LaTeX数学公式.docx

1、LaTeX数学公式LaTeX数学公式2012-03-12 16:26:46|分类：LaTeX|举报|字号订阅zz from: revised by Goldman20001261、数学公式的前后要加上$或(和)，比如：$f(x) = 3x + 7$和(f(x) = 3x + 7)效果是一样的；如果用和，或者使用$和$，则该公式独占一行；如果用beginequation和endequation，则公式除了独占一行还会自动被添加序号， 如何公式不想编号则使用beginequation*和endequation*.2、字符普通字符在数学公式中含义一样，除了# $ % & _ 若要在数学环境中表示这些

2、符号# $ % & _ ，需要分别表示为# $ % & _ ，即在个字符前加上。3、上标和下标用来表示上标，用_来表示下标，看一简单例子：$sum_i=1n a_i=0$f(x)=xxx$效果:这里有更多的LaTeX上标下标的设置4、希腊字母更多请参见这里5、数学函数例如sinx， 输入应该为sin x6、在公式中插入文本可以通过mboxtext在公式中添加text，比如：documentclassarticleusepackageCJKbeginCJK*GBKsongbegindocument$mbox对任意的$x0$, mbox有 f(x)0. $endCJK*enddocument效果:

3、7、分数及开方fracnumeratordenominator sqrtexpression_r_r_r表示开平方，sqrtnexpression_r_r_r表示开n次方.8、省略号（3个点）ldots表示跟文本底线对齐的省略号；cdots表示跟文本中线对齐的省略号，比如：表示为$f(x_1,x_x,ldots,x_n) = x_12 + x_22 + cdots + x_n2 $9、括号和分隔符()和 和对应于自己；对应于 ；|对应于|。当要显示大号的括号或分隔符时，要对应用left和right，如：f(x,y,z) = 3y2 z left( 3 + frac7x+51 + y2 righ

4、t).对应于left.和right.只用与匹配，本身是不显示的，比如，要输出：则用$left. fracdudx right|_x=0.$10、多行的数学公式可以表示为：begineqnarray*cos 2theta & = & cos2 theta - sin2 theta & = & 2 cos2 theta - 1.endeqnarray*其中&是对其点，表示在此对齐。*使latex不自动显示序号，如果想让latex自动标上序号，则把*去掉11、矩阵表示为：The emphcharacteristic polynomial $chi(lambda)$ of the$3 times 3$

5、matrix left( beginarrayccca & b & c d & e & f g & h & i endarray right)is given by the formula chi(lambda) = left| beginarrayccclambda - a & -b & -c -d & lambda - e & -f -g & -h & lambda - i endarray right|.c表示向中对齐，l表示向左对齐，r表示向右对齐。12、导数、极限、求和、积分(Derivatives, Limits, Sums and Integrals)The expression

6、_r_r_rsare obtained in LaTeX by typingfracdudtand fracd2 udx2respectively. The mathematical symbolis produced usingpartial. Thus the Heat Equationis obtained in LaTeX by typing fracpartial upartial t= h2 left( fracpartial2 upartial x2+ fracpartial2 upartial y2+ fracpartial2 upartial z2right)To obtai

7、n mathematicalexpression_r_r_rssuch asin displayed equations we typelim_x to +infty, inf_x sandsup_Krespectively. Thus to obtain(in LaTeX) we type lim_x to 0 frac3x2 +7x3x2 +5x4 = 3.Added by Goldman2000126:-To compulsively display u to infty under the limit,we type in LaTeXfrac1lim_u rightarrow inft

8、y, frac1limlimits_u rightarrow infty orfrac1 displaystyle lim_u rightarrow infty respectively.Ended by Goldman2000126:-To obtain a summation sign such aswe type sum_i=12n. Thusis obtained by typing sum_k=1n k2 = frac12 n (n+1).We now discuss how to obtain integrals in mathematical documents. A typic

9、al integral is the following:This is typeset using int_ab 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 treated as a subscript and a superscript on the integral sign.Most integrals occurring in mathematical documents begi

10、n with an integral sign and contain one or more instances of d followed by another (Latin or Greek) letter, as in dx, dy and dt. To obtain the correct appearance one should put extra space before the d, using ,. Thusandare obtained by typing int_0+infty xn e-x ,dx = n!. int cos theta ,dtheta = sin t

11、heta. int_x2 + y2 leq R2 f(x,y),dx,dy= int_theta=02pi int_r=0Rf(rcostheta,rsintheta) r,dr,dtheta.and int_0R frac2x,dx1+x2 = log(1+R2).respectively.In some multiple integrals (i.e., integrals containing more than one integral sign) one finds that LaTeX puts too much space between the integral signs.

12、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_01 ! int_01 x2 y2,dx,dy.Had we typed int_01 int_01 x2 y2,dx,dy.we would have obtainedA particularly notewo

13、rthy 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

14、) 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$psi(mathbfr,t)$ of a particle satisfies theemphSchrodinger Wave Equation ihbarfracpartial psipartial t= frac-hbar22m left(fracpart

15、ial2partial x2+ fracpartial2partial y2+ fracpartial2partial z2right) psi + V psi.It is customary to normalize the wave equation bydemanding that int ! int ! int_textbfR3left| psi(mathbfr,0) right|2,dx,dy,dz = 1.A simple calculation using the Schrodinger waveequation shows that fracddt int ! int ! in

16、t_textbfR3left| psi(mathbfr,t) right|2,dx,dy,dz = 0,and hence int ! int ! int_textbfR3left| psi(mathbfr,t) right|2,dx,dy,dz = 1for all times$t$. If we normalize the wave function in thisway then, for any (measurable) subset$V$ of $textbfR3$and time$t$, int ! int ! int_Vleft| psi(mathbfr,t) right|2,dx,dy,dzrepresents the probability that the particle is to be foundwithin the region$V$ at time$t$.