LaTeX and MathML help
This guide shows keyboard notation for rendering mathematical expressions in LaTeX and converting them to MathML. The examples cover arithmetic, algebra, calculus, geometry, sets and statistics.
1. Arithmetic
1.1 Basic operations
- Addition:
a + b - Subtraction:
a - b - Multiplication:
a * bora \cdot b - Division:
a / bor\frac{a}{b}
1.2 Powers and roots
- Powers:
a^b(e.g.2^3for 23) - Square roots:
\sqrt{a}ora^{1/2}(e.g.\sqrt{4}for √4) - nth roots:
\sqrt[n]{a}(e.g.\sqrt[3]{8}for ∛8)
2. Algebra
2.1 Linear equations
- Equation:
ax + b = c - System of equations:
\begin{cases} ax + by = c \\ dx + ey = f \end{cases}
2.2 Quadratic equations
- General form:
ax^2 + bx + c = 0
2.3 Matrices
- Matrix notation:
\begin{bmatrix} a & b \\ c & d \end{bmatrix} - Matrix multiplication:
AB - Determinant:
\det Aor|A|
3. Calculus
3.1 Derivatives
- First derivative:
\frac{d}{dx} f(x)orf'(x) - Second derivative:
\frac{d^2}{dx^2} f(x)orf''(x)
3.2 Integrals
- Indefinite integral:
\int f(x) \, dx - Definite integral:
\int_{a}^{b} f(x) \, dx
3.3 Limits
- Limit:
\lim_{x \to a} f(x) - Limit at infinity:
\lim_{x \to \infty} f(x)
4. Trigonometry
- Sine:
\sin(\theta) - Cosine:
\cos(\theta) - Tangent:
\tan(\theta) - Arcsine:
\arcsin(x) - Arccosine:
\arccos(x) - Arctangent:
\arctan(x)
5. Logarithmic functions
- Natural logarithm:
\ln(x) - Base-10 logarithm:
\log(x) - Logarithm with an arbitrary base:
\log_b(x)
6. Sets and logic
6.1 Basic operations
- Union:
A \cup B - Intersection:
A \cap B - Difference:
A \setminus B - Subset:
A \subset B
6.2 Logical operations
- A and B:
A \land B - not A:
\neg A - Implication:
A \implies B - Equivalence:
A \iff B
6.3 Set symbols
- Element of a set:
x \in A - Not an element of a set:
x \notin A
7. Greek letters
Greek letters are often used for variables and constants. Here are some examples:
- Alpha:
\alpha - Beta:
\beta - Gamma:
\gamma - Delta:
\delta - Epsilon:
\epsilon - Lambda:
\lambda - Pi:
\pi - Sigma:
\sigma - Omega:
\omega
8. Statistics
- Mean:
\bar x - Variance:
\sigma^2 - Standard deviation:
\sigma - Covariance:
\operatorname{cov}(X, Y) - Correlation coefficient:
\rho_{x,y}
Using the converter
The converter renders your LaTeX and produces MathML. It does not calculate or simplify expressions; use the scientific calculator or expression simplifier.