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\begin{document}
    \begin{table}[h]
        % \begin{minipage}[b]{0.5\linewidth}
        \centering
        \renewcommand{\arraystretch}{1.6}
        \begin{tabular}{|l|r|c|c|c|}
            \hline
             &  & Cartesian & Cylindrical & Spherical \\
            \hline
            Coordinate variables &  & $x,y,z$ & $r,\phi,z$ & $R,\theta,\phi$ \\
            \hline
            Vector representation & $\vec{A}=$ & $\vect{x}A_x+\vect{y}A_y+\vect{z}A_z$ & $\vect{r}A_r+\vect{\phi}A_\phi+\vect{z}A_z$ & $\vect{R}A_R+\vect{\theta}A_\theta+\vect{\phi}A_\phi$ \\
            \hline
            Magnitude of A & $|\vec{A}|=$ & $+\sqrt{A_x^2+A_y^2+A_z^2}$ & $+\sqrt{A_r^2+A_\phi^2+A_z^2}$ & $+\sqrt{A_R^2+A_\theta^2+A_\phi^2}$ \\
            \hline
            Position vector & $\vec{OP_1}=$ & $\vect{x}x_1+\vect{y}y_1+\vect{z}z_1$ & $\vect{r}r_1+\vect{z}z_1$ & $\vect{R}R_1$ \\
            \hline
            Base vectors properties &  & $\vect{x}\cdot\vect{x}=\vect{y}\cdot\vect{y}=\vect{z}\cdot\vect{z}=1$ & $\vect{r}\cdot\vect{r}=\vect{\phi}\cdot\vect{\phi}=\vect{z}\cdot\vect{z}=1$ & $\vect{R}\cdot\vect{R}=\vect{\theta}\cdot\vect{\theta}=\vect{\phi}\cdot\vect{\phi}=1$ \\
             &  & $\vect{x}\cdot\vect{y}=\vect{y}\cdot\vect{z}=\vect{z}\cdot\vect{x}=0$ & $\vect{r}\cdot\vect{\phi}=\vect{\phi}\cdot\vect{z}=\vect{z}\cdot\vect{r}=0$ & $\vect{R}\cdot\vect{\theta}=\vect{\theta}\cdot\vect{\phi}=\vect{\phi}\cdot\vect{R}=0$ \\
             &  & $\vect{x}\times\vect{y}=\vect{z}$ & $\vect{r}\times\vect{\phi}=\vect{z}$ & $\vect{R}\times\vect{\theta}=\vect{\phi}$ \\
             &  & $\vect{y}\times\vect{z}=\vect{x}$ & $\vect{\phi}\times\vect{z}=\vect{r}$ & $\vect{\theta}\times\vect{\phi}=\vect{R}$ \\
             &  & $\vect{z}\times\vect{x}=\vect{y}$ & $\vect{z}\times\vect{r}=\vect{\phi}$ & $\vect{\phi}\times\vect{R}=\vect{\theta}$ \\
            \hline
            Dot product & $\vec{A}\cdot\vec{B}=$ & $A_xB_x+A_yB_y+A_zB_z$ & $A_rB_r+A_\phi B_\phi+A_zB_z$ & $A_RB_R+A_\theta B_\theta+A_\phi B_\phi$ \\
            \hline
            Cross product & $\vec{A}\times\vec{B}=$ &  &  &  \\
             &  & $\renewcommand{\arraystretch}{1.0} \left| \begin{array}{ccc} \vect{x} & \vect{y} & \vect{z} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \\ \end{array} \right|$ & $\renewcommand{\arraystretch}{1.0} \left| \begin{array}{ccc} \vect{r} & \vect{\phi} & \vect{z} \\ A_r & A_\phi & A_z \\ B_r & B_\phi & B_z \\ \end{array} \right|$ & $\renewcommand{\arraystretch}{1.0} \left| \begin{array}{ccc} \vect{R} & \vect{\theta} & \vect{\phi} \\ A_R & A_\theta & A_\phi \\ B_R & B_\theta & B_\phi \\ \end{array} \right|$ \\
             &  &  &  &  \\
            \hline
            Differential length & $dl=$ & $\vect{x}\,dx+\vect{y}\,dy+\vect{z}\,dz$ & $\vect{r}\,dr+\vect{\phi}r\,d\phi+\vect{z}\,dz$ & $\vect{R}\,dR+\vect{\theta}R\,d\theta+\vect{\phi}R\sin{\theta}\,d\phi$ \\
            \hline
            Differential surface areas & $ds=$ & $ds_x=\vect{x}\,dx\,dz$ & $ds_r=\vect{r}r\,d\phi\,dz$ & $ds_R=\vect{R}R^2\sin{\theta}\,d\theta\,d\phi$ \\
             &  & $ds_y=\vect{y}\,dx\,dz$ & $ds_\phi=\vect{\phi}\,dr\,dz$ & $ds_\theta=\vect{\theta}R\sin{\theta}\,dR\,d\phi$ \\
             &  & $ds_z=\vect{z}\,dx\,dy$ & $ds_z=\vect{z}r\,dr\,d\phi$ & $ds_\phi=\vect{\phi}R\,dR\,d\theta$ \\
            \hline
            Differential volume & $dv=$ & $dx\,dy\,dz$ & $r\,dr\,d\phi\,dz$ & $R^2\sin{\theta}\,dR\,d\theta\,d\phi$ \\
            \hline
        \end{tabular}
        \caption{Table 3-1 from Fundamentals of Applied Electromagnetics 6E.}
    \end{table}

    \begin{table}[h]
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        \centering
        \begin{tabular}{|c|c|c|c|}
            \hline
             & Coordinate Variables & Unit Vectors & Vector Components \\
            \hline
            Cartesian to Cylindrical & $r=+\sqrt{x^2+y^2}$ & $\vect{r}=\vect{x}\cos{\phi}+\vect{y}\sin{\phi}$ & $A_r=A_x\cos{\phi}+A_y\sin{\phi}$ \\
             & $\phi=\tan^{-1}({y/x})$ & $\vect{\phi}=-\vect{x}\sin{\phi}+\vect{y}\cos{\phi}$ & $A_\phi=-A_x\sin{\phi}+A_y\cos{\phi}$ \\
             & $z=z$ & $\vect{z}=\vect{z}$ & $A_z=A_z$ \\
            \hline
            Cylindrical to Cartesian &  &  &  \\
             &  &  &  \\
             &  &  &  \\
            \hline
            Cartesian to Spherical &  &  &  \\
             &  &  &  \\
             &  &  &  \\
            \hline
            Spherical to Cartesian &  &  &  \\
             &  &  &  \\
             &  &  &  \\
            \hline
            Cylindrical to Spherical &  &  &  \\
             &  &  &  \\
             &  &  &  \\
            \hline
            Spherical to Cylindrical &  &  &  \\
             &  &  &  \\
             &  &  &  \\
            \hline
        \end{tabular}
        \caption{Table 3-2 from Fundamentals of Applied Electromagnetics 6E.}
    \end{table}
\end{document}