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}

Quadratic Formula:

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

Gradient/Covariant Derivative:

\( \nabla \) := \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

Read 4213 times Last modified on Saturday, 16 August 2014 19:09
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1 comment

  • Comment Link Kalvin Monday, 25 February 2013 06:34 posted by Kalvin

    Mmmmmmm, nice picture! And helpful sheet too!

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