Show More
Typesetting Math Using MathJax.ipynb
346 lines
| 10.8 KiB
| text/plain
|
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", | |||
| "These equation reference examples are adapted from an [example page in the MathJax documentation](http://cdn.mathjax.org/mathjax/latest/test/sample-eqrefs.html). Note that it's okay to reference equations across cells. Click inside this cell to see the source.\n", | |||
| "\n", | |||
| "## Labeled equations and references\n", | |||
| "\n", | |||
| "Here is a labeled equation:\n", | |||
| "\\begin{equation}\n", | |||
| "x+1\\over\\sqrt{1-x^2}\\label{ref1}\n", | |||
| "\\end{equation}\n", | |||
| "\n", | |||
| "with a reference to ref1: \\ref{ref1},\n", | |||
| "and another numbered one with no label:\n", | |||
| "\\begin{equation}\n", | |||
| "x+1\\over\\sqrt{1-x^2}\n", | |||
| "\\end{equation}" | |||
| ] | |||
| }, | |||
| { | |||
| "cell_type": "markdown", | |||
| "metadata": {}, | |||
| "source": [ | |||
| "## \\nonumber and equation*\n", | |||
| "\n", | |||
| "This one uses \\nonumber:\n", | |||
| "\\begin{equation}\n", | |||
| "x+1\\over\\sqrt{1-x^2}\\nonumber\n", | |||
| "\\end{equation}\n", | |||
| "\n", | |||
| "Here's one with the equation* environment:\n", | |||
| "\\begin{equation*}\n", | |||
| "x+1\\over\\sqrt{1-x^2}\n", | |||
| "\\end{equation*}" | |||
| ] | |||
| }, | |||
| { | |||
| "cell_type": "markdown", | |||
| "metadata": {}, | |||
| "source": [ | |||
| "## Forward references\n", | |||
| "\n", | |||
| "This is a forward reference [\\ref{ref2}] and another \\eqref{ref2} for the \n", | |||
| "following equation:\n", | |||
| "\n", | |||
| "\\begin{equation}\n", | |||
| "x+1\\over\\sqrt{1-x^2}\\label{ref2}\n", | |||
| "\\end{equation}\n", | |||
| "\n", | |||
| "More math:\n", | |||
| "\\begin{equation}\n", | |||
| "x+1\\over\\sqrt{1-x^2}\n", | |||
| "\\end{equation}" | |||
| ] | |||
| }, | |||
| { | |||
| "cell_type": "markdown", | |||
| "metadata": {}, | |||
| "source": [ | |||
| "### References inline and in environments\n", | |||
| "\n", | |||
| "Here is a ref inside math: $\\ref{ref2}+1$ and text after it.\n", | |||
| "\n", | |||
| "\\begin{align} \n", | |||
| "x& = y_1-y_2+y_3-y_5+y_8-\\dots \n", | |||
| "&& \\text{by \\eqref{ref1}}\\\\ \n", | |||
| "& = y'\\circ y^* && \\text{(by \\eqref{ref3})}\\\\ \n", | |||
| "& = y(0) y' && \\text {by Axiom 1.} \n", | |||
| "\\end{align} \n", | |||
| "\n", | |||
| "### Missing references\n", | |||
| "Here's a bad ref [\\ref{ref4}] to a nonexistent label.\n", | |||
| "\n", | |||
| "### Numbering align environments\n", | |||
| "An alignment:\n", | |||
| "\\begin{align}\n", | |||
| "a&=b\\label{ref3}\\cr\n", | |||
| "&=c+d\n", | |||
| "\\end{align}\n", | |||
| "and a starred one:\n", | |||
| "\\begin{align*}\n", | |||
| "a&=b\\cr\n", | |||
| "&=c+d\n", | |||
| "\\end{align*}" | |||
| ] | |||
| }, | |||
| { | |||
| "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", | |||
| "$$" | |||
| ] | |||
| }, | |||
| { | |||
| "cell_type": "code", | |||
| "collapsed": false, | |||
| "input": [], | |||
| "language": "python", | |||
| "metadata": {}, | |||
| "outputs": [] | |||
| } | |||
| ], | |||
| "metadata": {} | |||
| } | |||
| ] | |||
| } |