var DATA = { links: [{ name: 'Ace Editor', link: 'https://ace.c9.io/', }, { name: 'Bootstrap', link: 'https://getbootstrap.com/', }, { name: 'Font Awesome', link: 'http://fontawesome.io/', }, { name: 'jQuery', link: 'https://jquery.com', }, { name: 'MathJax', link: 'https://www.mathjax.org/', }], examples: [{ name: "Some Limit", text: [ "\\lim_{x \\to \\infty}{\\frac{1}{x^2}}", ], }, { name: "Quadratic Formula", text: [ "\\text{Quadratic Formula} \\\\", "x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}", ], }, { name: "Cross Product", 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*}", ], }, { name: "Derivative Rules", 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*}", ], }, { name: "Cubic Formula", 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*}", ], }, { name: "Linear Regression", 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*}", ], }, { name: "Permutations and Combinations", text: [ "\\text{Permutations and Combinations} \\\\", "", "\\begin{array}{|c|c|c|c|}", "\\hline", " \\text{Name} &", " \\text{Ordering} &", " \\text{Repetition} &", " \\text{Formula} \\\\ ", "\\hline", " \\text{Permutation}&", " \\text{Yes} &", " \\text{Yes} &", " n^k \\\\", "\\hline", " \\text{Permutation} &", " \\text{Yes} &", " \\text{No} &", " \\frac{n!}{(n - k)!} \\\\", "\\hline", " \\text{Combination} &", " \\text{No} &", " \\text{Yes} &", " % \\frac{(n + k - 1)!}{k!(n - 1)!} = ", " {n + k - 1 \\choose k} \\\\ ", "\\hline", " \\text{Combination} &", " \\text{No} &", " \\text{No} &", " % \\frac{n!}{k!(n - k)!} = ", " {n \\choose k} \\\\ ", "\\hline", "\\end{array} \\\\", "", "\\text{ } \\\\", "\\text{Permutations and Combinations} \\\\", "\\begin{array}{|c|c|c|}", "\\hline", " \\text{Name} &", " \\text{With Repetition} &", " \\text{Without Repetition} \\\\", "\\hline", " \\text{Permutation} &", " n^k & ", " \\frac{n!}{(n - k)!} \\\\", "\\hline", " \\text{Combination} &", " {n + k - 1 \\choose k} &", " {n \\choose k} \\\\", "\\hline", "\\end{array} \\\\", "", "", "\\text{ } \\\\", "\\text{Definitions} \\\\", "\\begin{array}{|c|c|c|l|}", "\\hline", " \\text{Denoted} &", " \\text{Read As} &", " \\text{Formula} \\\\", "\\hline", " n! &", " \\text{\"N factorial\"} &", " n! = \\prod_{i=1}^n{i} \\\\", " % = 1 \\cdot 2 \\cdot \\ldots \\cdot (n - 1) \\cdot n \\\\", "\\hline", " {n \\choose k} &", " \\text{\"N choose K\"} &", " {n \\choose k} = \\frac{n!}{k!(n - k)!} \\\\", "\\hline", "\\end{array}", ], }], themes: [ "ambiance", "chaos", "chrome", "clouds", "clouds_midnight", "cobalt", "crimson_editor", "dawn", "dracula", "dreamweaver", "eclipse", "github", "gob", "gruvbox", "idle_fingers", "iplastic", "katzenmilch", "kr_theme", "kuroir", "merbivore", "merbivore_soft", "mono_industrial", "monokai", "pastel_on_dark", "solarized_dark", "solarized_light", "sqlserver", "terminal", "textmate", "tomorrow", "tomorrow_night_blue", "tomorrow_night_bright", "tomorrow_night_eighties", "tomorrow_night", "twilight", "vibrant_ink", "xcode", ], };