h***o
发帖数: 539 | 1 BBS水木清华站∶精华区
发信人: FangQ (奥萨马·本·拉登), 信区: MathTools
标 题: Mathematica函数及使用方法
发信站: BBS 水木清华站 (Wed Nov 18 21:35:55 1998)
Mathematica函数及使用方法
—————————————————————————————————————
四、解方程
Solve[eqns, vars] 从方程组eqns中解出vars
Solve[eqns, vars, elims] 从方程组eqns中削去变量elims,解出vars
DSolve[eqn, y, x] 解微分方程，其中y是x的函数
DSolve[{eqn1,eqn2,...},{y1,y2...},x]解微分方程组，其中yi是x的函数
DSolve[eqn, y, {x1,x2...}] 解偏微分方程
Eli |
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d*****o
发帖数: 2868 | 2 God, i guess im passionate about math and engineering, thats why i reply
this post so actively, lol. Anyway, personally, i believe the greatest
mathematical eqn is the maxwell eqn, because maxwell's eqn is really the
foundation of telecommunication. W/out maxwell's eqn, electrical signals
won't be able to transfer from place A to place B, wifi won't even exist. |
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q*******n
发帖数: 1334 | 3 Assume X = [X1, X2]^t is bivariate normal distributed with mean vector m = [
m1, m2]^t and covariance matrix C = [c1, r; r, c2].
1. Define s = [s1, s2]^t as the dumb variable vector for MGF, then the MGF
of the vector X is
M_X(s) = E[exp(s^t * X)] = exp(m^t s + 1/2*s^t*C*s). (eqn. 1)
2. Set s1 = s2 = u in (eqn. 2), then we can get the MGF of X1+X2
M_{X1+X2}(u) = E[exp( (X1+X2)u ) = exp((m1+m2)u + 1/2*(c1+c2+2r)*u^2) (eqn.
2)
3. Eqn. 2 is in the form of the MGF for Normal RV. Therefore, X1+X2 is |
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f***a
发帖数: 329 | 4 我觉得你这个题目就有问题。。。你是不是漏条件了？
let (x'Ay)(x'Ay)= x'Ayx'Ay= a'Bb
where a'=x'A, B=yx', b=Ay
then if (x'Ay)(x'Ay)<=(x'Ax)(y'Ay) correct
we have a'Bb <= a'B'b (1)
notice x and y are arbitrary n*1 vectors,
then B=yx' can be arbitrary matrix as well
and eqn.(1) is correct for any choice of B.
Let choose D=B' and use eqn.(1) for D, we have
a'Db <= a'D'b
which is actually a'B'b <= a'Bb (2)
Apparently, eqn.(1) and (2) conflict except the situation "=".
Thus, assumption that eqn.(1) is always true is denied. |
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h***o
发帖数: 539 | 5 BBS水木清华站∶精华区
发信人: FangQ (奥萨马·本·拉登), 信区: MathTools
标 题: Mathematica函数及使用方法
发信站: BBS 水木清华站 (Fri Nov 20 21:39:10 1998)
Mathematica函数及使用方法
—————————————————————————————————————
八、数值函数
N[expr] 表达式的机器精度近似值
N[expr, n] 表达式的n位近似值，n为任意正整数
NSolve[lhs==rhs, var] 求方程数值解
NSolve[eqn, var, n] 求方程数值解，结果精度到n位
NDSolve[eqns, y, {x, xmin, xmax}]微分方程数值解
NDSolve[eqns, {y1,y2,...}, {x, xmin, xmax}]
|
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u******o
发帖数: 483 | 6 【 以下文字转载自 Postdoc 讨论区 】
发信人: ultraiso (goodman), 信区: Postdoc
标 题: 遇到垃圾审稿意见怎么办？
发信站: BBS 未名空间站 (Wed Jun 1 16:24:08 2011, 美东)
几个月前投了一篇稿子，今天收到审稿意见。其中有一个审稿人的审稿意见，英文错误
百出。基本上
每一句都有若干错误，尤其是一些非常低级的拼写错误，还有很多让人读不懂的句子。
提的意见也基
本上属于垃圾。很显然，他没有看懂我的文章的内容，就开始胡喷一气，看得我非常火
大。想写信驳
斥几句，或者直接告诉副主编这个人根本就不能正确理解基本的英文。大家遇到这个情
况怎么办？
我举两个例子（原句摘抄，省略号省去了与专业相关的个别词）
The main of this study was focused on ... in fluence on ... via ....
