Basic LaTeX Julie Mitchell
1 1.1
Basic Formatting Beginning a document
\documentstyle{article} \usepackage{graphicx, amssymb} \begin{document} \textwidth 6.5 truein \oddsidemargin 0 truein \evensidemargin -0.50 truein \topmargin -.5 truein \textheight 8.5in
template for changing margin sizes insert after document opener
\title{...} \author{...} \thanks{...} \date{...} \maketitle
template for title and author
\begin{abstract} \end{abstract}
template for abstract
1
1.2
Format
\section{ \section*{ \subsection{ \subsection*{ \begin{center} \end{center} \centerline{ \hfill \begin{flushleft} \end{flushleft} \begin{flushright} \end{flushright} \begin{quotation} \end{quotation} \noindent \\ \newpage %
1.3 { } \/} ( ) [ ] \{ \} “ � h i
numbered section unnumbered section numbered subsection unnumbered subsection centers intermediate text centers a line fills line with horizontal space places text flush with left margin places text flush with right margin offsets intermediate text by wider margins new paragraph starts without indent newline starts new page following text on same line is invisible
Basic Braces and Parentheses open brace closing (end) brace end brace for italics open parenthesis end parenthesis open bracket end bracket left literal braces right literal braces begin quotation mark end quotation mark \langle \rangle
2
1.4
Lists and Tables
\begin{enumerate} \end{enumerate} \begin{itemize} \end{itemize} \begin{description} \end{description} \item \item[ \setcounter{enumi}{ \setcounter{. . . }{. . . } \begin{tabbing} \end{tabbing} \> \begin{tabular}{|c|c|} \end{tabular} \hline &
1.5
makes a numbered list; makes list with bullets; makes an unnumbered list; produces items for above lists for customized items, in enumerate lists sets counter for enumerate list fill in braces (don’t leave spaces) starts tabbing environment next tab stop tabular with vertical lines horizontal line separates columns in tabular environment
Labels, References and Bibliography
\footnote{ \index{ \label{ \ref{ (\ref{ }) \cite{ }
footnote use for index entries to label an equation, theorem, etc. to cross reference an equation, theorem, etc. put cursor between { } by hand reference a bibitem entry
The following are designed for the author-year style of bibliography that is used after \begin{thebibliography} and before \end{thebibliography}
\bibitem[artref] Author [year] Title. {\it Journal\/} {\bf 11}, 123–223.
for articles
\bibitem[bookref] Author [year] {\it Title.\/} Publisher.
for books
3
1.6 ´e `e ¨a ¨o u ¨
Foreign Accents
´ E ` E ¨ A ¨ O ¨ U
1.7
\’{e} \‘{e} \”{a} \”{o} \”{u}
Miscellaneous
@ c ¶ § ß
1.8
\’{E} \‘{E} \”{A} \”{O} \”{U}
@ \copyright \P \S \ss
at symbol copyright paragraph section german ss
Spaces
\vspace{0.2in} \hspace{0.2in} \quad \qquad \,
vertical space 0.2in horizontal space 0.2in single character space double space small space
\: \; \! \! \!
medium space; only in math mode thick space; only in math mode negative space; only in math mode negative double space; only in math mode
4
2
Basic Mathematical Formatting
2.1
Equation Commands
$
starts and terminates in-text formulas
\[ \]
displayed one line formula, not numbered
\begin{equation} \begin{equation}\label{ \end{equation}
displayed one line formula, numbered add label
\begin{eqnarray} \begin{eqnarray}\label{ \end{eqnarray}
displayed multiline formula, numbered; add label
\begin{eqnarray*} \end{eqnarray*}
displayed multiline formula, not numbered
\begin {array}{ccc} \end{array}
produces matrices (see also §5.3)
& &=& \nonumber \mbox{ } \quad \mbox{. . . }\quad \quad \mbox{and}\quad
use between columns for aligning equals in equation arrays suppresses numbering use before − and + signs in split equations for text within a formula makes box “and” within a formula
\begin{eqnarray} \lefteqn{ } \nonumber \\ && \end\{eqnarray}
numbered equation split over two lines, for equations with long lefthand sides use “lequs” for the unnumbered version
2.2
Basic Displayed Equations – Examples
\[
Z F (b) − F (a) =
f (x)dx a
beqex
\begin{equation}
5
b
Z
b
F (b) − F (a) =
f (x)dx
(1)
a
\[ containing text
n X
x2i + yi2 ≥ 0
for all real numbers xi and yi
i=1
\begin{eqnarray*}
2
= y+1 z +1 = u+v 2
\begin{eqnarray}
2 2
z +1
= y+1 = u+v
(2) (3)
\begin{eqnarray} \begin{array}{c} numbered as a group
a=b+c d=e+f +g
(4)
\begin{eqnarray*} split (with leading minus sign on second line)
a = b + c + (c + d) −e+f
2.3
Specialized Displayed Equations – Examples
\begin{equation} \begin{array}{l}
x=y a = b2 + b + 1
6
) (5)
\begin{equation} \begin{array}{c}
x=y a = b2 + b + 1
) (6)
\begin{equation} \fbox{
x2 + 1 =y 5
(7)
evaluation of expression
f
t
2 t=0
\begin{eqnarray}\lefteqn{ }
ax2 + 2bxy + cy 2 + dx + ey + f = ιu + βv + γw + δ
equation array with big brackets on different lines
ˆ c (âˆ†Ď‰) : = H
Z D
1 âˆ†Ď‰(−∇2 )−1 âˆ†Ď‰ + ÎŚ(ωe + âˆ†Ď‰) − ÎŚ(ωe ) 2 0 − ÎŚ (ωe )âˆ†Ď‰ dx dy
equation array with big braces on different lines
H0s (T M )
=
∈ H (T M )
there exists an H s -extension s ˜ ˜ ˜ X ∈ H (T M ) with X zero on M \M . s
7
(8)
2.4
Theorem Like Environments
\newtheorem{cor}{Corollary} \newtheorem{dfn}{Definition} \newtheorem{lem}{Lemma} \newtheorem{prop}{Proposition} \newtheorem{thm}{Theorem}
to to to to to
\begin{cor} \end{cor} \begin{dfn} \end{dfn} \begin{lem} \end{lem} \begin{prop} \end{prop} \begin{thm} \begin{thm}[Gauss’ Theorem] \end{thm}
to begin a Corollary to end a Corollary
Example Remarks
5 5 H H
new new new new new
series series series series series
of of of of of
Corollaries Definitions Lemmas Propositions Theorems
to begin a Theorem with title
\noindent{\large \bf Example\,} \noindent{\large \bf Remarks\,} \noindent{\bf Proof\,} \noindent{\bf Solution\,}
Proof Solution
2.5
make make make make make
End of Proofs, etc. \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad
\blacklozenge $\blacklozenge$ \blacksquare $\blacksquare$ \square $\square$ \bigtriangledown $\bigtriangledown$ \blacktriangledown $\blacktriangledown$
end proof dollar end proof empty square dollar empty square empty triangle down dollar empty triangle down black triangle down dollar black triangle down
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3 3.1
Alphabets and Fonts Greek Letters
All greek letters are available as sub- and superscripts by preceding the codes below with “l� or “h�. For example, “lxa� is “ \alpha� and “hxa� is “ˆ\alpha�. They are also available enclosed by $, for example “dxa� produces “$\alpha $�.
\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \vartheta \iota \kappa \lambda \mu \nu \pi \varpi \rho \varrho \sigma \varsigma \tau \upsilon \phi \varphi \chi \psi \omega
Îą β Îł δ Îľ Îś Ρ θ Ď‘ Κ Îş Îť Âľ ν Ď€ $ Ď % Ďƒ Ď‚ Ď„ Ď… φ Ď• χ Ďˆ ω
3.2
xcg xcd
Γ ∆
\Gamma \Delta
xcth
Θ
\Theta
xcl
Λ
\Lambda
xcp
Î
\Pi
xcs
ÎŁ
\Sigma
xcu xcph
ÎĽ ÎŚ
\Upsilon \Phi
xcps xco
Ψ ℌ
\Psi \Omega
Italics, Bold, etc.
For the universal blank bricks, use “. . . u� (universal). To complete it, after typing the entry, use “eb� and “eit�. [Note about “bi�: If you do your papers in 12pt, modify the definition of \tenbi at the beginning.]
example example example example example
{\it {\rm {\bf {\sc {\sf
italic type, “eit� to finish roman type boldface type small caps type sans serif type 9
example example example ξ A g R
3.3
0 – 10 a–d e f g–x y z A–Z e1
3.4
ω ξ
3.5
A–Z
3.6
b g h k p t
{\sl {\tt {\em \mbox{\boldmath$. . . $} {\cal \mathfrac {\mathbb
slanted type typewriter type emphasized type only in math mode, only cap.letters only in math mode only in math mode
Boldface Letters {\bf {\bf {\bf {\bf {\bf {\bf {\bf {\bf {\bf {\bf
0} – {\bf 10} a} – {\bf d} e} f} g} – {\bf x} y} z} A} – {\bf Z} e} 1
(because of the word “be”) (because of the command “bf”) (because of the word “by”)
Boldmath Symbols \mbox{\boldmath$. . . $} \mbox{\boldmath$\omega$} \mbox{\boldmath$\xi$}
Calligraphic Letters {\cal {\cal A} –{\cal Z}
only in math mode, cap. letters
German (Fraktur) Letters \mathfrak. . . \mathfrak b \mathfrak g \mathfrak h \mathfrak k \mathfrak p \mathfrak t
only in math mode german b, german g, german h, german k, german p, german t, 10
A G H K T X
3.7
C I R R1 R2 R3 Rm Rn T Z
\mathfrak \mathfrak \mathfrak \mathfrak \mathfrak \mathfrak
A G H K T X
german german german german german german
A, G, H, K, T, X,
Open Letters {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb {\mathbb
C} I} R} R}ˆ1 R}ˆ2 R}ˆ3 R}ˆm R}ˆn T} Z}
only in math mode $
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4
Basic Mathematical Operations and Symbols
4.1
√
lim ~a a a ¯ a ˇ a˙ a ¨ a ˆ a ˜ {|} {|}
4.2 a–z A–Z 1 – 10 a–z A–Z 0 – 10
4.3 √ √2 π √ 3 2 √ n 2
Universal Operations \frac{ }{} \sqrt{ {ˆ
for general fractions universal square root superscript universal subscript universal limit universal
{ \lim { \vec{ \overline{ \bar{ \check{ \dot{ \ddot{ \hat{ \tilde{ {\mid} in-line set \left\{ \left. \! \right| \right\} sized set for large displays {\displaystyle for larger math mode formulas
Single Symbols included in $ Signs $a$ – $z$ $A$ – $Z$ $1$ – $10$ ${\bf a}$ – ${\bf z}$ ${\bf A}$ – ${\bf Z}$ ${\bf 0}$ – ${\bf 10}$
(except: “doo” for $o$)
Roots \sqrt{2} \sqrt{\pi} \sqrt[3]{2} \sqrt[n]{2}
cube root over 2 n-root over 2
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4.4
Specific Fractions
1 2
\frac{1}{2}
1 3
\frac{1}{3}
1 4
\frac{1}{4}
d dt
\frac{d}{dt}
du dt
\frac{du}{dt}
dx dt
\frac{dx}{dt}
dy dt
\frac{dy}{dt}
dz dt
\frac{dz}{dt}
∂ ∂x
\frac{\partial}{\partial x}
∂ ∂y
\frac{\partial}{\partial y}
∂z ∂x
\frac{\partial z}{\partial x}
∂2 ∂x∂y
\frac{\partialˆ2}{\partial x \partial y}
∂3 ∂x∂y∂z
\frac{\partialˆ3}{\partial x \partial y \partial z}
4.5
Superscripts
All letters, capital letters and numbers from 0 to 10 are available as superscripts, by preceding the desired letter or number with “h”. E.g. “ha” gives ˆa, “hca” gives “ˆA”, “h1” gives “ˆ1”. Exceptions, to avoid conflict with words and the universal macro, are “hee” for superscript e, “huu” for superscript u. ˆ{ a –z A –Z 0 – 10 2 3
x2 , y 2 , z 2
ˆa – ˆz ˆA – ˆZ ˆ0 – ˆ{10} ˆ2 ˆ3 xˆ2, yˆ2, zˆ2
high universal (except: “hee” for e , “huu” for u )
to avoid typing the number to avoid typing the number
13
−1 ij ijk jk † ⊥ 0 ∗ ?
4.6
ˆ{-1} ˆ {ij} ˆ {ijk} ˆ {jk} ˆ\dagger ˆ\perp ˆ\prime ˆ\ast ˆ\star
Subscripts
All letters, capital letters and numbers from 0 to 10 are available as subscripts, preceding with “l”. E.g. “la” gives “ a”, “lca” gives “ A”, “l1” gives “ 1”.
{ –z A – Z 0 – 10 a
ij ijk jk
yn zn ∗ ?
a– z A– Z 0 – {10} {ij} {ijk} {jk} yn zn \ast \star
low universal (except: “luu” for u )
14
4.7 p¯ α ¯ p˙ p¨ p pˆ ~a −→ PP −→ PQ
4.8 + − ± ∓ ÷ ◦ • ⊕ × ⊗ s ∧ = =0 ≥ ≤ 6 = ∼ = ≡ ≈
Overcharacters \bar{p} \bar{\alpha} \dot{p} \ddot{p} \overline{p} \hat{p} \vec{a} \stackrel{\textstyle\longrightarrow}{\rm PP} \stackrel{\textstyle\longrightarrow}{\rm PQ};
Binary Operations and Relations + − \pm \mp \div \circ \bullet \oplus \ominus \times \otimes \,\circledS\, \wedge
plus minus plus-minus minus-plus divide composite bullet direct sum direct difference times tensor product semi direct product wedge product
\geq \leq \neq \cong \equiv \ll \gg \approx
equals equals zero greater than or equal less than equal not equal isomorphic equivalent much less than much greater than approximately
15
4.9 ( ) [ ] { } h hh i ii
4.10 ℵ ~ 0 [ ] ♥ ∝ k £ t ` k ∇ ∂ ∞ ℘ < = ∠
Sized Parentheses \left( The “left” and “right” commands \right) effect the size of the braces. \left[ They always have to appear in pairs! \right] Invisible braces are made with \left. and \right. \left\{ \right\} \left\langle \left\langle \! \left\langle \right\rangle \right\rangle \! \right\rangle \left. \right.
Single Mathematical Symbols \aleph \hbar \prime \flat \sharp \heartsuit \propto \| \pounds \pitchfork \ell \| \nabla \partial \infty \wp \Re \Im \angle
aleph Planck’s constant prime, use “hpr” for superscript flat sign, “hfl” for superscript sharp sign, “hsh” for superscript sweetheart proportional to Lie derivative transversal script l norm nabla partial derivative infinity Weierstrass p-function real part alternate imaginary part alternate angle
16
4.11 ⇒ ⇐ ⇔ ∅ ∅ ∈ 6∈ \ ⊂ ⊆ ⊃ ⊇ ∩ T ∪ S | ∃ ∀
4.12 7→ → −→ ↔ ← ↑ % & · ··· .. . ... .. .
Set Theoretic Symbols \Rightarrow \Leftarrow \Leftrightarrow \varnothing \emptyset \in \not\in \setminus \subset \subseteq \supset \supseteq \cap \bigcap \cup \bigcup \mid \exists \forall
implies implied by equivalent to empty set empty set alternate element of not an element of set difference subset subset or equals superset superset or equals intersection big intersection union big union vertical bar, with spacing there exists for all
Arrows and Dots \mapsto \rightarrow \longrightarrow \leftrightarrow \leftarrow \uparrow \upharpoonright \nearrow \searrow \cdot \cdots
arrow with tail rightarrow longrightarrow leftrightarrow leftarrow uparrow upharpoonright slanted up right slanted down right centered dot centered dots
\ddots \ldots
diagonal dots lower dots
\vdots
vertical dots
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4.13
Trig Functions
cos cosh cos2 cos θ cos φ sin sinh sin2 sin θ sin φ sech tan tanh
\cos \cosh \cosˆ2 \cos \theta \cos \phi \sin \sinh \sinˆ2 \sin \theta \sin \phi {\rm sech}\, \tan \tanh
4.14
Log-like Symbols
exp log ln sup inf max min lim lim inf lim sup det ker dim arg gcd
\exp \log \ln \sup \inf \max \min \lim \liminf \limsup \det \ker \dim \arg \gcd
hyperbolic cosine cosine squared cosine of theta cosine of phi hyperbolic sine sine squared sine of theta sine of phi hyperbolic sech hyperbolic tangent
exponential logarithm natural logarithm supremum infimum maximum minimum limit universal limit inferior limit superior determinant kernel dimension argument greatest common divisor
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4.15
Combinations of Mathematical Symbols
−1 kuk |a| Aia LA µ vA ν g∗ g∗ so(3) so(3) SO(3) T ∗Q Tq∗ Q div Aut( Diff( Im( Im(z) Re( Re(z) (0) (0, 0) (0, 0, 0) (a1 , a2 , a3 ) (x, y) (x, y, z) x2 + y 2 dx dy dx dy dz dy/dt dx/dt dz/dt ∂z/∂y a+b a×b (a × b)
-1 \ | {\bf u} \ | |a| Aˆi {\;a} L A{}ˆ\mu vˆA{} \nu \mathfrak g ˆ{\ast} $\mathfrak g ˆ{\ast}$ \mathfrak{so}(3) so(3) SO(3) Tˆ\ast Q Tˆ{\ast} {q} Q {\rm div}\, {\rm Aut}( {\rm Diff}( {\rm Im}( {\rm Im}(z) {\rm Re}( {\rm Re}(z)
minus one absolute value; staggered, high and low staggered, variation 1 staggered, variation 2 german g star;
divergence automorphism universal diffeomorphism universal real part universal real part of z real part universal real part of z
dy/dt dx/dt dz/dt \partial z/\partial y {\bf a} + {\bf b} {\bf a} \times {\bf b} ({\bf a} \times {\bf b})
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5
Integrals, Sums, Products and Matrices
5.1
Integrals
Z \int
integral universal; add limits with “hu” and “lu”
\int \!\!\! \int
double integral
ZZ
ZZZ \int \!\!\!\int \!\!\!\int triple integral I \oint Z
contour integral
1
\intˆ1 0 0
Z
b
\intˆb a a
Z \int D D
Z \int {{\mathbb R}ˆ3} R3
Z
∞
\intˆ\infty {−\infty} −∞
Z
2π
\intˆ{2 \pi} 0 0
20
5.2
Sums, Limits, etc.
X
\sum
P
(in-text)
(displayed)
Pn
(in-text)
(displayed)
Qn
(in-text)
(displayed)
Sn
(in-text)
(displayed)
Tn
(in-text)
(displayed)
lim(x,y)→(0,0)
(in-text)
lim
(displayed)
lima→∞
(in-text)
lim
(displayed)
limx→x0
(in-text)
n X
i=1
i=1 n Y
i=1
i=1 n [
i=1
i=1 n \
i=1
i=1
lim (x,y)→(0,0)
a→∞
x→x0
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5.3
Sample Matrices
x1 x2 x3
x y
\left( \begin{array}{c} x1 \\ x2 \\ x3 \end{array} \right)
\left[ \begin{array}{c} x \\ y \end{array} \right]
a b c d
a b c d
1 0
1 0 0
\left[ \begin{array}{cc} a & b \\ c & d \end{array} \right]
0 1
0 −1
\left( \begin{array}{cc} a & b \\ c & d \end{array} \right)
\left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] 1 0
0 1 0
a b
d e
g h
a b d e g h
\left[ \begin{array}{cc} 0 & 1 \\ - 1 & 0 \end{array} \right] 0 0 1
\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right)
\left| \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right|
c f i
\left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right)
c f i
a
b
c
d
e
f
g
h
i
\left[ \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right]
22
6 6.1
Boxes, Tabbing and Tabular Environment Samples Boxes
Note:
framed box, edit its size
text
type header
framed box, edit its size
text
type header
double framed box, edit its size
text
6.2
Tabbing tabbing example 1
items items
for for
row row
one two
23
6.3
Tabular tabular example 1 (5 columns)
Partials exist and are continuous
=⇒
Definition of derivative ↓ Differentiable =⇒ Partials exist
tabular example 2 (2 columns within a fbox-parbox)
Summary of Important Formulas for §2.1
Box 2.1.1 Velocity V =
∂φ ∂t
Va =
vt = Vt ◦ φ−1 t
∂φa ∂t
vta = Vta ◦ φ−1 t
Covariant Derivative Dv · w = ∇w v
(∇w v)a =
∂v a b a b c w + γbc w v ∂xb
tabular example 3 (3 columns without a frame)
Classical Tensor Analysis {xa } ea =
∂z i ˙ ii ∂xa
∂xb e¯a = eb ∂x ¯a a
∂x ¯ b e¯a = e b ∂x ¯
Tensor Analysis on Manifolds Coordinates
{xa }
coordinate basis vectors
∂ = ea ∂xa ∂xb ∂ ∂ = ∂x ¯a ∂x ¯a ∂xb ∂x ¯a b d¯ xa = dx ∂xb
change of coordinates
24
tabular example 4 (2 columns with lines)
Classical Mechanics immersed Lagrangian manifold Λ → (T ∗ Q, Ω) Λ = graph of dS T ∗Q Lagrangian manifold Ω ⊂ (T ∗ Q, ΩQ ) × (T ∗ R, −ΩR ) composition of canonical relations
Quantum Mechanics element of L2 (Q) or D0 (Q) ψ = exp(iS/~) Hilbertspace (possibly unbounded) L2 (R) to L2 (Q) composition of operators
tabular example 5 (same as tabex4, but within a framed box)
Classical Mechanics immersed Lagrangian manifold Λ → (T ∗ Q, Ω) Λ = graph of dS T ∗Q Lagrangian manifold Ω ⊂ (T ∗ Q, ΩQ ) × (T ∗ R, −ΩR ) composition of canonical relations
Quantum Mechanics element of L2 (Q) or D0 (Q) ψ = exp(iS/~) Hilbertspace (possibly unbounded) L2 (R) to L2 (Q) composition of operators
tabular example 6 (3 columns with lines)
Case Unconstrained Purely Kinematic Horizontal symmetries General principal bundle case
Conditions D q = Tq Q
Connection Asym (q) ˙ = I−1 J(q) ˙
Dq ∩ Tq (Orb(q)) = {0}
Akin (q) ˙ =0
Dq ∩ Tq (Orb(q))G = Tq (Orb(q))H
Asym (q) ˙ + Akin (q) ˙ = I−1 JH (q) ˙
Dq + Tq (Orb(q)) = Tq Q
Asym (q) ˙ + Akin (q) ˙ = I−1 J nhc (q) ˙
25
7
Pictures
You must include the line
\usepackage{graphicx}
at the beginning of your document in order to use these commands.
\begin{figure} \vspace{2in} \hspaceâ&#x2C6;&#x2014;{.4in} \includegraphics{myfigure.eps} \caption{} \end{figure}
26