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+<!DOCTYPE html>
+<html lang='en-US'>
+ <head>
+ <meta charset='utf-8'/>
+ <title>Mathy</title>
+ <link rel='stylesheet' type='text/css' href='css/font-awesome-4.7.0/css/font-awesome.min.css'/>
+ <link rel='stylesheet' type='text/css' href='js/bootstrap-3.3.7/css/bootstrap.min.css'/>
+ <link rel='stylesheet' type='text/css' href='js/bootstrap-3.3.7/css/bootstrap-theme.min.css'/>
+ <link rel='stylesheet' type='text/css' href='css/mathy.css' media='screen'/>
+ </head>
+
+ <body>
+ <div id='editor'>function foo(items) {
+ var x = 'All this is syntax highlighted';
+ return x;
+ }</div>
+ <div id='math-wrap'>
+ <div id='MathPreview'></div>
+ <div id='MathBuffer' style='visibility:hidden; position:absolute; top:0; left: 0'></div>
+ </div>
+
+ <div id='buttons' class='btn-toolbar'>
+ <div class='btn-group btn-group-sm dropup'>
+ <a
+ href='#'
+ class='btn btn-default dropdown-toggle'
+ title='load saved result'
+ data-toggle='dropdown'
+ >
+ <i class='fa fa-upload'></i>
+ Load
+ <i class='fa fa-caret-down'></i>
+ </a><!-- btn -->
+
+ <ul id='saves' class='dropdown-menu'>
+ </ul><!-- dropdown-menu -->
+ </div><!-- btn-group -->
+
+ <div class='btn-group btn-group-sm'>
+ <a
+ href='#'
+ id='btn-save'
+ class='btn btn-default'
+ title='save'
+ >
+ <i class='fa fa-save'></i>
+ Save
+ </a><!-- btn -->
+ </div><!-- btn-group -->
+
+ <div class='btn-group btn-group-sm pull-right dropup'>
+ <a
+ href='#'
+ class='btn btn-default dropdown-toggle'
+ title='get help'
+ data-toggle='dropdown'
+ >
+ <i class='fa fa-question-circle'></i>
+ Help
+ <i class='fa fa-caret-down'></i>
+ </a><!-- btn -->
+
+ <ul id='help' class='dropdown-menu'>
+ <li class='dropdown-header'>
+ Examples
+ </li>
+
+ <li>
+ <a
+ href='#'
+ class='example'
+ data-text='
+ \lim_{x \to \infty}{\frac{1}{x^2}}
+ '
+ >1. Some Limit</a>
+ </li>
+
+ <!-- li>
+ <a
+ href='#'
+ class='example'
+ data-text='
+ \begin{align*}
+ &= \int_0^2{x^2 + 5x + 2}\,\text{d}x \\
+ &= \int{x^2 + 5x + 2}\,\text{d}x \\
+ &= \frac{1}{3}x^3 + \frac{5}{2}x^2 + 2x + c \\
+ &= \frac{1}{3}2^3 + \frac{5}{2}2^2 + 2\times2 -
+ (\frac{1}{3}0^3 + \frac{5}{2}0^2 + 2\times0) \\
+ &= \frac{8}{3} + \frac{20}{2} + 4 \\
+ &= 14 + \frac{8}{3} \\
+ &= \frac{50}{3}
+ \end{align*}
+ '
+ >Test 2</a>
+ </li -->
+
+ <li>
+ <a
+ href='#'
+ class='example'
+ data-text='
+\text{Quadratic Formula} \\
+x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
+ '
+ >2. Quadratic Formula</a>
