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vectors.html
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vectors.html
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<html>
<head>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/lib/p5.js"></script>
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']]
}
};
</script>
<script id="MathJax-script" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
</script>
<link rel="stylesheet" href="styles.css" />
</head>
<body>
<a href="index.html">Home</a>
<hr />
<main>
$$\begin{array}{c}
\begin{matrix}
\delta_{ij}=\begin{cases}1&i=j\\0&i\ne j\end{cases}&
\epsilon_{ijk}=\begin{cases}1&\text{cyclic}\\-1&\text{anti-cyclic}\\0&\text{repeated}\end{cases}
\end{matrix}\\
\begin{matrix}
(a\times b)_k=\epsilon_{ijk}a_ib_j&
a\times b=\begin{Bmatrix}a_2b_3-a_3b_2\\a_3b_1-a_1b_3\\a_1b_2-a_2b_1\end{Bmatrix}&
\tilde a=\begin{bmatrix}0&-a_3&a_2\\a_3&0&-a_1\\-a_2&a_1&0\end{bmatrix}
\end{matrix}\\
a\cdot b=a_ib_i\\
a_{\parallel b}=\frac{a\cdot b}{b\cdot b}b\\
a_{\perp b}=a-a_{\parallel b}\\
\cos\theta=\frac{a\cdot b}{|a||b|}\\
\nabla=\partial_i\\
\nabla p=p_i\\
\nabla\vec v=u_{i,j}\\
\nabla\cdot\vec v=u_{i,i}\\
u\otimes u=u_iu_j\\
\nabla (u\otimes u)=\nabla uu=u_{i,j}u_j\\
D\rho=\rho_{,t}+u_i\rho_{,i}\\
\end{array}$$
</main>
</body>
</html>