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Math
LATEX Math Tricks
K. Cooper
2012
Math
Prerequisites
Prerequisites
\documentclass\usepackageEnvironments
Math mode
Math
Prerequisites
Math Mode
Uses math italic font
Uses di�erent spacing, ignoring all but explicit spaces
More �exibility in moving o� of baseline
Sometimes displayed
Math
Texmaker
Why LATEX?
Defacto standard for mathematical typesetting
Many journals accept papers in that format, and even supplystyle �les
Superior quality
Multiple platforms
Programmable
Math
Texmaker
Texmaker
http://www.xm1math.net/texmaker/
Free
Knows symbols and environments
PDF synchronization
Text folding
Math
Math Typesetting
Points of Style
Mathematical notation is a subset of English.
Punctuation
Math italic vs. roman fonts
Math
Math Typesetting
Points of Style
Mathematical notation is a subset of English.
Punctuation
Math italic vs. roman fonts
Math
Math Typesetting
Points of Style
Mathematical notation is a subset of English.
Punctuation
Math italic vs. roman fonts
Math
Math Typesetting
Points of Style
Mathematical notation is a subset of English.
Punctuation
Math italic vs. roman fonts
Math
Math Typesetting
Points of Style
Mathematical notation is a subset of English.
Punctuation
Math italic vs. roman fonts
In the sequel we shall use
f(x) =
{0 x < 0,sinx otherwise.
Math
Math Typesetting
AMS Math
\usepackage{amsmath,amsfonts,amssymb}Provides blackboard bold fonts ( Rn )
Provides \align and \cases
Math
Math Typesetting
Alignment
. . . and a corresponding sequence of closed form mesoscopiccontinuum equations (written here for an isolated system with zeroexterior forces)
∂tρ̄η + ∂x(ρ̄ηv̄η) = 0(3.1)
∂t(ρ̄ηv̄η) + ∂x(ρ̄η(v̄η)2)− ∂x(T η(c),n + T η(int),n) = 0(3.2)
Math
Math Typesetting
Alignment
\ldots and a corresponding sequence of closed form
mesoscopic continuum equations (written here for an
isolated system with zero exterior forces)
\begin{align}
\partial_t\bar{\rho}^\eta +
\partial_x(\bar{\rho}^\eta\bar{v}^\eta) &= 0\\
\partial_t(\bar{\rho}^\eta\bar{v}^\eta) +
\partial_x(\bar{\rho}^\eta(\bar{v}^\eta)^2) -
\partial_x(T_{(\text{c}),n}^\eta +
T_{(\text{int}),n}^\eta) &=0
\end{align}
Math
Math Typesetting
align
To get only one equation number, use \notag on lines not to benumbered.
To get no equation numbers, use the align* environment.
To get an equation number using the align* environment, usee.g. \tag{2.1} to put the number in explicitly.
Align starts math mode. You cannot use it when you arealready in math mode.
Math
Math Typesetting
Align
Align can do more than one column, but it can be problematic. Ingeneral, use tabular or array environments for complex layouts.
u = arctanx, dv = 1 dx
du =1
1 + x2dx, v = x.
\begin{align*}
u &= \arctan x, & dv &= 1 \, dx\\
du &= \frac{1}{1 + x^2}\, dx, & v &= x.
\end{align*}
Math
Math Typesetting
Matrices
Consider the matrix
A =(
3 −4α α
2
).
Math
Math Typesetting
Matrices
Consider the matrix
\begin{equation*}
A =
\begin{pmatrix}
3 & -4\\
\alpha & \frac{\alpha}{2}
\end{pmatrix}
\end{equation*}
Math
Math Typesetting
Matrices
Several di�erent environments
pmatrix - parenthesis matrix
bmatrix - bracket matrix
array - just make an array and specify delimiters using \leftand \right. This requires an argument to describe alignmentof each column.
Math
Math Typesetting
Matrices
Consider the array
A ={
3 −4α α
2
}.
Math
Math Typesetting
Piecewise-de�ned functions
In the sequel we shall use
f(x) =
{0 x < 0,sinx otherwise.
Math
Math Typesetting
\cases
In the sequel we shall use
$$
f(x) =
\begin{cases}
0 & x<0,\\
\sin x & \text{otherwise}.
\end{cases}
$$
Math
Math Typesetting
Display Math
Display formulas that would force text to be badly spacedvertically
Display long lines
If the displayed line is still too long, break the line before anequal sign or addition symbol. Shift the continuation line by a\qquad.
Math
Math Typesetting
Mathematical Spacing
LATEX usually spaces mathematics properly
Sometimes you need to put in explicit space for clarity.
Use a thin space (\,) for integrals:∫∞0 sinxdx vs.
∫∞0 sinx dx
Use an ordinary space (\ ) for quali�cations:fN (x) =
∑Ni=0 x
i for N = 1, 2, . . .Use a \qquad for continuations:
∞∑n=1
1n> 1 +
12
+14
+14
\qquad here−→ +
4 times︷ ︸︸ ︷18
+ · · ·+ 18
+ · · ·
Math
Math Typesetting
Details
Use \left and \right liberally
Use\sum when you want a sum - not \SigmaMatch ellipses to the surrounding notation: , . . . , vs. + · · ·+.
Plain TEX commands still work in LATEX.
