Hi, thaught it may be of some use:
Introduction to LaTeX: 2. Typing Math
Introduction to LaTeX: 2. Typing Math
Text and math modes (review from Part 1)
TeX has three basic modes: a text mode, used for typesetting ordinary text,
and two types of math modes, an ordinary math mode for math formulas set
"inline", and a display math mode, used for displayed math formulas. At any
given point during the processing of a document, TeX is in one of those three
modes. The behavior of TeX depends on the mode it's in. For example, certain
characters (like the underline or caret symbols) are only allowed in a math
mode, while others (like the "greater than" symbol) take on completely
different meanings, depending on whether TeX is in text or in math mode. (Try
this: write some ordinary text that includes the string ">From" (which is often
generated by email software), and see what the ">" symbol becomes after
compiling the document. In math mode, by contrast, ">" does what you'd expect:
it serves as the "greater than" symbol.)
Text mode.
This is the normal, or default, mode of TeX. TeX stays in that mode unless it
encounters a special instruction that causes it to switch to one of the math
modes, and it returns to text mode following a corresponding instruction that
indicates the end of math mode.
Ordinary (inline) math mode.
Mathematical material to be typeset inline must be surrounded by single dollar
signs. For example: "$a^2 + b^2 = c^2$". The single dollar signs surrounding
this expression cause TeX to enter and exit (ordinary) math mode.
Display math mode.
Material that is surrounded by a pair of escaped brackets ("\[" and "\]"), or
by "equation environments" such as \begin{align} ... \end{align}, or
\begin{equation} ... \end{equation} is being processed by TeX in "display math
mode." This means that the expression enclosed gets displayed on a separate
line (or several lines, in case of multiline equations). Longer mathematical
formulas and numbered formulas are usually "displayed" in this manner. Note
that the commands for entering and leaving display math mode are distinct
(\begin{...} or \[ for entering and \end{...} or \]), in contrast to the
ordinary math mode, where a single dollar sign serves both as entry and exit
command. This allows for better error checking. (This is a major difference
between LaTeX and AmSTeX or Plain TeX. In the latter two TeX versions, a double
dollar sign ($$) is used to indicate the beginning and end of display math
mode.
While the double dollar sign (still) works in LaTeX, it is not part of the
"official" LaTeX command set (in fact, most books on LaTeX don't even mention
it) and its use is discouraged. Use the bracket pair "\[", "\]" instead.
)
Basic math
Elementary arithmetic operations:
The plus (+), minus (-), division (/) symbols have the usual meaning. To
denote multiplication explicitly (this is rarely necessary), use \cdot
(producing a centered dot) or \times (producing an "x"). The "equal", "less
than", and "greater than" symbols on the keyboard work as expected; to get
"less than or equal", use "\le"; similarly, "\ge" gives "greater than or
equal".
Square roots: Square roots are generated with the command \sqrt{...}. For
example, $z=\sqrt{x^2+y^2}$.
Subscripts and superscripts:
These are indicated by carets (^) and underscores (_), as in $2^n$ or $a_1$.
If the sub/superscript contains more than one character, it must be enclosed in
curly braces, as in $2^{x+y}$.
Fractions and binomial coefficients:
Fractions are typeset with $\frac{x}{y}$, where x stands for the numerator and
y for the denominator. There is a similar construct $\binom{x}{y}$ for binomial
coefficients. (The latter is part of the amsmath enhancements which you get
when using "amsart" as documentclass.)
Sums and integrals:
The symbols for sums and integrals are \sum and \int, respectively. These are
examples of "large" operators, and their sizes are adjusted by TeX
automatically, depending on the context (e.g., inline vs. display math). Note
that the symbol generated by \sum is very different from the "cap-Sigma"
symbol, \Sigma; the latter should never be used to denote sums. TeX uses a
simple, but effective scheme to typeset summation and integration limits:
Namely, lower and upper limits are specified as sub- and superscripts to \sum
and \int. For example, $\sum_{k=1}^n k = \frac{n(n+1)}{2}$. (Note that the
"lower limit" "k=1" here must be enclosed in braces.)
Limits:
The "subscript" trick works also for limits; "\lim" produces the "lim" symbol,
and the expression underneath this symbol (for example, "x tends to infinity")
is typeset as a subscript to \lim: $\lim_{x\to\infty}f(x)=0$. Here "\to"
produces the arrow, and "\infty" (note the abbreviation - \infinity does not
work!) produces the "infinity" symbol. "\limsup" and "\liminf" work similarly,
as do "\sup" and "\inf" (for supremum and infinimum), and "\max" and "\min"
(for maximum and minimum). For example, $\max_{0\le x\le 1}x(1-x)=1/4$.
block quote
Exercise 2.1:
Continuity of a function f(x) at a point x=c can be defined in terms of a
limit: "f(x) is continuous at x=c if lim .....". Fill in the blanks and typeset
the statement first inline, and then with the "lim ..." formula displayed on a
single line. Observe how TeX typesets the limit differently, depending on the
context.
block quote end
block quote
Exercise 2.2:
Typeset the binomial theorem (giving an expansion for (x+y)^n) in TeX, first
as an "inline" formula (enclosed in a pair of single dollar signs), then as a
displayed formula (enclosed in a pair \[, \]). Compile the TeX file, and
observe the differences in the appearance of the output of the inline and the
displayed formulas.
