{"id":252,"date":"2019-04-20T18:44:43","date_gmt":"2019-04-20T22:44:43","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/?post_type=chapter&p=252"},"modified":"2019-05-27T20:29:55","modified_gmt":"2019-05-28T00:29:55","slug":"motivating-examples","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/chapter\/motivating-examples\/","title":{"raw":"Motivating Examples","rendered":"Motivating Examples"},"content":{"raw":"Latex is best known for typesetting math equations. However, many packages have been developed to create other difficult to typeset elements including plots, chemical equations, multi-lingual documents, and music. Below are examples of some of the applications of Latex.\r\n\r\n

Mathematics<\/h1>\r\nSuppose we want to solve the general quadratic equation [latex]ax^2 + bx + c = 0[\/latex]. If you isolate for x, you derive the well-known quadratic formula:\r\n[latex]$$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}.$$[\/latex]\r\n\r\nThe default distribution of Latex offers over 10,000 symbols.<\/a> So, you can easily typeset most equations:\r\n[latex]\r\n\\begin{tabular}{r c l}\r\n$\\displaystyle |L_\\beta(f) - L_\\beta(g)|$ &=& $\\int_a^b f(x) - g(x) d \\beta$\\\\\r\n&=& $\\displaystyle \\sup_{P,T} \\{ \\sum_{i=1}^n f(t_i) - g(t_i) \\Delta \\beta \\}$\\\\\r\n&=& $\\displaystyle \\sup_{P,T} \\{ \\sum_{i =1}^n \\frac{\\epsilon}{2 (\\beta(b) - \\beta(a))} \\Delta \\beta \\}$\\\\\r\n&=& $\\displaystyle \\frac{\\epsilon}{2(\\beta(b) - \\beta(a))} (\\beta(b) - \\beta(a))$\\\\\r\n&=& $\\displaystyle \\frac{\\epsilon}{2}$\\\\\r\n\\end{tabular}\r\n[\/latex]\r\n\r\n

Chemical Equations:<\/h1>\r\n[latex]\r\n\\begin{tabular}{l}\r\n\\ce{Na2SO4 ->[H2O] Na+ + SO4^2-}\\\\\r\n\\ce{(2Na+,SO4^2- ) + (Ba^2+, 2Cl- ) -> BaSO4 v + 2NaCl}\r\n\\end{tabular}\r\n[\/latex]\r\n\r\nCredit: Stack Exchange<\/a>\r\n\r\n

Phonetic Transcription:<\/h1>\r\n[latex]\r\n\\begin{tabular}{c | c| c| c | c}\r\n{\\bf Gloss} & `innate' & `intolerant' & `impolite' & `inconsistent'\\\\ \\hline\r\n{\\bf UR} & \\ipaUR{IneIt} & \\ipaUR{IntAl\\s{r}\\s{n}t} & \\ipaUR{ InpAUlAIt} & \\ipaUR{Ink@nsIst\\s{n}t}\\\\ \\hline\r\n{\\bf Assimilation} & NA & NA & \\ipa{ I{\\bf m}pAUlAIt} & \\ipa{I{\\bf \\ipa{N}}k@nsIst\\s{n}t}\\\\ \\hline\r\n{\\bf SR} & [\\ipa{IneIt}] & [\\ipa{intAl\\s{r}\\s{n}t}]& [\\ipa{ImpAUlAIt}] & [\\ipa{iNk@nsIst\\s{n}t}]\\\\\r\n\\end{tabular}\r\n[\/latex]\r\n\r\n

Music:<\/h1>\r\n[latex]\r\n\\begin{music}\r\n\\parindent10mm\r\n\\instrumentnumber{1}\r\n\\setname1{Piano}\r\n\\setstaffs1{2}\r\n\\generalmeter{\\meterfrac44}\r\n\\startextract\r\n\u02c7\u02c7\u02c7\u02c7\u02c7\u02c7\u02c7\r\n% a single instrument\r\n% whose name is Piano\r\n% with two staffs\r\n% 4\/4 meter chosen\r\n\u02c7\r\n\u02c7\u02c7\u02c7\u02c7\r\n% starting real score\r\n\\Notes\\ibu0f0\\qb0{cge}\\tbu0\\qb0g|\\hl j\\en\r\n\\Notes\\ibu0f0\\qb0{cge}\\tbu0\\qb0g|\\ql l\\sk\\ql n\\en\r\n\\bar\r\n\\Notes\\ibu0f0\\qb0{dgf}|\\qlp i\\en\r\n\\notes\\tbu0\\qb0g|\\ibbl1j3\\qb1j\\tbl1\\qb1k\\en\r\n\\Notes\\ibu0f0\\qb0{cge}\\tbu0\\qb0g|\\hl j\\en\r\n\\zendextract % terminate excerpt\r\n\\end{music}\r\n[\/latex]\r\nCredit: Musixtex Documentation<\/a>\r\n\r\n

Plots:<\/h1>\r\n[latex]\r\n\\begin{tikzpicture}\r\n\\begin{axis}[xlabel=$x$, ylabel=$y$]\r\n\\addplot3[surf,domain=-180:180,samples=40] {((x-y)\/180)*sin(0.5*x)*cos(1.5*y)};\r\n\\end{axis}\r\n\\end{tikzpicture}\r\n[\/latex]","rendered":"

Latex is best known for typesetting math equations. However, many packages have been developed to create other difficult to typeset elements including plots, chemical equations, multi-lingual documents, and music. Below are examples of some of the applications of Latex.<\/p>\n

Mathematics<\/h1>\n

Suppose we want to solve the general quadratic equation \"ax^2 + bx + c = 0\". If you isolate for x, you derive the well-known quadratic formula:<\/p>\n

  <\/span>   <\/span>\"$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$$\"<\/p>\n

The default distribution of Latex offers over 10,000 symbols.<\/a> So, you can easily typeset most equations:
\n\"\begin{tabular}{r c l}<\/p>\n

Chemical Equations:<\/h1>\n

\"\begin{tabular}{l}<\/p>\n

Credit: Stack Exchange<\/a><\/p>\n

Phonetic Transcription:<\/h1>\n

\"\begin{tabular}{c | c| c| c | c}<\/p>\n

Music:<\/h1>\n

\"\begin{music}
\nCredit: Musixtex Documentation<\/a><\/p>\n

Plots:<\/h1>\n

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