MathJax Tutorial:

Inline and Display Math

Use \( ... \) for inline and \[ ... \]

Inline example: The area of a circle is \( A = \pi r^2 \), where \( r \) is the radius.

Display example:

\[  E = mc^2\]

Equation Numbering and References

Use \begin{equation}\label{...}\end{equation} for numbered equations, and \eqref{...} to reference them.

\begin{equation}\label{eq:pythagoras}  a^2 + b^2 = c^2\end{equation}

Pythagoras' theorem is shown in Equation \eqref{eq:pythagoras}.

Fractions, Sums, and Limits

Fractions: \( \frac{a}{b} \)

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

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

Integration and Differentiation

Definite integrals:

\[  \int_{0}^{1} x^2 \, dx = \frac{1}{3}\]

Indefinite:

\[  \int \sin x \, dx = -\cos x + C\]

Differentiation:

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

Partial derivatives:

\[  \frac{\partial f}{\partial x} = \nabla \cdot \mathbf{E}\]

Symbols and Operators

Greek letters: \( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu, \nu, \xi, \pi, \rho, \sigma, \tau, \upsilon, \phi, \chi, \psi, \omega \)

Operators: \( \pm, \times, \div, \cdot, \circ, \oplus, \otimes \)

Relations: \( =, \neq, \leq, \geq, \subset, \supset, \in, \notin \)

Arrows: \( \leftarrow, \rightarrow, \uparrow, \downarrow, \leftrightarrow \)

Special sets: \( \mathbb{R}, \mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{C} \)

Matrices and Arrays

Use the matrix environment for arrays:

\[  \begin{pmatrix}    a & b \\    c & d  \end{pmatrix}  \begin{bmatrix}    1 & 2 \\    3 & 4  \end{bmatrix}  \begin{vmatrix}    x & y \\    z & w  \end{vmatrix}\]

Larger matrices:

\[  \begin{pmatrix}    1 & 0 & 0 \\    0 & 1 & 0 \\    0 & 0 & 1  \end{pmatrix}\]

Systems of Equations

Use align or cases:

\[  \begin{cases}    x + y = 1 \\    x - y = 0  \end{cases}\]

Aligned systems:

\[  \begin{aligned}    2x + 3y &= 5 \\    4x - y &= 3  \end{aligned}\]

Tables and Arrays

\[  \begin{array}{c|c}    x & f(x) \\    \hline    0 & 0 \\    1 & 1 \\    2 & 4  \end{array}\]

More complex:

\[  \begin{array}{|c|c|c|}    \hline    Name & Symbol & Value \\    \hline    Pi & \pi & 3.14159 \\    Euler & e & 2.71828 \\    \hline  \end{array}\]

Multi-Line Equations and Align

Use align for step-by-step:

\[  \begin{align}    (x + 1)^2 &= x^2 + 2x + 1 \\    &= (x^2 + 2x) + 1  \end{align}\]

Graphs and Diagrams (Basic)

MathJax doesn't natively support graphs. You can embed images instead. For LaTeX-style plots, consider generating them separately and uploading as images.

Link to image:

TikZ can also be used for graphs, but that would require importing the full MathJax library, better to pre-render complex diagrams.

Tips for "Your Blog Editor"

 
• Always use \( ... \) and \[ ... \] to avoid editor mangling.
 
• If backslashes get escaped, paste in source mode or use raw HTML.
 
• For complex expressions, test in a local HTML file first.
 
• Equations are numbered automatically in amsmath environments.
 
• Use \text{...} for text inside math: \( \text{For } x > 0 \)