &x \\cos\\phi &+& z \\sin\\phi \\\\\n", | |||
"\\end{eqnarray}$$\n", | |||
"\n", | |||
"$$\n", | |||
"x=4\n", | |||
"$$" | |||
] | |||
} | |||
], | |||
"metadata": {} | |||
} | |||
] | |||
} |