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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -215,79 +215,6 @@ "\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. " ] } ], "metadata": { -
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -265,11 +265,9 @@ "\n", "### Display\n", "\n", "$$ \\begin{array}{c} y_1 \\\\\\\n", "y_2 \\mathtt{t}_i \\\\\\\n", "z_{3,4} \\end{array} $$\n", "\n", "$$\n", "\\begin{array}{c}\n", -
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -266,11 +266,9 @@ "### Display\n", "\n", "$$\n", "\\begin{array}{c} y_1 \\\\\\\n", "y_2 \\mathtt{t}_i \\\\\\\n", "z_{3,4} \\end{array}\n", "$$\n", "\n", "$$\n", -
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -206,9 +206,13 @@ "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", "\n", "``` \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", "\n", "## Display\n", "\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. " ] }, @@ -245,7 +249,8 @@ "```\n", "\n", "```\n", "$$\n", "\\begin{eqnarray} \n", "x' &=& &x \\sin\\phi &+& z \\cos\\phi \\\\\n", "z' &=& - &x \\cos\\phi &+& z \\sin\\phi \\\\\n", "\\end{eqnarray}\n", @@ -276,10 +281,12 @@ "\\end{array}\n", "$$\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", "x=4\n", -
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -18,14 +18,19 @@ "---\n", "\n", "## The Lorenz Equations\n", "\n", "### Source\n", "\n", "```latex\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", "\n", "### Display\n", "\n", "\\begin{aligned}\n", "\\dot{x} & = \\sigma(y-x) \\\\\n", "\\dot{y} & = \\rho x - y - xz \\\\\n", @@ -38,12 +43,17 @@ "metadata": {}, "source": [ "## The Cauchy-Schwarz Inequality\n", "\n", "### Source\n", "\n", "```latex\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", "\n", "### Display\n", "\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*}" @@ -54,16 +64,21 @@ "metadata": {}, "source": [ "## A Cross Product Formula\n", "\n", "### Source\n", "\n", "```latex\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", "\n", "### Display\n", "\n", "\\begin{equation*}\n", "\\mathbf{V}_1 \\times \\mathbf{V}_2 = \\begin{vmatrix}\n", "\\mathbf{i} & \\mathbf{j} & \\mathbf{k} \\\\\n", @@ -78,12 +93,17 @@ "metadata": {}, "source": [ "## The probability of getting \\(k\\) heads when flipping \\(n\\) coins is\n", "\n", "### Source\n", "\n", "```latex\n", "\\begin{equation*}\n", "P(E) = {n \\choose k} p^k (1-p)^{ n-k} \n", "\\end{equation*}\n", "```\n", "\n", "### Display\n", "\n", "\\begin{equation*}\n", "P(E) = {n \\choose k} p^k (1-p)^{ n-k} \n", "\\end{equation*}" @@ -94,14 +114,19 @@ "metadata": {}, "source": [ "## An Identity of Ramanujan\n", "\n", "### Source\n", "\n", "```latex\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", "\n", "### Display\n", "\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", @@ -114,14 +139,19 @@ "metadata": {}, "source": [ "## A Rogers-Ramanujan Identity\n", "\n", "### Source\n", "\n", "```latex\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", "\n", "### Display\n", "\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", @@ -134,14 +164,19 @@ "metadata": {}, "source": [ "## Maxwell's Equations\n", "\n", "### Source\n", "\n", "```latex\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", "\n", "### Display\n", "\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", @@ -188,7 +223,9 @@ "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", "```\n", "$$\n", "\\begin{array}{c}\n", "y_1 \\\\\\\n", "y_2 \\mathtt{t}_i \\\\\\\n", @@ -211,7 +248,8 @@ "$$\\begin{eqnarray} \n", "x' &=& &x \\sin\\phi &+& z \\cos\\phi \\\\\n", "z' &=& - &x \\cos\\phi &+& z \\sin\\phi \\\\\n", "\\end{eqnarray}\n", "$$\n", "```\n", "\n", "```\n", @@ -221,6 +259,7 @@ "```\n", "\n", "### Display\n", "\n", "$$\n", "\\begin{array}{c}\n", "y_1 \\\\\\\n", -
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,272 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Grabbed from https://github.com/odewahn/ipynb-examples.\n", "\n", "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", "Equation numbering and referencing will be available in a future version of IPython." ] }, { "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": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }