2024年1月21日发(作者：幼师中班数学试卷)

frac{1}{ displaystyle lim_{u rightarrow infty}} by Goldman2000@126: -------------------------

To obtain a summation sign such aswe type sum_{i=1}^{2n}. Thusis obtained by typing[ sum_{k=1}^n k^2 = frac{1}{2} n (n+1).]We now discuss how to obtain integrals in mathematical documents. A typical integral is the following:This is typeset using[ int_a^b f(x),dx.]The integral sign is typeset using the control sequence int, and the limits of integration (in this case a and b are treatedas a subscript and a superscript on the integral integrals occurring in mathematical documents begin with an integral sign and contain one or more instances of dfollowed by another (Latin or Greek) letter, as in dx, dy and dt. To obtain the correct appearance one should put extraspace before the d, using ,. Thusandare obtained by typing[ int_0^{+infty} x^n e^{-x} ,dx = n!.][ int cos theta ,dtheta = sin theta.][ int_{x^2 + y^2 leq R^2} f(x,y),dx,dy= int_{theta=0}^{2pi} int_{r=0}^Rf(rcostheta,rsintheta) r,dr,dtheta.]and[ int_0^R frac{2x,dx}{1+x^2} = log(1+R^2).] some multiple integrals (i.e., integrals containing more than one integral sign) one finds that LaTeX puts too muchspace between the integral signs. The way to improve the appearance of of the integral is to use the control sequence !to remove a thin strip of unwanted space. Thus, for example, the multiple integralis obtained by typing[ int_0^1 ! int_0^1 x^2 y^2,dx,dy.]Had we typed[ int_0^1 int_0^1 x^2 y^2,dx,dy.]we would have obtainedA particularly noteworthy example comes when we are typesetting a multiple integral such asHere we use ! three times to obtain suitable spacing between the integral signs. We typeset this integral using[ int !!! int_D f(x,y),dx,dy.]Had we typed

[ int int_D f(x,y),dx,dy.]we would have obtainedThe following (reasonably complicated) passage exhibits a number of the features which we have been discussing:One would typeset this in LaTeX by typing In non-relativistic wave mechanics, the wave function$psi(mathbf{r},t)$ of a particle satisfies theemph{Schr\"{o}dinger Wave Equation}[ ihbarfrac{partial psi}{partial t}= frac{-hbar^2}{2m} left(frac{partial^2}{partial x^2}+ frac{partial^2}{partial y^2}+ frac{partial^2}{partial z^2}right) psi + V psi.]It is customary to normalize the wave equation bydemanding that[ int !!! int !!! int_{textbf{R}^3}left| psi(mathbf{r},0) right|^2,dx,dy,dz = 1.]A simple calculation using the Schr\"{o}dinger waveequation shows that[ frac{d}{dt} int !!! int !!! int_{textbf{R}^3}left| psi(mathbf{r},t) right|^2,dx,dy,dz = 0,]and hence[ int !!! int !!! int_{textbf{R}^3}left| psi(mathbf{r},t) right|^2,dx,dy,dz = 1]for all times~$t$. If we normalize the wave function in thisway then, for any (measurable) subset~$V$ of $textbf{R}^3$and time~$t$,[ int !!! int !!! int_Vleft| psi(mathbf{r},t) right|^2,dx,dy,dz]represents the probability that the particle is to be foundwithin the region~$V$ at time~$t$.三、在线公式编辑器

四、Miktex模板% This is , a variation of % (the demonstration file of% the LaTeX macro package from Springer-Verlag% for Lecture Notes in Computer Science,

%institute{Princeton University, Princeton NJ 08544, USA,email{d@}, WWW home page:texttt{users/homedir iekeland/web/}}maketitle % typeset the title of the contributionabstract{2017.3.22. textbf{Keyword:} XXX; XXX; XXX.}section{First Paper}Well, it is just testing. I don\'t know what begin{equation}e^{pi{i}}+1=0end{equation}section{Second Paper}begin{eqnarray*}cos 2theta & = & cos^2 theta - sin^2 theta & = & 2 cos^2 theta - {eqnarray*}section{Third begin{figure}centeringincludegraphics[width=0.5textwidth]{}

caption{Test figure}label{Figure name}end{figure}end{document} 五、默认字体设置Preference->Editor


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