me22b054.tex

\section{me22b054}
I am going to explain about one of the most important equation that changed the course of history, \\ \textbf{\textit{The Wave equation}} \footnote{Reference:Non linear Wave equation- Walter Alexander Strauss,1989}

\begin{equation}
\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}
\end{equation}
 \textbf{Note:} The above one is the \textbf{\textit{one-dimensional wave equation.}}
 
 the equation for a \textbf{three-dimensional wave } is as follows:
 \begin{equation}
 \frac{\partial^2 u}{\partial t^2} = c^2 \nabla^2 u
 \end{equation}
  where \textbf{$nabla^2 u$} is the \textbf{\textit{Laplacian of the wave displacement}}.
  
  
 This is a Differential equation, or an equation that describes how a property is changing through time in \\ terms of that property's  derivative, as above. The wave equation describes the \\ behaviour  of waves - a vibrating guitar string, ripples in a pond after a stone is \\ thrown,  or light coming out of an incandescent bulb. The wave equation was \\ an  early differential equation, and the techniques developed to solve the equation \\ opened the door to understanding other differential equations as well.\par
 
 
 Name:\textbf{SAISIVARAM A U} \\
 Git-hub user-id:\textbf{Saisivaram054}