Introducing LaTeX Math Typesetting

[KaneOris]

Speed of Satellite
$$v = \frac {2\pi R}{T}$$

Acceleration of a Satellite in Orbit

$$a = \frac {v^2}{R} = \frac {4\pi^2R}{T^2} = \frac {GM}{R^2} = g$$

Gravitational force on body in Orbit
$$F_g = mg = \frac {mv^2}{R} = \frac {4\pi^2Rm}{T^2} = \frac {GMm}{R^2} = g$$

Gravitational Constant G
$$G = 6.67\times10^{-11} N m^2 kg^{-2}$$

Motion at uniform acceleration
$$x = \frac {u+v}{2}t$$
$$v = u + at$$
$$x = ut + \frac {at^2}{2}$$
$$x = vt - \frac {at^2}{2}$$
$$v^2 = u^2 + 2ax$$

Newtons 2nd Law
$$\sum{F} = ma$$

Inclined Plane
$$a = g\sin\theta$$

Momentum & Impulse
$$\Delta{p} = m\Delta{v} = \sum{F\Delta{t}} = I$$

Kinetic Energy
$$E_k = \frac {mv^2}{2}$$

Potential Grav Energy
$$U_g = mgh$$

Work
$$Fx\cos\theta$$

Hooke's Law
$$F_s = -kx$$

 

[saltydog]

Check of alignment of equal signs (use of * disables auto gen of equation numbers):

For this sum:

$$\sum_{n=1}^{\infty}\frac{(-2)^{-n}}{n+1}$$

Consider:

$$ln(1+x)=\sum_{n=1}^{\infty}\frac{(-1)^{n+1}x^n}{n}\quad\text{for}\quad-1<x<1$$

Letting $x=\frac{1}{2}$

$$ln(3/2)=\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2^n n}$$

Letting i=n-1 we obtain:

$$\begin{align*}<br /> <br /> ln(3/2)=\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2^n n}&=\sum_{i=0}^{\infty}\frac{(-1)^{i+2}}{2^{i+1} (i+1)}\\<br /> <br /> &=\frac{1}{2}+\sum_{i=1}^{\infty}\frac{(-1)^2 (-1)^i}{(2)2^i(i+1)}\\<br /> <br /> &=\frac{1}{2}+\frac{1}{2}\sum_{i=1}^{\infty}\frac{(-1)^i}{2^i(i+1)}\\<br /> <br /> &=\frac{1}{2}+\frac{1}{2}\sum_{i=1}^{\infty}\frac{(-2)^{-i}}{i+1}<br /> <br /> \end{align}$$

Solving for the series, I obtain:

$$\sum_{i=1}^{\infty}\frac{(-2)^{-i}}{(i+1)}=-1+2ln(3)-2ln(2)$$

This result agrees with Mathematica.

 

[saltydog]

check of equation numbering

$$\reqno<br /> \begin{align}<br /> a&=b \\<br /> c&=d \\<br /> x+4x-7y&=z \\<br /> a+b+c+d+e+f &= k\\<br /> &=h+k+l+m <br /> \end{align}$$

 

[lawtonfogle]

I hope you don't mine be using this since i cannot get latex working on my computer.

 

[lawtonfogle]

Pre 1

DO NOT USE ANY CALCULATORS

1. $$\begin{array} 890 + 437 + 873 + 1024 + 273.3 + 1267 = X \\<br /> X = \end{array}$$

 

[bomba923]

Don't mind this, just testing LaTex:

$$\left\{ \begin{gathered}<br /> A_n = \frac{{\left( { - 1} \right)^n + 2n - 1}}<br /> {4} \hfill \\<br /> B_n = \frac{{ - \left( { - 1} \right)^n + 2n + 1}}<br /> {4} \hfill \\<br /> C_n = \frac{{\left( { - 1} \right)^n + 2n + 3}}<br /> {4} \hfill \\ <br /> \end{gathered} \right\}$$
$$\right\} \frac{1}{2}\mathop {\lim }\limits_{\Delta t \to \infty } \sum\limits_{n = 0}^{2\left( {\frac{{b - a}}{{\Delta t}}} \right) - 1} {\left\{ {\left[ {\vec r_1 \left( {a + A_n \Delta t} \right) - \vec r_2 \left( {a + B_n \Delta t} \right)} \right] \times \left[ {\vec r_3 \left( {a + B_n \Delta t} \right) - \vec r_4 \left( {a + C_n \Delta t} \right)} \right]} \right\}}$$