block quote end
Operators:
TeX has commands for common mathematical "operators" or "functions", such as
\sin, \cos, \log, \ln, \exp, \arctan, etc. You should always use these commands
instead of simply typing "sin", "cos", etc., without the backslash. Using the
TeX commands ensures that the operators get typeset in the proper font and
takes care of the spacing surrounding these operators.
block quote
Exercise 2.3:
Typeset the addition formula for the sine: sin(x+y) = sin x cos y + cos x sin
y, first using the proper TeX commands \sin and \cos and then by just typing
sin and cos without the backslash. Observe the difference.
block quote end
More math
Greek letters and other special characters:
The commands for Greek letters are easy and intuitive: Just type $\epsilon$,
$\delta$, $\nu$, $\phi$, etc. To get upper case versions of these letters,
capitalize the appropriate command; e.g., $\Delta$ gives a "cap-Delta" (which
looks like a triangle). The most common notation for the reals, rationals, and
integers involves the so-called "blackboard bold" font; to get these symbols
use \mathbb{...} (in math mode): $\mathbb{R}$, $\mathbb{Q}$, $\mathbb{Z}$.
Similarly \mathcal{...} produces a symbol in "script" or "caligraph" font,
often used to denote sets: For example, $\mathcal{A}$ generates "script A".
Parentheses:
The symbol pairs (), [], and \{ \} (note the backslash!) generate round,
square, and curly parentheses in normal size. They work fine in math mode, but
mathematical expressions often look better if the parentheses are enlarged to
match the size of the expression. There are ways to manually enlarge these
parentheses (by preceding the symbol with a command like \big, \bigg, \Big,
etc.), but one rarely has to use these, since TeX can (in most cases)
automatically size parentheses. To let TeX do the sizing, precede the left
brace by \left, and the right brace by \right. This also works for other
parentheses-like constructs, such as the absolute value symbol "|". Here is an
example:
\[
\left|\sum_{i=1}^n a_ib_i\right|
\le
\left(\sum_{i=1}^n a_i^2\right)^{1/2}
\left(\sum_{i=1}^n b_i^2\right)^{1/2}
\]
block quote
Exercise 2.4:
Typeset the above expression and look at the output. (It's a famous
mathematical theorem!). Then remove, or comment out, one of the bracket
expressions (say, one instance of "\left("), and see what error messages you
get. All bracket expressions generated by \left.. or \right.. must occur in
pairs, and TeX gives an error message if this is not the case. (The left and
right brackets don't have to be of the same type; for example,
$\left\[\frac{3}{4}, \frac{4}{5}\right[$ to denote the half-open interval [3/4,
4/5[ is perfectly legal.)
block quote end
Displayed equations
Single line displays:
To get a single line, displayed equation (without equation number), just use
the pair "\[", "\]". If you want TeX to automatically number the equation, use
instead the \begin{equation} ... \end{equation} environment. (The asterisk
variant, \begin{equation*} ... \end{equation*}, turns off the equation
numbering, and is equivalent to typing \[ ... \].)
Multi-line equation environments:
Things get more complicated if you have multiline equations that need to be
lined up at suitable places. For most situations, the \begin{align} ...
\end{align} environment, and its variant \begin{align*} ... \end{align*}, are
sufficient. As with the equation environment, the asterisk version does not
automatically number equations.
The use of align is best illustrated with an example:
\begin{align} (a+b)^3 = (a+b)^2(a+b)\\
=(a^2+2ab+b^2)(a+b)\\
=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
=a^3+3a^2b+3ab^2+b^3
\end{align}
Here a double backslash (\\) is used to separate the lines, and an ampersand
symbol () is used to indicate the place at which the formulas should be
aligned. You can include more than one ampersand symbol per line to specify
alignment at multiple columns, but the number of alignment symbols must be the
same for each line of the display. Multiple alignments are rarely needed; in
almost all cases a single alignment symbol, usually placed right before an
equality (or inequality) sign, is enough.
block quote
Exercise 2.5:
Typeset the above multiline equation, compile it, and look at the output on
the screen. Also, make some intentional mistakes (like leaving out the
ampersand symbol, or leaving out one of the \\'s), and see what kind of error
messages you get. Errors in multiline displays are among the most difficult to
track down and diagnose.
block quote end
Spacing in math mode
In math mode (both ordinary and display math), TeX decides on spacings between
symbols in math mode, using rather sophisticated algorithms; in particular,
any blank spaces inside math mode are ignored
, For example, the formula "$a^2 + b^2 = c^2$ could have been typed as
"$a^2+b^2=c^2$", or even placed on two different lines, without any difference
in the output. Letting TeX figure out the spacings almost always results in
very good looking output, and you should avoid putting explicit spaces into
mathematical formulas. However, there are a few situations where one does need
appropriate spacing instructions. For those cases, there is a standard spacing
command, "\quad" which generates the right amount of horizontal spacing to
separate two equations on the same line, or a formula from an associated range
or condition (such as "n=2,3,...") that is given on the same line, usually in
parentheses.
block quote
Exercise 2.6:
Typeset the recurrence defining the Fibbonacci numbers, along with appropriate
initial conditions. Use a single line display, with appropriate spacing
commands (\quad's) separating the parts.
Was it helpfull?
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http://www.math.uiuc.edu/~hildebr/tex/course/intro2.html
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Jeet.delhi
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your message folowes:
Hi
As I have to submit my assignments online in DOC format, I want to
know how I can type the simbols like "Delta", "To the power of",
"Squire root of A" or "B". These simbols are not available in Jfws
"Select a simbol to print" diolog. any idea on how to do it?
With best regards
Syed Imran
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