{"id":138,"date":"2019-03-10T21:54:56","date_gmt":"2019-03-11T01:54:56","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/?post_type=chapter&p=138"},"modified":"2019-05-08T17:59:34","modified_gmt":"2019-05-08T21:59:34","slug":"equations","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/chapter\/equations\/","title":{"raw":"Equations","rendered":"Equations"},"content":{"raw":"

Commands<\/h2>\r\nLatex allows you to quickly write mathematical equations by specifying characters using commands you can type using the keyboard.\u00a0For example, we can write [latex] ax^2 + bx + c = 0 [\/latex] using the code\r\n\r\n[\u200clatex] ax^2 + bx + c = 0 [\/latex]<\/code>\r\n\r\nWhile some common math symbols like +\/- and exponentiation have a single symbol on the keyboard, most commands start with \"\\\" and then describe the command. An example of an equation that requires \\ commands is\u00a0[latex] \\cos^2 \\theta + \\sin^2 \\theta = 1 [\/latex], which requires commands for the sine, cosine, and angle:\r\n\r\n[\u200clatex] \\cos^2 \\theta + \\sin^2 \\theta = 1 [\/latex]<\/code>\r\n\r\nThe table below shows some common \"\\\" commands for symbols, in addition to the trigonometric functions and Greek letters used in the previous example.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Algebra<\/strong><\/td>\r\nCalculus<\/strong><\/td>\r\nLogic<\/strong><\/td>\r\n<\/tr>\r\n
[latex]\\times[\/latex]<\/td>\r\n\\times<\/td>\r\n[latex]\\lim[\/latex]<\/td>\r\n\\lim<\/td>\r\n[latex]\\neg[\/latex]<\/td>\r\n\\neg<\/td>\r\n<\/tr>\r\n
[latex]\\div[\/latex]<\/td>\r\n\\div<\/td>\r\n[latex]\\int[\/latex]<\/td>\r\n\\int<\/td>\r\n[latex]\\rightarrow[\/latex]<\/td>\r\n\\rightarrow<\/td>\r\n<\/tr>\r\n
[latex]\\pm[\/latex]<\/td>\r\n\\pm<\/td>\r\n[latex]\\nabla[\/latex]<\/td>\r\n\\nabla<\/td>\r\n[latex]\\exists[\/latex]<\/td>\r\n\\exists<\/td>\r\n<\/tr>\r\n
[latex]\\approx[\/latex]<\/td>\r\n\\approx<\/td>\r\n[latex]\\partial[\/latex]<\/td>\r\n\\partial<\/td>\r\n[latex]\\forall[\/latex]<\/td>\r\n\\forall<\/td>\r\n<\/tr>\r\n
[latex]\\equiv[\/latex]<\/td>\r\n\\equiv<\/td>\r\n[latex]\\sum[\/latex]<\/td>\r\n\\sum<\/td>\r\n[latex]\\in[\/latex]<\/td>\r\n\\in<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nCommands can also take arguments using curly brackets. For example, the fraction and square root in the quadratic formula both take arguments.\r\n\r\n[\u200clatex] x = \\frac{-b \\pm \\sqrt{b^2 + 4ac}}{2a} [\/latex]<\/code>\r\n\r\n[latex] \\displaystyle x = \\frac{-b \\pm \\sqrt{b^2 + 4ac}}{2a} [\/latex]\r\n\r\nSuperscripts and subscripts are also considered arguments. Use ^{} to create a superscript. If, no brackets are used, only the first character will be part of the superscript.\r\n[\u200clatex]e^{i \\pi} = -1[\/latex]<\/code>\r\n\r\n[latex]\\displaystyle e^{i \\pi} = -1[\/latex]\r\n\r\nUse _{} to create a subscript. Again, if no brackets are used only the first character will be part of the subscript.\r\n\r\n[\u200clatex] x_1 + x_2 = 2x_3[\/latex]<\/code>\r\n\r\n[latex]\\displaystyle x_1 + x_2 = 2x_3[\/latex]\r\n\r\nYou can add a subscript and a superscript to the same item. The order of the subscript and superscript does not matter. For example:\r\n\r\n[\u200clatex]\\int_{a}^{b} u dv = u(x)v(x)|_a^b - \\int^{b}_a v du [\/latex]<\/code>\r\n\r\n[latex]\\displaystyle \\int_{a}^{b} u dv = u(x)v(x)|_a^b - \\int^{b}_a v du [\/latex]\r\n\r\nLatex is generally not sensitive to white space when typesetting math. Outside of Pressbooks, the commands \\;, \\:, \\,<\/code> explicitly add large, medium, and small spaces respectively. However, these commands do not seem to be compatible with the QuickLaTeX plugin. As a workaround, you can use the command \\hspace{}<\/code> to add a specific amount of horizontal white space. For example, we can add a space between the functions and the differential variable:\r\n\r\n[\u200clatex]\\int_{a}^{b} u \\hspace{2pt} dv = u(x)v(x)|_a^b \\int^{b}_a v \\hspace{2pt} du[\/latex]<\/code>\r\n\r\n[latex]\\displaystyle \\int_{a}^{b} u \\hspace{2pt} dv = u(x)v(x)|_a^b - \\int^{b}_a v \\hspace{2pt} du[\/latex]\r\n\r\n

Errors<\/h3>\r\nIf a statement is not entered correctly, the equation may not display as expected or QuickLaTeX may display an error. Errors take practice to read. For example, if I were to try to write the quadratic formula as\r\n\r\n[\u200clatex] x = \\frac{-b \\pm \\sqrt{b^2 + 4ac}{2a} [\/latex]<\/code>\r\n\r\nI would get the error\r\n\"\"\r\n\r\nTry to spot what is causing the error. The answer is given in the solutions to the exercises for this section.","rendered":"

