Example: Using Mathematical Formulas with MathJax

This site supports mathematical formulas using MathJax, which renders LaTeX math notation. This post demonstrates how to include mathematical formulas in your content.

Inline Math

You can include inline mathematical expressions by surrounding them with $ symbols. For example, typing $E = mc^2$ renders as $E = mc^2$.

Some more examples of inline math:

• The quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• Euler's identity: $e^{i\pi} + 1 = 0$
• The sum of a series: $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$

Display Math

For larger formulas that deserve their own line, use double dollar signs $$ to create display math. For example:

$$\int_{a}^{b} f(x) , dx = F(b) - F(a)$$

Here's a more complex example, the Fourier transform:

$$\mathcal{F}[f(t)] = \int_{-\infty}^{\infty} f(t) e^{-i2\pi ft} , dt$$

Examples from Physics

The Schrödinger equation in quantum mechanics:

$$i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)$$

Maxwell's equations in differential form:

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

Examples from Computer Science

The time complexity of an algorithm:

$$O(n \log n)$$

The recurrence relation for merge sort:

$$T(n) = 2T\left(\frac{n}{2}\right) + O(n)$$

Conclusion

Using MathJax, you can include a wide variety of mathematical expressions in your blog posts. This makes it perfect for technical writing, scientific articles, or teaching materials. Just wrap your LaTeX-formatted math in single dollars ($...$) for inline expressions, or double dollars ($$...$$) for display equations.