+ </li>
+
+ <li>
+ <a
+ href='#'
+ class='example'
+ data-text='
+\text{Cross Product via Matrix Determinant} \\
+
+\begin{align*}
+ \vec{a} \times \vec{b} & = \begin{vmatrix}
+ \hat{i} & \hat{j} & \hat{k} \\
+ \vec{a}_x & \vec{a}_y & \vec{a}_z \\
+ \vec{b}_x & \vec{b}_y & \vec{b}_z
+ \end{vmatrix} \\
+
+ & =
+ \begin{vmatrix}
+ \vec{a}_y & \vec{a}_z \\
+ \vec{b}_y & \vec{b}_z
+ \end{vmatrix} \hat{i} -
+
+ \begin{vmatrix}
+ \vec{a}_x & \vec{a}_z \\
+ \vec{b}_x & \vec{b}_z
+ \end{vmatrix} \hat{j} +
+
+ \begin{vmatrix}
+ \vec{a}_x & \vec{a}_y \\
+ \vec{b}_x & \vec{b}_y
+ \end{vmatrix} \hat{k} \\
+
+ & =
+ (\vec{a}_y\vec{b}_z - \vec{a}_z\vec{b}_y)\hat{i} -
+ (\vec{a}_x\vec{b}_z - \vec{a}_z\vec{b}_x)\hat{j} +
+ (\vec{a}_x\vec{b}_y - \vec{a}_x\vec{b}_y)\hat{k} \\
+
+ & =
+ \langle
+ \vec{a}_y\vec{b}_z - \vec{a}_z\vec{b}_y\text{, }
+ \vec{a}_x\vec{b}_z - \vec{a}_z\vec{b}_x\text{, }
+ \vec{a}_x\vec{b}_y - \vec{a}_y\vec{b}_z
+ \rangle \\
+
+ \vec{a} & = \langle2, 1, -1\rangle \\
+ \vec{b} & = \langle-3, 4, 1\rangle \\
+ \vec{a} \times \vec{b} & = \langle
+ (1)(1) - (-1)(4),
+ (2)(1) - (-1)(-3),
+ (2)(4) - (1)(-3)
+ \rangle \\
+
+ & = \langle
+ 5, 5, 11
+ \rangle \\
+ \vec{b} \times \vec{a} & = \langle
+ (4)(-1) - (1)(1),
+ (-3)(-1) - (1)(2),
+ (-3)(1) - (4)(2)
+ \rangle \\
+ & = \langle
+ -5, -5, -11
+ \rangle
+\end{align*}
+ '
+ >3. Cross Product</a>
+ </li>
+
+ <li>
+ <a
+ href='#'
+ class='example'
+ data-text="
+\text{Derivative Rules} \\
+
+\begin{align*}
+% sum/difference rule
+\frac{\text{d}}{\text{d}x} \,
+f(x) \pm g(x) &=
+\frac{\text{d}}{\text{d}x} \, f(x) \pm
+\frac{\text{d}}{\text{d}x} \, g(x) &
+\text{Sum/Difference Rule} \\
+
+% constant factor rule
+\frac{\text{d}}{\text{d}x} \,
+k f(x) &=
+k \frac{\text{d}}{\text{d}x} \, f(x) &
+\text{Constant Factor Rule} \\
+
+% constant rule
+\frac{\text{d}}{\text{d}x} \,
+k &=
+0 &
+\text{Constant Rule} \\
+
+% power rule
+\frac{\text{d}}{\text{d}x} \,
+x^n &=
+nx^{n-1} &
+\text{Power Rule} \\
+
+% exponent rule
+\frac{\text{d}}{\text{d}x} \,
+b^x &=
+b^xln(b) &
+\text{Exponent Rule} \\
+
+% chain rule
+\frac{\text{d}}{\text{d}x} \,
+f(g(x)) &=
+% (f \cdot g)(x) &=
+f'(g(x))g'(x) &
+\text{Chain Rule} \\
+
+% product rule
+\frac{\text{d}}{\text{d}x} \,
+f(x)g(x) &=
+f'(x)g(x) + f(x)g'(x) &
+\text{Product Rule} \\
+
+% quotient rule
+\frac{\text{d}}{\text{d}x} \,
+\frac{f(x)}{g(x)} &=
+\frac{f'(x)g(x) - f(x)g'(x)}{g(x)^2} &
+\text{Quotient Rule} \\
+
+% logarithm rule
+\frac{\text{d}}{\text{d}x} \,
