Sample Course

Math & Physics Macros

Apr 4, 2021

Table of Contents!

Item wrapping

If you’re interested in wrapping items in parenthesis, no matter how big, use the \pqty{..} macro to do so. For example,

\[\pqty{\int_{0}^{1} e^{-x/2a}dx}\]

it wraps the largest one for the given expression you have. The same effect happens for brackets as well using \bqty{..}, bars for \abs{..} and double bars for \norms{..} all of which is given below respectively:

\[\bqty{\sum x^6 + 3} \ \ \ \ % a quantity in brakets \abs{\int 3x^2y} \ \ \ \ % a quantity in vertical bars \norm{\int 23} \ \ % a norm ||a||\]

Orders & Integrals

When evaluating things like integrals, just use the \evl^{..}_{..} macro to make the upper and lower limits shown:

\[\frac{1}{2x}\evl_{\infty}^{0.9}\]

If you want to write the order of magnitude of something for example “the order of 30 is $\order{30}$” the \order{..} macro gives the way to typeset it.

Vectors

For various types of vectors, there are many commands. For a simple bolded vector (or symbol in general) use \vb{..} to make it bold as in $\vb{a}$ or $\vb{\alpha}$. If you want an arrow above it use \va{..} macro to give $\va{a}$ or $\va{\alpha}$ and if you want a hat above your symbol, use \vu{..} to give things like $\vu{w}$. For basic vector operations like dot product and cross product to give things like $\va{a} \vdot \va{b}$ or $\va{e} \cp \va{i}$, use \vdot and \cp respectively.

Bra-Ket Vectors

If you need to use these vectors, then \ket{..} gives $\ket{\phi}$, \bra{..} gives $\bra{\psi}$, \braket{..}{..} gives $\braket{\alpha}{\beta}$, \ketbra{..}{..} gives $\ketbra{\gamma}{\omega}$, \ev{..} gives $\ev{\beta}$, and \mel{..}{..}{..} for matricies with those vectors to give $\mel{\ze}{A}{\be}$.

Gradients and Calculus Things

For things like gradients and other calculus things, use \grad to yield $\grad$, \div to yield $\div$, \curl to yield $\curl$, \laplacian to yield $\laplacian$. If you’re doing matrix operations, you can use \tr for $\tr$, \Tr for $\Tr$, \rank for $\rank$, and \erf for $\erf$. If you want to add a functional variation, you can use \var.. to yield $\var f(x)$. For derivatives, you can use \dv{..}{..}, \pdv{..}{..}, and \fdv{..}{..} to get respectively

\[\dv{x}{y} \ \ \pdv{f(x,y)}{y} \ \ \fdv{w}{x}\]

If you have more than one derivative taken, you can use the multi-derivative macro known as \mdv{..}{..}{..}, \mpdv{..}{..}{..}, and \mfdv{..}{..}{..} to get

\[\mdv{4}{x}{y} \ \ \mpdv{4}{f(x,u)}{u} \ \ \mfdv{9}{x}{y}\]

Note: the mult-derivative macros given here are custom for the site, the physics package has other notation, but won’t load for this site.

For things like residues of complex functions you can use \Res to get $\Res$, \pv or \PV for the Cauchy Principle Value to get $\pv$ or $\PV$ respectively. For the real or imaginaary parts of numbers you can use \Re{..} ot \Im{..} to get $\Re{f(x + yi)}$ and $\Im{q(r + iu)}$. If you have things like in-line text or cases, you can have \qq{..} for a quick quad text arguments as in

\[f(x,y) = \begin{cases} x^2 & \qq{early} \\ \sin(x) & \qq{afternoon} \\ \cos(y) & \qq{evening} \end{cases}\]

For other things like logical phrases and complex conjugates we have other \q... macros all given below (check the .md file for the way to write them):

\[\qc \ \ \qcc \qif \ \ \qthen \ \ \qelse \ \ \qotherwise \ \ \qunless \ \ \\ \qgiven \ \ \qusing \ \ \qassume \ \ \qsince \ \ \qlet \ \ \qfor \ \ \qall \ \ \qeven \ \ \\ \qodd \ \ \qinteger \ \ \qand \ \ \qor \ \ \qas \ \ \qin\]

Sets and Things

If you want to write a set use the \set{..} macro to give things like $\set{1, 4, 2}$ and if you want to join or find the intersection of the sets, then use the \sor and \sand macros to give respectively $\sor$ and $\sand$. These are also useful for anti-commutators too! For the opening and ending of a set, you can also use \lset and \rset to have the opening and closing of set respectively: $\lset$ and $\rset$. and If you want to talk about a set’s cardinality, you can have \card{..} to give $\card{A} = 4$. For things like minimum and maximum, you can use the \mn{..} and \mx{..} macros to yield $\mn{g(x)}$ and $\mx{y(s)}$ respectively. If you have domains or constraints, they can be subscripts like \mn{..}_{..} for $\mn{x(y)}_D$ over domain $D$. For the logical operation ‘implies’, you can use \impl as a macro for \Rightarrow that gives $\impl$. If you like writing definitions symbolically, there is also a \as macro that gives $\as$. Writing out a definition is more like $A \as \set{1, 3, 5}$ (see the .md file to see how it flows).

If you want to write a sum easily you can use the \sum{..}{..}{..} macro to indicate the variable, starting index, and ending index. It’s used to write the formula below:

\[\bs{x}{1}{\infty} \frac{1}{x} = \infty\]

Also, if you want to write below any formula you have, you can use the \bel{..}{..} to indicate what you want the formula to be as well as what you want underneath it. For example if we wanted to label the sum as a series, we can have:

\[\bel{\bs{x}{1}{\infty} \frac{1}{x}}{\text{series}} = \infty\]

For the sets commonly used in mathematics to indicate numbers, we have \R, \Nat, \S, \O, \Q, \C, \H, \Z. Given below for your convenience.

\[\R \ \ \Nat \ \ \S \ \ \O \ \ \Q \ \ \C \ \ \H \ \ \Z\]

Greek Letters

Greek letters that have been simplified in macro length are all given here. They have, in macro form 2-3 characters, for example \alpha is now \al and gives $\al$. They are all given below (check the .md file for this page for the ways to write them)…

\[\al \ \ %alpha \be \ \ %beta \ga \ \ %gamma \de \ \ %delta \ep \ \ %epsilon \ze \ \ %zeta \ta \ \ %theta \io \ \ %iota \kap \ \ %kappa \lam \ \ %lambda \omc \ \ %omicron \ups \ \ %upsilon \om \ \ %omega \sig \ \ %sigma \Ga \ \ %Gamma \De \ \ %Delta \Ta \ \ %Theta \Lam \ \ %Lambda \Ups \ \ %Upsilon \Om \ \ %Omega \Sig %Sigma\]

That’s about if for the math and physics related vectors given here! Enjoy the day and have a positive outlook on things.