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					\documentclass{article} | 
				
			
			
		
	
		
			
				
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					\usepackage[utf8]{inputenc} | 
				
			
			
		
	
		
			
				
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					\usepackage[english]{babel} | 
				
			
			
		
	
		
			
				
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					\usepackage{amssymb,amsmath} | 
				
			
			
		
	
		
			
				
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					\begin{document} | 
				
			
			
		
	
		
			
				
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					\section{Simple equations on text} | 
				
			
			
		
	
		
			
				
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					\label{sec:eq-text} | 
				
			
			
		
	
		
			
				
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					Here you can see simple equations along with text $x$, $y$ and \(z\) are in math mode. This mode is known as \textbf{inline} mode and it is recommended to write short equations like: $-10 \leq x \leq 10$. Thus, if complex and long equations are required, it is recommended to use the equation environment.\par | 
				
			
			
		
	
		
			
				
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					\section{Equation environment} | 
				
			
			
		
	
		
			
				
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					\label{sec:environment} | 
				
			
			
		
	
		
			
				
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					Here we can find a way to write long equations like \eqref{eq:fraction}: | 
				
			
			
		
	
		
			
				
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					\begin{equation} | 
				
			
			
		
	
		
			
				
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					  \label{eq:fraction} | 
				
			
			
		
	
		
			
				
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					  f(t)=\sqrt{\frac{t-a}{t+a}} | 
				
			
			
		
	
		
			
				
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					\end{equation} | 
				
			
			
		
	
		
			
				
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					\noindent here $t$ is time in seconds. | 
				
			
			
		
	
		
			
				
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					More complex equations can be written using symbols and commands from math-mode. An example is the Fourier coefficients equations \eqref{eq:a0},\eqref{eq:an} and \eqref{eq:bn}: | 
				
			
			
		
	
		
			
				
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					\begin{eqnarray} | 
				
			
			
		
	
		
			
				
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					  a_0=\frac{1}{T}\int_0^T f(t)dt  \label{eq:a0}\\ | 
				
			
			
		
	
		
			
				
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					  a_n=\frac{2}{T}\int_0^T f(t)\cdot \cos{\left(\frac{2\pi nt}{T}\right)}dt  \label{eq:an}\\ | 
				
			
			
		
	
		
			
				
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					  b_n=\frac{2}{T}\int_0^T f(t)\cdot \sin{\left(\frac{2\pi nt}{T}\right)}dt  \label{eq:bn} | 
				
			
			
		
	
		
			
				
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					\end{eqnarray} | 
				
			
			
		
	
		
			
				
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					Previous equations are used to define the Fourier series as: | 
				
			
			
		
	
		
			
				
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					\begin{equation} | 
				
			
			
		
	
		
			
				
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					  \label{eq:fourier} | 
				
			
			
		
	
		
			
				
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					  g(t)=a_0+\sum_{m=1}^{\infty}a_m \cos{\left(\frac{2\pi mt}{T}\right)}++\sum_{m=1}^{\infty}b_n \sin{\left(\frac{2\pi nt}{T}\right)} | 
				
			
			
		
	
		
			
				
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					\end{equation} | 
				
			
			
		
	
		
			
				
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					\end{document} | 
				
			
			
		
	
		
			
				
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