 

[bomba923]

Sorry, the limit in my last post was to go to zero! And my vectors are wrong. Again, don't mind this:

$$\left\{ \begin{gathered}<br /> A_n = \frac{{\left( { - 1} \right)^n + 2n - 1}}<br /> {4} \hfill \\<br /> B_n = \frac{{ - \left( { - 1} \right)^n + 2n + 1}}<br /> {4} \hfill \\<br /> C_n = \frac{{\left( { - 1} \right)^n + 2n + 3}}<br /> {4} \hfill \\ <br /> \end{gathered} \right\}$$
$$\right\} \frac{1}{2}\mathop {\lim }\limits_{\Delta t \to 0 } \sum\limits_{n = 0}^{2\left( {\frac{{b - a}}{{\Delta t}}} \right) - 1} {\left\{ {\left[ {\vec r_1 \left( {a + A_n \Delta t} \right) - \vec r_2 \left( {a + B_n \Delta t} \right)} \right] \times \left[ {\vec r_1 \left( {a + B_n \Delta t} \right) - \vec r_2 \left( {a + C_n \Delta t} \right)} \right]} \right\}}$$

 

[MalleusScientiarum]

$$\sum_n R_{n,n'} v_n = v_{n'} [\tex]<br /> <br /> Okay...what went wrong there?$$

 

[Integral]

$$\sum_n R_{n,n'} v_n = v_{n'}$$

Okay...what went wrong there?

change [\tex] to [/tex]

$$\sum_n R_{n,n'} v_n = v_{n'}$$

 

[dextercioby]

Sorry, the limit in my last post was to go to zero! And my vectors are wrong. Again, don't mind this:

$$\left\{ \begin{gathered}<br /> A_n = \frac{{\left( { - 1} \right)^n + 2n - 1}}<br /> {4} \hfill \\<br /> B_n = \frac{{ - \left( { - 1} \right)^n + 2n + 1}}<br /> {4} \hfill \\<br /> C_n = \frac{{\left( { - 1} \right)^n + 2n + 3}}<br /> {4} \hfill \\ <br /> \end{gathered} \right\}$$
$$\right\} \frac{1}{2}\mathop {\lim }\limits_{\Delta t \to 0 } \sum\limits_{n = 0}^{2\left( {\frac{{b - a}}{{\Delta t}}} \right) - 1} {\left\{ {\left[ {\vec r_1 \left( {a + A_n \Delta t} \right) - \vec r_2 \left( {a + B_n \Delta t} \right)} \right] \times \left[ {\vec r_1 \left( {a + B_n \Delta t} \right) - \vec r_2 \left( {a + C_n \Delta t} \right)} \right]} \right\}}$$

You know, rather than abusing our LaTex compiler, maybe you should get a hand on a version of TeXAide or other application which can compile LaTex code. It's not really fair towards the users of the site, and neither to its owner.

Daniel.

 

[MalleusScientiarum]

I personally recommend MikTeX, I'm very pleased with it.

 

[bomba923]

You know, rather than abusing our LaTex compiler, maybe you should get a hand on a version of TeXAide or other application which can compile LaTex code. It's not really fair towards the users of the site, and neither to its owner.

Daniel.

Abusing the compiler?
*How am I abusing the LaTex compiler?
(was the LaTex code too long?)

My post was an equation for the area of a certain kind of ruled surface,
as seen on the thread https://www.physicsforums.com/showthread.php?t=77312
(apparently I wasn't abusing at that time?)
*And TeXAide is not needed, uc, for my equation came out just the way I intended without "Aid". What exactly is wrong with it?

 

[dextercioby]

You've already been told about the "preview post" feature which allows you to see the compiled code before submitting the message. Use it.

Daniel.

 

[aricho]

is there any way to produce a numberplane using LaTeX? or anythin simialir?