The topic studied has current appeal and may be made certain
contribution on the relate acad... 阅读全帖 |
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u******o
发帖数: 483 | 7 几个月前投了一篇稿子，今天收到审稿意见。其中有一个审稿人的审稿意见，英文错误
百出。基本上
每一句都有若干错误，尤其是一些非常低级的拼写错误，还有很多让人读不懂的句子。
提的意见也基
本上属于垃圾。很显然，他没有看懂我的文章的内容，就开始胡喷一气，看得我非常火
大。想写信驳
斥几句，或者直接告诉副主编这个人根本就不能正确理解基本的英文。大家遇到这个情
况怎么办？
我举两个例子（原句摘抄，省略号省去了与专业相关的个别词）
The main of this study was focused on ... in fluence on ... via ....
The topic studied has current appeal and may be made certain
contribution on the relate academic circle. However, based on the
prevent paper, this reviewer found that the technical contest and the
paper itself are not... 阅读全帖 |
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d*****o
发帖数: 2868 | 8 i remember the derivative of e^(ax)=a*e^(ax), but i don't know how to prove
it, i wasn't a math major when i was in college and i never had to do proofs
. As for the 2nd eqn, cos(x) is the real part and isin(x) is the imaginary
part, euler's identity? cos(x)=(e^ix+e^-ix)/2 and sin(x)=(e^ix-e^-ix)/(2j).
I guess if you plug those 2 expressions back into the 2nd eqn that you
wrote, it does equal to e^ix? im kinda tired right now, had a long day and
will have a longer day tmr, lol, so i don't feel l... 阅读全帖 |
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z****c
发帖数: 2 | 9 简单来说就是用代数图像画一副图画,还得写出代数式子. 最后还得涂上颜色..~.~!
各位试试??
Worth 15 Test Points
1. On graph paper, draw something that inspires you. Be creative! Now,
redraw your picture using only straight line segments, parabolic curves, and
shapes from any of the other seven basic graphs. (You can use shapes from
other graphs too, but be careful, you’ll need to write the equations of
them!)
2. You must find and write the equations of at least 4 straight lines and 6
other curves (from the other seven basics). You... 阅读全帖 |
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T*******n
发帖数: 493 | 10 I couldn't find an easier way.
\documentclass{minimal}
\usepackage{amsmath}
\begin{document}
\noindent
Equation~\eqref{eqn} includes Equations~\eqref{eqna} and~\eqref{eqnb}:
\begin{subequations}
\label{eqn}
\begin{alignat}{3}
&\smash{%
\raisebox{-0.5\baselineskip}%
{$\displaystyle |x|= \left\{
\vphantom{\begin{gathered}x\\x\end{gathered}}%
\right.$}%
}
& & x, &\quad &x\ge0; \label{eqna} \\
& & &{-}x, &\quad &x<0. \label{eqnb}
\end{alignat}
\end{su |
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k*******a
发帖数: 772 | 11 data temp;
input equation $;
cards;
1+1
1+2
1+3
;
run;
proc sql noprint;
select "B="||equation||";"||"output;" into :eqn separated by " " from temp;
quit;
data temp1;
&eqn
run; |
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c****s
发帖数: 5892 | 12 多伦多股市连续多日上升后，投资者获利离场，导致S&P/TSX指数劲跌135.85点，收在1万2916.63点。美元略微走强，让加元跌去0.36美分，收在99.27美分。
虽然12月铜期货大涨9美分至每磅4.04美元，基本金属股仍大跌2.56%。Teck资源(TSX：TCK.B)跌1.90元至48.44元，Equinox矿业(TSX：EQN)跌60分至5.79元。
投资者抢购黄金避险，使12月黄金期货小升6.90美元，创下每盎司1410.60美元的新纪录，但黄金股却走软。Goldcorp(TSX：G)跌1.24元至46.63元，Kinross黄金(TSX：K)跌62分至18.63元。
随12月原油期货小跌34美分至每桶86.72美元，能源股跌去0.42%。Suncor能源(TSX：SU)跌17分至35.96元，Cenovus能源(TSX：CVE)升29分至29.97元。
金融股下跌最多，跌去约1%。道明银行(TSX：TD)跌95分至73.65元，皇家银行(TSX：RY)跌85分至54.40元。