+log_b{x} &=
+\frac{1}{x ln(b)} &
+\text{Logarithm Rule} \\
+
+\end{align*}
+"
+ >4. Derivative Rules</a>
+ </li>
+
+ <li>
+ <a
+ href='#'
+ class='example'
+ data-text="
+% https://math.vanderbilt.edu/schectex/courses/cubic/
+\text{The Cubic Formula} \\
+\begin{align*}
+% first term
+x &= \sqrt[3]{
+ % first term, first subterm
+ \left (
+ \frac{-b^3}{27a^3} +
+ \frac{bc}{6a^2} -
+ \frac{d}{2a}
+ \right )
+
+ +
+
+ \sqrt{
+ % first term, second subterm
+ \left (
+ \frac{-b^3}{27a^3} +
+ \frac{bc}{6a^2} -
+ \frac{d}{2a}
+ \right )^2
+
+ +
+
+ % first term, third subterm
+ \left (
+ \frac{c}{3a} -
+ \frac{b^2}{9a^2}
+ \right )^3
+ }
+} \\
+
+&+
+
+% second term
+\sqrt[3]{
+ % first term, second subterm
+ \left (
+ \frac{-b^3}{27a^3} +
+ \frac{bc}{6a^2} -
+ \frac{d}{2a}
+ \right )
+
+ -
+
+ \sqrt{
+ % second term, second subterm
+ \left (
+ \frac{-b^3}{27a^3} +
+ \frac{bc}{6a^2} -
+ \frac{d}{2a}
+ \right )^2
+
+ +
+
+ % second term, third subterm
+ \left (
+ \frac{c}{3a} -
+ \frac{b^2}{9a^2}
+ \right )^3
+ }
+} \\
+
+&-
+
+% third part
+\frac{b}{3a}
+\end{align*}
+ "
+ >5. Cubic Formula</a>
+ </li>
+ <li>
+ <a
+ href='#'
+ class='example'
+ data-text="
+\text{Linear Regression} \\
+
+\begin{align*}
+ m &= \frac{
+ \sum(x_i - \bar{x})(y_i - \bar{y} )
+ }{
+ \sum(x_i - \bar{x})^2
+ } \\
+
+ b &= \bar{y} - m\bar{x} \\
+
+ y &= mx + b
+\end{align*}
+ "
+ >6. Linear Regression</a>
+ </li>
+ <li class='divider'></li>
+ </ul><!-- dropdown-menu -->
+ </div><!-- btn-group -->
+
+ <div class='btn-group btn-group-sm pull-right'>
+ <a
+ href='#'
+ id='btn-config'
+ class='btn btn-default disabled'
+ title='edit settings'
+ >
+ <i class='fa fa-cog'></i>
+ Config
+ </a><!-- btn -->
+ </div><!-- btn-group -->
+ </div><!-- btn-toolbar -->
+
+ <script type="text/x-mathjax-config">
+ MathJax.Hub.Config({
+ showProcessingMessages: false,
+ tex2jax: { inlineMath: [['$','$'],['\\(','\\)']] }
+ });
+ </script>
+ <script type='text/javascript' src='js/jquery-3.1.1.min.js'></script>
+ <script type='text/javascript' src='js/bootstrap-3.3.7/js/bootstrap.min.js'></script>
+ <script type='text/javascript' src='js/ace/ace.js' charset='utf-8'></script>
+ <script type='text/javascript' src='js/MathJax-2.7.0/MathJax.js?config=TeX-AMS-MML_SVG'></script>
+ <script type='text/javascript' src='js/luigi-template-0.4.1.min.js'></script>
+ <script type='text/javascript' src='js/mathy.js'></script>
+ </body>
+</html>
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-21 23:55:33 +0000