Mathematical Equations with MathJax

This post demonstrates how to use MathJax to render beautiful mathematical equations in your blog posts. MathJax is a JavaScript display engine that works in all browsers and uses LaTeX syntax for writing equations.

Inline Equations

You can include inline equations like $E = mc^2$ or $\pi \approx 3.14159$ within your text. Simply surround your LaTeX code with single dollar signs $...$.

Display Equations

For more complex equations or to display them on their own line, use double dollar signs:

$$
\frac{d}{dx}\left( \int_{a}^{x} f(u)\,du\right)=f(x)
$$

This is the Fundamental Theorem of Calculus.

More Examples

Quadratic Formula

The solutions to $ax^2 + bx + c = 0$ are given by:

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

Matrices

You can also display matrices:

$$
\begin{pmatrix}
a & b \
c & d
\end{pmatrix}
\begin{pmatrix}
x \
y
\end{pmatrix}
=
\begin{pmatrix}
ax + by \
cx + dy
\end{pmatrix}
$$

Calculus

The definition of a derivative:

$$
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
$$

Statistics

The normal distribution probability density function:

$$
f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}
$$

Physics

Maxwell's equations in differential form:

$$
\begin{align}
\nabla \cdot \vec{E} &= \frac{\rho}{\varepsilon_0} \
\nabla \cdot \vec{B} &= 0 \
\nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \
\nabla \times \vec{B} &= \mu_0 \vec{J} + \mu_0 \varepsilon_0 \frac{\partial \vec{E}}{\partial t}
\end{align}
$$

Using MathJax in Your Posts

To include mathematical equations in your posts, you can use:

1. Inline math with single dollar signs: $E = mc^2$ renders as $E = mc^2$
2. Display math with double dollar signs: $$E = mc^2$$ renders as:

$$
E = mc^2
$$

MathJax supports a wide range of LaTeX commands and environments, making it possible to display complex mathematical content on the web.

Conclusion

With MathJax support, you can now include beautiful mathematical equations in your blog posts, making it perfect for explaining scientific concepts, engineering principles, or mathematical theories.