# MandysNotes

Wednesday, 11 May 2011 00:00

## The Latex Cheat-Sheet

By  Gideon
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Here is a quick list of frequently used commands for mathematics in Latex.

All commands are in math mode, i.e. enclosed within either dollar signs or "$...$."

Arithmetic:

Fractions:

$$\frac{a}{b}$$ := \frac{a}{b}

(If you want to use "display"-size fractions in-line, use: \dfrac )

Inequalities:

$$\neq$$ := \neq

$$\leq$$ := \leq

$$\geq$$ := \geq

Algebra:

Parentheses:

(  := \left(

)  := \right)

Square Root:

$$\sqrt{a}$$ := \sqrt{a}

nth root

$$\sqrt[n]{a}$$ := \sqrt[n]{a}

X to the nth power:

$$x^{n}$$ := x^{n}

Binomial coefficients:

$$\binom{n}{m}$$ := \binom{n}{m}

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

Sums:

Sum of constants:

$$\sum_{k=a}^{b}a_k$$ :\sum_{k=a}^{b}a_k

Geometric series:

$$\sum_{k=a}^{b}a_kx^{k}$$ :=  \sum_{k=a}^{b}a_kx^{k}

Binomial Theorem:

$$(x + h)^{n} = \sum_{i=0}^{n}\binom{n}{i}x^{n-i}h^{i}$$ :=

(x + h)^{n} = \sum_{i=0}^{n}\binom{n}{i}x^{n-i}h^{i}

Exponential:

$$e^{x} = \sum_{k=0}^{\infty} \frac{x^{k}}{k!}$$ :=

e^{x} = \sum_{k=0}^{\infty} \frac{x^{k}}{k!}

Calculus:

Derivatives:

Total Derivative:

$$\frac{d}{dx}$$ := \frac{d}{dx}

Partial Derivatives:

$$\frac{\partial}{\partial x}$$ := \frac{\partial }{\partial x}

$$\partial_x$$ := \partial_x

$$\nabla$$ := \nabla

$$\nabla_{\frac{\partial}{\partial x}}$$ := \nabla_{\frac{\partial}{\partial x}}

The D'alembertian:

$$\square \$$ := \square

Integrals:

Indefinite integrals:

$$\int f(x) dx$$ := \int (x) dx

Definite Integrals:

$$\int_{a}^{b} f(x) dx$$ := \int_{a}^{b} f(x) dx

Contour Integrals:

$$\oint f(x) dx$$ := \oint f(x) dx

Multiple Integrals:

$$\iint f(x) d^{2} x$$ := \iint f(x) d^{2}x

$$\iiint f(x) d^{3}x$$ := \iiint f(x) d^{3}x

Etc.

Sets Of Numbers:

Natural Numbers: $$\mathbb{N}$$ := \mathbb{N}

Integers: $$\mathbb{Z}$$ := \mathbb{Z}

Rational Numbers: $$\mathbb{Q}$$ := \mathbb{Q}

Real Numbers: $$\mathbb{R}$$ := \mathbb{R}

Complex Numbers: $$\mathbb{C}$$ := \mathbb{C}

Quaternions: $$\mathbb{H}$$ : = \mathbb{H}

The field $$\mathbb{K}$$ := \mathbb{K}

The field $$\mathbb{F}_2$$ := \mathbb{F}_2

Trigonometry:

$$\sin{\theta}$$ := \sin{\theta}

$$\cos{\theta}$$ := \cos{\theta}

$$\tan{\theta}$$ := \tan{\theta}

$$\cot{\theta}$$ := \cot{\theta}

And so on for scs, sec, sinh, etc.

Greek:

$$\alpha$$ := \apha

$$\beta$$ := \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

$$\omicron$$ := \omicron

$$\pi$$ := \pi

$$\rho$$ := \rho

$$\sigma$$ := \sigma

$$\tau$$ := \tau

$$\upsilon$$ := \upsilon

$$\psi$$ := \psi

$$\chi$$ := \chi

$$\omega$$ := \omega

And my favorite, waw, or digamma, from Homeric Greek (Illios was actually Willios).

$$\digamma$$ := \digamma

For capitals, capitilize the first letter, e.g.

$$\Gamma \$$ := \Gamma

Infinities:

$$\infty$$ := \infty

Aleph = $$\aleph$$ := \aleph

$$\aleph_0$$  := \aleph_0

$$\aleph_1$$ := \aleph_1

$$2^{\infty} = \aleph$$ := 2^{\infty} = \aleph

Planck's Constant:

$$\hbar$$ := \hbar