\documentclass{article}
\usepackage{amsmath}
\usepackage{authblk}
% \usepackage{esint}
\title{Equations}

\author[1]{Rakshit Rabugotra}
\author[2]{Prof. Naveen Kumar}
\author[3]{Dr. Neeraj Kumar Sharma}
\affil[1]{Department of Computer Science, University of Delhi}
\affil[2]{Ram Lal Anand College, University of Delhi}
\affil[3]{SGTB Khalse College, University of Delhi}

\begin{document}
\maketitle


\section{Maxwell's equations}
"Maxwell's equations" are named for James Clark Maxwell and are as follow:
\begin{align}
&\Vec{\nabla}\cdot\Vec{E}=\frac{\rho}{\epsilon_0} && \text{Gauss's Law}\\
&\Vec{\nabla}\cdot\Vec{B} = 0 && \text{Gauss's Law for Magnetism} \\
&\Vec{\nabla} \times \Vec{E} = -\frac{\partial{\Vec{B}}}{\partial{t}} && \text{Faraday's Law of Induction} \\
&\Vec{\nabla} \times \Vec{B} = \mu_0(\epsilon_o\frac{\partial{\Vec{E}}}{\partial{t}} + \Vec{J}) && \text{Ampere's Circuital Law} \\
\end{align}

equations 1, 2, 3, and 4 are some of the most important in Physics.

\section{Matrix Equations}

\begin{align}
\begin{pmatrix}
a_{11} & a_{12} & \dots & a_{1n} \\
a_{21} & a_{22} & \dots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{n1} & a_{n2} & \dots & a_{nn}
\end{pmatrix}
\begin{bmatrix}
v_1 \\
v_2 \\
\vdots \\
v_n
\end{bmatrix}
=
\begin{matrix}
w_1 \\
w_2 \\
\vdots \\
w_n
\end{matrix}
\end{align}
\end{document}