信息技术企业CGI(TSX：GIB.A)的亮丽财报，推动公司股价大涨1.53元至17.07元，... 阅读全帖 |
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g******4
发帖数: 6339 | 13 下一阶段 (after EQn),小弟以为, Fed将紧叮通胀率. |
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y**s
发帖数: 6809 | 14 稳态就是个拉普拉斯方程么，只不过laplace's eqn没有图例..
你真的会啊。。。。 |
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L***n
发帖数: 6727 | 15 latex 对数学公式的表达方式基本上就是一个人念公式念出声的表达方式，
基本上不会有其他方式比这个更简明了（可能troff eqn好一点点，更接近
人类语言，但是也更verbose, 这俩基本上没啥本质区别），除了tex和troff，
还有其他什么更简明的写数学公式的方式么？ |
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a***n
发帖数: 3633 | 16 either is fine. Actually, I donot have numbers for those eqns.
you know how to do it? thx in advance. |
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c**********g
发帖数: 222 | 17 合作者发回的草稿里每一行后都多了三个点...。这些...在别的文本处理器里看不到，
但是在emacs里可以看到。结果latex把文本后面的...理解为换行。至于方程里的...则
以错误处理。下面是例子
$C^{\kappa}_l$ is related to the 3D matter power spectrum $P_m(k,z)$ by the
...
Limber's equation
...
\be ...
\label{eqn:cl} ...
C^{\kappa}_l(x_1,x_2)=\int ...
P_m(\frac{l}{x_L};z_L)W(x_L,x_1)W(x_L,x_2)\frac{dx_L}{x_L^2} \ . ...
\ee ...
请问谁对这种情况有经验？如何解决？手动删除几千个...太郁闷了。
另外，我用linux，但是合作者用苹果，跟这个有关吗？
多谢！ |
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a***6
发帖数: 44 | 18 thermo, kinetics, and transport是核心
不过啊，statistical mechanics (eq + non-eq)才是最基础的东西，我说啊，这里没
多少人能由Boltzmann eqn推出diffusion equation， 由partition function推出
Langmuir isotherm的 |
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s*****l
发帖数: 167 | 19 What kind of computational problems are you dealing with in solid mechanics?
solving nonlinear elasticity eqns? |
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s*****l
发帖数: 167 | 20 That is currectly the most difficult computational problem ah.
What is your approach then.
I would use MD at cracks and elasticity eqns away from it.
But I donot know how to actually do it :(
mechanics?
入。 |
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z*****g
发帖数: 356 | 21 given the parametric eqns for a spiral
x=kt cos t
y=kt sin t
where k is a constant，t starts from 0
Could anyone give a function of 't' that calculates the length of the spiral.
thanks |
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j*****g
发帖数: 98 | 22 $$\left\{\begin{array}{l}
eqn1\\
eqn2\end{array}\right.
$$
a drawback of this method is not able to creat
eqn ref automatically.... |
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d*****o
发帖数: 2868 | 23 I absolutely agree w/ what domini said. During ur first 2 yrs of college, u
will most likely take a lot of math/science courses. Later on, you will
learn maxwell's eqns, ohm's law, signal processing both digital and analog,
probability theory, solid state, logic design... I came to the States when i
was 12, so i have no idea how to say those words in chinese. During ur
senior year, once u finish taking all the required courses, u will pick a
field in EE that u want to study and take courses r |
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g****v
发帖数: 971 | 24 Because I need transform verilog to EQN format which can be further handled
by my own algorithm.
