\documentclass[12 pt]{book}
\usepackage{amsmath}
\usepackage[table]{xcolor}
\begin{document}
\begin{table}
\caption{Definition of Linear Finite Difference Operators}\label{Table1}
\centering
\begin{tabular}{l l c l }
%baraye naboudan khotute amoudi | ha ro hazf kardim {|c|c|c|c|}%
\hline & \textcolor{red}{Operators} & \cellcolor{yellow}{Symbol} & Difference Representation \\ \arrayrulecolor{green} \hline
$(2.1.9a)$ & Forward Difference & \textcolor{blue}{$\Delta$} & $\Delta u_r=u_{r+1}-u_r$ \\
$(2.1.9b)$ & Backward Difference & $\nabla $ & $\nabla u_r=u_r - u_{r-1}$ \\ \arrayrulecolor{black}\hline
\end{tabular}
\end{table}
\end{document}