 

[bomba923]

You've already been told about the "preview post" feature which allows you to see the compiled code before submitting the message. Use it.

Daniel.

I did, but I couldn't do it for my first post. When I returned to this thread (after visiting some other site), I could not at all find that "Edit" button--and could not change the post. (and then i wrote that second post)\-(very Sorry for the inconvenience !//)
------------------------------------------------------
Btw, what notation is used to express limits of a sequence?
Let's say I have the simple arithmetic sequence $A_n$ defined as
$A_n = n$, and I want to express this sequence up to 1631. Do
I have to write out $\left\{ {0,1,2, \ldots ,1631} \right\}$, or can I just simply write:
$$\left\{ {A_n } \right\}_0^{1631}$$ ..or just $$\left\{ {n} \right\}_0^{1631}$$
?? Is it ok to use the latter??

 

[Orion1]

My Latex 'texify.exe' program currently compiles my *.dvi files at an apparent default character screen width of '13 cm', I manually determined this value by measuring a physical hard copy of a default *.dvi character printout.

Is there a simple command or option of increasing this width value?

 

[lonelyphysicist]

The simple_wick.tex file works very well. I could not get the other one to work. I also did not have any of the problems the author gives for simple_wick.tex.

Norman

Could you explain how to use this simple_wick.tex file? I don't understand the example given at all.

Thanks!

 

[syd]

Very nice forum you've got here!

I just wondered, how do you create the 1-bit transparent PNGs for the equations on this forum?? I'm setting up a website of my own where I'll be displaying lots of latex-generated equations. I have tried with both 'convert' and 'dvipng' to create the PNGs, but all I can get is alpha-channel transparent PNGs, which of course don't work in Internet Explorer. I've tried everything, or so it seems, but with no luck whatsoever. Can anyone give me a hint on how to do this?

Thanks!

 

[brian0918]

$$\frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}}$$

 

[Hurkyl]

Crossing my fingers:

$$\begin{CD}<br /> S^{{\mathcal{W}}_\Lambda} \otimes T @>j>> T\\<br /> @VVV @VV{\End P}V \\<br /> (S \otimes T) / I @= (Z \otimes T) / J<br /> \end{CD}$$

Oh well, no amscd.

 

[JamesU]

$$\sqrt{this is Very cool} \Upsilon \varrho \varsigma \overrightarrow{it} \overleftarrow{is}$$

 

[Castilla]

$$f(x,y) = \int_y^{x}t^{xy}dt$$

Nice.

 

[Castilla]

Testing...

$${\int_1^\sqrt{x}} t^{x}dt$$

 

[Castilla]

Testing...

If the functions $$f(x,t)$$ and
$$\frac{\partial}{\partial t}f(x,t)$$ are continuous in
$$[a,b] \times [c,d]$$, then $$\frac{d}{dt}\int_a^{b}f(x,t)dx = \int_a^{b}\frac{\partial}{\partial t}f(x,t)dx.$$

 

[JamesU]

$$\sqrt{Opposite^2 + Adjacent^2} = Hypotenuse$$

 

[beautiful1]

I too am just testing
$$\int dx \int dy \exp (-a (x+y)^2 +ib(x-y)) sinc(cx+dy) sinc(dx+cy)$$

 

[JamesU]

$$\sqrt{cool} = \sqrt{me} . \ me^2=me. \ cool^2=awesome. \ so \ me = awesome$$

 

[fliptomato]

QUESTION...

In the archives for this forum, someone suggested the following site for a script on how to put in wick contractions into latex:

http://www.fzu.cz/~kolorenc/tex.php

The post suggested using simple_wick.tex, saying it worked very well.

I agree that it works... but I can't figure out how to use it. That is, the example works well, and I can toy around and get random results, but I can't figure out what the logical rules are to use this script. Any ideas?


Flip

 

[Neohaven]

As x tends to infinity, the limit of 1/x is such that

$$\mathop {\lim }\limits_{x \to \infty } f(x) = 0$$

Works kinda well, doesn't it? Too bad it doesn't work on my computer...

 

[tomfitzyuk]

$$T = \frac{1}{f} = 2 \pi \sqrt \frac{l}{g}$$