Thanks. |
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x*****d
发帖数: 427 | 25 \label{eqn:haha}, \label{sec:haha}, \label{thm:haha}, ... |
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r**g
发帖数: 120 | 26 我去年秋天投的稿，除了系统回复的交稿确认外，至今没有收到任何消息。不知这样的
情况是不是常见？不只各位有何建议？另外，是不是以后都不要向 Elsvier 投稿了？ |
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B********e
发帖数: 10014 | 27 maybe start with
heat eqn/green function/decay rate...
or maximal principle
or from semi-group theory
then semilinear/quasilinear case |
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Q******g
发帖数: 607 | 28 The factor i in front of time derivative makes the difference.
With i as in Shroedinger eqn, the solution is oscillatory, it
makes no sense to study the long time behavior.
posedness |
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h********0
发帖数: 12056 | 29 The original eqn can be converted into the following form:
y'+p(t)y=a where y=(1-S), p(t)=a+X'(t), a is const.
the other steps are trivial. The problem simplifies a bit. |
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f*****y
发帖数: 31 | 30 Any one read or is reading Dr. Belytschko's 'Nonlinear Finite Elements for
Continua and Structures' book?
I am reading chapter 5 of this book now,
and I couldn't understand, on page 280, the derivation of
linearization of equation(5.9.9) in fully implicit backward Euler scheme for
integrating the constitutive eqns
I think the derivation on the book is wrong somehow, and it doesn't make sense
to me at all.
I really want to know how they got this crazy final form.
If any of you happen to know this |
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N***r
发帖数: 2539 | 31 the contact angle of a water-air-solid system is determined by Young-Laplace
eqn, and is a function of water-air surface tension, air-solid surface
tension and water-solid surface tension.
comparing your two cases, water-vacuum and water-air, two parameters change,
water-air -> water-vacuum, and air-solid -> vacuum-solid.
u may need some detailed analysis.
btw, liquid can't stay in vacuum long, it's gonna evaporate anyway.
in this case, the problem turns to a water-vapor-solid system. |
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z*********r
发帖数: 298 | 32 这个是最基本的Gerneralized Linear Eqn， 任何SDE的初等课都会学的。 |
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s***e
发帖数: 267 | 33 If you are sure the problem has a solution (it may not, depending on those
parameter values), you can think in this way:
(1) a1*r1+a2*r2+a3*r3+a4*r4+a5*r5 = 0
(2) a1+a2+a3+a4+a5 = A
(3) 0 <= ai <= Ai (i =1~5)
Find x and y which both satisfy (2) and (3), but will lead to a positive and
negative value for (1). This step should be fairly easy.
Suppose their values for eqn (1) are f(x) > 0 and f(y) < 0.
Your solution will be
x * p + y * q
where p = -f(y)/[f(x) - f(y)] and q = 1-p = f(x) /[f(x)- f(y)... 阅读全帖 |
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c*******o
发帖数: 1722 | 34 to use the Fourier transformation to sovle the differential Eqn, you can
get the system transform function. this is mathematically equivalent to
assume exp(i \omega t) dependence. so, it takes care of only the linear
response. it does not give you anything from nonlinearity.
as for 光刻, it probably use high intensity lasers, which will interact
with the material. that is where the nonlinearity kicks in. for weak
nonlinearity, you can taylor expand the \kai (susceptibility). for strong
nonlinearit |
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t******t
发帖数: 13 | 35 Tgif is very cool tool to draw schematic picture.
You can insert any math eqn into the figure
using latex grammer. Google Tgif.
For curves generated by equation, matlab.
Xfig is just so so. |
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