The ability to beautifully and accurately write mathematical expressions is crucial to many fields, particularly in scientific research. Luckily, R Markdown provides an excellent platform for doing this, thanks to its compatibility with LaTeX, a popular typesetting system renowned for high-quality typesetting of mathematical and scientific content.
Mathematical Formulas
To write mathematical formulas in R Markdown, we use LaTeX syntax. This is enclosed in dollar signs ($) for inline formulas and double dollar signs ($$) for display formulas1.
Inline mathematical
The formula for the area of a circle is $A = \pi r^2$.
And it will render as:
\[A = \pi r^2\]
Display Formula
The formula for the area of a circle is:
$$
A = \pi r^2
$$Which will render as:
\[A = \pi r^2\]
Examples
- Fraction:
$$
\begin{align*}
\frac{a}{b}
\end{align*}
$$renders as:
\[ \begin{align*} \frac{a}{b} \end{align*} \]
- Exponents and Subscripts:
we use ^ for superscripts (exponents) and _for subscripts.
$$
\begin{align*}
a^{b}\\
c_{d}
\end{align*}
$$renders as:
\[ \begin{align*} a^{b}\\ c_{d} \end{align*} \]
- Roots and Logarithms:
$$
\begin{align*}
Square\ root: \sqrt{a}\\
nth\ root: \sqrt[n]{b}\\
natural\ log: \ln{c}\\
log\ base\ n: \log_{n}{d}
\end{align*}
$$renders as:
\[ \begin{align*} Square\ root: \sqrt{a}\\ nth\ root: \sqrt[n]{b}\\ natural\ log: \ln{c}\\ log\ base\ n: \log_{n}{d} \end{align*} \]
- Quadratic equation:
$$
\begin{align*}
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{align*}
$$renders as:
\[ \begin{align*} x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{align*} \]
- Summation:
$$
\begin{align*}
\sum_{i=1}^{n} i = \frac{n*(n + 1)}{2}
\end{align*}
$$renders as:
\[ \begin{align*} \sum_{i=1}^{n} i = \frac{n*(n + 1)}{2} \end{align*} \]
- Integral:
$$
\begin{align*}
\int_{0}^{\infty} e^{-x} dx = 1\\
\int_{a}^{b} f(x) \, dx
\end{align*}
$$renders as:
\[ \begin{align*} \int_{0}^{\infty} e^{-x} dx = 1\\ \int_{a}^{b} f(x) \, dx \end{align*} \]
- Matrix representation:
$$
\begin{align*}
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
\end{align*}
$$
$$
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
$$Renders as:
\[ \begin{align*} \begin{bmatrix} a & b \\ c & d \end{bmatrix} \end{align*} \] \[ \begin{align*} \begin{pmatrix} a & b \\ c & d \end{pmatrix} \end{align*} \]
- Trigonometric functions:
$$
\begin{align*}
Sine: \sin(x)\\
Cosine: \cos(x)\\
Tangent: \tan(x)\\
Cotangent: \cot(x)\\
Secant: \sec(x)\\
Cosecant: \csc(x) \\
Degree: 30^\circ
\end{align*}
$$renders as:
\[ \begin{align*} Sine: \sin(x)\\ Cosine: \cos(x)\\ Tangent: \tan(x)\\ Cotangent: \cot(x)\\ Secant: \sec(x)\\ Cosecant: \csc(x) \\ Degree: 30^\circ \end{align*} \]
- Inverse trigonometric functions:
$$
\\begin{flalign}
Inverse\ sine (arcsine): \arcsin(x) &\\
Inverse\ cosine (arccosine): \arccos(x) &\\
Inverse\ tangent (arctangent): \arctan(x) &
\end{flalign}
$$render as:
\[ \small \begin{flalign*} \text{Inverse sine (arcsine):} \quad & \arcsin(x) &\\ \text{Inverse cosine (arccosine):} \quad & \arccos(x) &\\ \text{Inverse tangent (arctangent):} \quad & \arctan(x) & \end{flalign*} \small \]
Mathematical Symbols
R Markdown (through LaTeX) provides a wealth of mathematical symbols. Here are some of the most commonly used ones:
| Symbol | Code |
|---|---|
| \(+\) | + |
| \(-\) | - |
| \(\times\) | \times |
| \(\div\) | \div |
| \(\pm\) | \pm |
| \(\cdot\) | \cdot |
| \(\circ\) | \circ |
| \(\sqrt{x}\) | \sqrt{x} |
| \(\frac{a}{b}\) | \frac{a}{b} |
| \(\sum\) | \sum |
| \(\prod\) | \prod |
| \(\int\) | \int |
| \(\partial\) | \partial |
| \(\infty\) | \infty |
| \(\forall\) | \forall |
| \(\exists\) | \exists |
| \(\Rightarrow\) | \Rightarrow |
| \(\Leftrightarrow\) | \Leftrightarrow |
| \(\to\) | \to |
| \(\subset\) | \subset |
| \(\supset\) | \supset |
| \(\subseteq\) | \subseteq |
| \(\supseteq\) | \supseteq |
| \(\notin\) | \notin |
| \(\neq\) | \neq |
| \(\approx\) | \approx |
| \(\equiv\) | \equiv |
| \(\leq\) | \leq |
| \(\geq\) | \geq |
| \(\ll\) | \ll |
| \(\gg\) | \gg |
| \(\alpha\) | \alpha |
| \(\beta\) | \beta |
| \(\gamma\) | \gamma |
| \(\delta\) | \delta |
| \(\epsilon\) | \epsilon |
| \(\zeta\) | \zeta |
| \(\eta\) | \eta |
| \(\theta\) | \theta |
| \(\iota\) | \iota |
| \(\kappa\) | \kappa |
| \(\lambda\) | \lambda. |
| \(\mu\) | \mu |
| \(\nu\) | \nu |
| \(\xi\) | \xi |
| \(\pi\) | \pi |
| \(\rho\) | \rho |
| \(\sigma\) | \sigma |
| \(\tau\) | \tau |
| \(\upsilon\) | \upsilon |
| \(\phi\) | \phi |
| \(\chi\) | \chi |
| \(\psi\) | \psi |
| \(\omega\) | \omega |
| \(\Gamma\) | \Gamma |
| \(\Delta\) | \Delta |
| \(\Theta\) | \Theta |
| \(\Lambda\) | \Lambda |
| \(\Xi\) | \Xi |
| \(\Pi\) | \Pi |
| \(\Sigma\) | \Sigma |
| \(\Phi\) | \Phi |
| \(\Psi\) | \Psi |
| \(\Omega\) | \Omega |
Footnotes
https://www.cnblogs.com/nowgood/p/latexstart.html#_nav_4↩︎