Commands<\/h2>\n

Latex allows you to quickly write mathematical equations by specifying characters using commands you can type using the keyboard.\u00a0For example, we can write \" ax^2 + bx + c = 0 \" using the code<\/p>\n

[\u200clatex] ax^2 + bx + c = 0 [\/latex]<\/code><\/p>\n

While some common math symbols like +\/- and exponentiation have a single symbol on the keyboard, most commands start with “\\” and then describe the command. An example of an equation that requires \\ commands is\u00a0\" \cos^2 \theta + \sin^2 \theta = 1 \", which requires commands for the sine, cosine, and angle:<\/p>\n

[\u200clatex] \\cos^2 \\theta + \\sin^2 \\theta = 1 [\/latex]<\/code><\/p>\n

The table below shows some common “\\” commands for symbols, in addition to the trigonometric functions and Greek letters used in the previous example.<\/p>\n\n\n\n\n\n\n\n\n
Algebra<\/strong><\/td>\nCalculus<\/strong><\/td>\nLogic<\/strong><\/td>\n<\/tr>\n
\"\times\"<\/td>\n\\times<\/td>\n\"\lim\"<\/td>\n\\lim<\/td>\n\"\neg\"<\/td>\n\\neg<\/td>\n<\/tr>\n
\"\div\"<\/td>\n\\div<\/td>\n\"\int\"<\/td>\n\\int<\/td>\n\"\rightarrow\"<\/td>\n\\rightarrow<\/td>\n<\/tr>\n
\"\pm\"<\/td>\n\\pm<\/td>\n\"\nabla\"<\/td>\n\\nabla<\/td>\n\"\exists\"<\/td>\n\\exists<\/td>\n<\/tr>\n
\"\approx\"<\/td>\n\\approx<\/td>\n\"\partial\"<\/td>\n\\partial<\/td>\n\"\forall\"<\/td>\n\\forall<\/td>\n<\/tr>\n
\"\equiv\"<\/td>\n\\equiv<\/td>\n\"\sum\"<\/td>\n\\sum<\/td>\n\"\in\"<\/td>\n\\in<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Commands can also take arguments using curly brackets. For example, the fraction and square root in the quadratic formula both take arguments.<\/p>\n

[\u200clatex] x = \\frac{-b \\pm \\sqrt{b^2 + 4ac}}{2a} [\/latex]<\/code><\/p>\n

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

Superscripts and subscripts are also considered arguments. Use ^{} to create a superscript. If, no brackets are used, only the first character will be part of the superscript.
\n[\u200clatex]e^{i \\pi} = -1[\/latex]<\/code><\/p>\n

\"\displaystyle e^{i \pi} = -1\"<\/p>\n

Use _{} to create a subscript. Again, if no brackets are used only the first character will be part of the subscript.<\/p>\n

[\u200clatex] x_1 + x_2 = 2x_3[\/latex]<\/code><\/p>\n

\"\displaystyle x_1 + x_2 = 2x_3\"<\/p>\n

You can add a subscript and a superscript to the same item. The order of the subscript and superscript does not matter. For example:<\/p>\n

[\u200clatex]\\int_{a}^{b} u dv = u(x)v(x)|_a^b - \\int^{b}_a v du [\/latex]<\/code><\/p>\n

\"\displaystyle \int_{a}^{b} u dv = u(x)v(x)|_a^b - \int^{b}_a v du \"<\/p>\n

Latex is generally not sensitive to white space when typesetting math. Outside of Pressbooks, the commands \\;, \\:, \\,<\/code> explicitly add large, medium, and small spaces respectively. However, these commands do not seem to be compatible with the QuickLaTeX plugin. As a workaround, you can use the command \\hspace{}<\/code> to add a specific amount of horizontal white space. For example, we can add a space between the functions and the differential variable:<\/p>\n

[\u200clatex]\\int_{a}^{b} u \\hspace{2pt} dv = u(x)v(x)|_a^b \\int^{b}_a v \\hspace{2pt} du[\/latex]<\/code><\/p>\n

\"\displaystyle \int_{a}^{b} u \hspace{2pt} dv = u(x)v(x)|_a^b - \int^{b}_a v \hspace{2pt} du\"<\/p>\n

Errors<\/h3>\n

If a statement is not entered correctly, the equation may not display as expected or QuickLaTeX may display an error. Errors take practice to read. For example, if I were to try to write the quadratic formula as<\/p>\n

[\u200clatex] x = \\frac{-b \\pm \\sqrt{b^2 + 4ac}{2a} [\/latex]<\/code><\/p>\n

I would get the error
\n\"\"<\/p>\n

Try to spot what is causing the error. The answer is given in the solutions to the exercises for this section.<\/p>\n","protected":false},"author":671,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[47],"contributor":[],"license":[],"class_list":["post-138","chapter","type-chapter","status-publish","hentry","chapter-type-standard"],"part":119,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/chapters\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/wp\/v2\/users\/671"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/chapters\/138\/revisions"}],"predecessor-version":[{"id":787,"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/chapters\/138\/revisions\/787"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/parts\/119"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/chapters\/138\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/wp\/v2\/media?parent=138"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/pressbooks\/v2\/chapter-type?post=138"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/wp\/v2\/contributor?post=138"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/introtolatex\/wp-json\/wp\/v2\/license?post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}