Math Rendering Test with KaTeX

This post demonstrates mathematical notation rendering using KaTeX.

Inline Math

You can write inline math like this: $E = mc^2$, or the quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$.

The area of a circle is $A = \pi r^2$, and the Pythagorean theorem states that $a^2 + b^2 = c^2$.

Display Math

Quadratic Formula

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

Summation

$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$

Integration

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

Matrix

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

Limits

$$\lim_{x \to \infty} \frac{1}{x} = 0$$

Complex Formulas

Euler’s Formula

$$e^{i\pi} + 1 = 0$$

Taylor Series

$$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \cdots$$

Fourier Transform

$$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx$$

Maxwell’s Equations

$$\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}$$

Probability and Statistics

Normal Distribution

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

Bayes’ Theorem

$$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$$

Calculus

Chain Rule

$$\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$$

Product Rule

$$\frac{d}{dx}[u(x) \cdot v(x)] = u'(x) \cdot v(x) + u(x) \cdot v'(x)$$

Linear Algebra

Eigenvalue Equation

$$A\mathbf{v} = \lambda\mathbf{v}$$

Determinant

$$\det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$$

Special Functions

Gamma Function

$$\Gamma(n) = (n-1)! = \int_0^{\infty} t^{n-1} e^{-t} \, dt$$

Binomial Coefficient

$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$

Greek Letters and Symbols

Common symbols: $\alpha$, $\beta$, $\gamma$, $\Delta$, $\Sigma$, $\Omega$, $\theta$, $\phi$, $\psi$

Operators: $\leq$, $\geq$, $\neq$, $\approx$, $\infty$, $\partial$, $\nabla$

Conclusion

KaTeX supports a wide range of mathematical notation and renders beautifully in the browser!