Mathematics Examples

This post demonstrates various mathematical notations and equations that can be used in blog posts.

Basic Mathematical Notation

Inline Math

You can include inline mathematical expressions like $E = mc^2$ or $\pi \approx 3.14159$ .

Block Math

For larger equations, use block math:

\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}

Common Mathematical Formulas

Quadratic Formula

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

Euler’s Identity

e^{i\pi} + 1 = 0

Summation

\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}

Matrix Operations

Matrix Multiplication

\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix} = \begin{bmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{bmatrix}

Determinant

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

Calculus Examples

Derivative

\frac{d}{dx} \left( x^n \right) = nx^{n-1}

Integral

\int x^n dx = \frac{x^{n+1}}{n+1} + C \quad \text{for } n \neq -1

Limit

\lim_{x \to 0} \frac{\sin(x)}{x} = 1

Statistics

Normal Distribution

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

Standard Deviation

\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}

Conclusion

These examples show how to properly format mathematical expressions in blog posts. Make sure to use the appropriate delimiters for inline ( $...$ ) and block ( $...$ ) math expressions.

Thanks for reading!

Mathematics Examples

周一 7月 01 2024 New

169 字 · 2 分钟

Mathematics Examples Math Equations LaTeX