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- \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}
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