3.tex

\documentclass[10pt,a4paper]{article}

\usepackage{amsmath, amssymb, amsthm}

\usepackage{hyperref}

\hypersetup{

colorlinks=true,

linkcolor=blue,

}

\begin{document}

\begin{center}

{\Large Equations}\\[0.8em]

Prof.\ Naveen Kumar $^1$ , Dr.\ Neeraj Kumar Sharma $^2$ , and Sakeena Shahid $^3$ \\[0.5em]

{\small

$^1$ Department of Computer Science, University of Delhi\\

$^2$ Ram Lal Anand College, University of Delhi\\

$^3$ SGTB Khalsa College, University of Delhi

}\\[0.5em]

\vspace{1em}

November 15, 2022

\end{center}

\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} \label{eq:gauss} \\

\vec{\nabla} \cdot \vec{B} &= 0

& &\text{Gauss's Law for Magnetism} \label{eq:gaussmag} \\

\vec{\nabla} \times \vec{E} &= -\frac{\partial\vec{B}}{\partial t}

& &\text{Faraday's Law of Induction} \label{eq:faraday} \\

\vec{\nabla} \times \vec{B} &= \mu0\!\left(\epsilon0

\frac{\partial\vec{E}}{\partial t}+\vec{J}\right)

& &\text{Ampere's Circuital Law} \label{eq:ampere}

\end{align}

Equations \ref{eq:gauss}, \ref{eq:gaussmag}, \ref{eq:faraday}, and \ref{eq:ampere} are some of the most important in Physics.

\section{Matrix Equations}

\begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & 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{document}