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#26 Re: Help Me ! » The best way into multivariate calculus » 2010-05-19 20:47:02

Identity

There is a fantastic book called Stewart's Calculus, which I used in preparation for multivariable calculus in uni:

http://rapidshare.com/files/389478283/C … s.pdf.html

Otherwise, as rzaidan said, MIT is excellent.

#27 Re: Help Me ! » Complexifying a problem » 2010-05-16 13:44:22

Identity

lol bobbym this is just some fun. I know the answer is

#28 Re: Help Me ! » Complexifying a problem » 2010-05-16 02:53:36

Identity

Thanks ZHero, I'm not sure what to do with the absolute value signs though. It acts as the modulus doesn't it? And everytime I evaluate the modulus of the stuff it comes out to be 1 hmm

#29 Help Me ! » Complexifying a problem » 2010-05-16 01:49:30

Identity
Replies: 7

I'm trying to get the integral of

by factoring, partial fractions, and finally integration.

Here's where I'm up to so far

Now I have a feeling that this approach should work. I've been using complex numbers a lot recently and they've never failed me in all kinds of ridiculous tasks. So where do I go from here, if it is possible to go from here?

Thanks

#30 Help Me ! » Showing the steps » 2010-05-07 05:24:59

Identity
Replies: 3

Can someone please go through the steps in showing the LHS = RHS?

Thanks

#31 Re: Help Me ! » physics formula, dont understand the maths » 2010-04-17 11:07:13

Identity

If you have a closed surface, at each point on the surface you take the dot product of

and
and add them up. This will equal the charge contained inside the surface divided by epsilon nought.

The symbol

just means a surface integral of a closed surface.

In general, for the surface

The surface integral of the vector field

is

Where the RHS is a simple area integral. Note that different orders of the cross product will give different answers. This is because each surface has two orientations (two surface area vectors pointing out from every point on the surface).

This allows you to compute a surface integral.

If you want examples see http://tutorial.math.lamar.edu/Classes/ … grals.aspx

The differential form is derived through an application of Stoke's theorem.

If

This is called the divergence of the vector field.

It's easy enough to compute examples in the differential form.

#32 Re: Help Me ! » exp/ln problem » 2010-03-17 03:07:11

Identity

Edit: Lol looks like soroban beat me to it smile

Oh ok,

Take the log to the base 'e' of both sides:

Now,

(using log laws)

So

Log of both sides again:

#33 Re: Help Me ! » exp/ln problem » 2010-03-16 20:57:55

Identity

Hi toitu, what is the definition of the workflow?

#34 Re: Help Me ! » Implicit differentiation? » 2010-03-16 20:53:15

Identity

I get

#35 Re: Help Me ! » tom is... » 2010-03-07 19:39:15

Identity

At the start, his bro is 4.
Let x be the number of years until Tom is twice his bro
12+x = 2(4+x)
Which can be solved to find the solution

#36 Re: Help Me ! » bijective inverse function » 2010-03-05 14:42:23

Identity

Thanks Jane!

Proof of onto-ness:

Ok, so
"

is onto if for every
s.t.
"

Choose

Then we have

is onto!


Is that all there is to it?

#37 Re: Help Me ! » bijective inverse function » 2010-03-05 05:45:03

Identity

Proof of one-to-one-ness:

Let

and let

Since

(this step seems a bit flimsy to me... it's just what I'm used to... am I taking it for granted?)

and

So

is one-to-one.

Converse:

If

then
?? Not sure about the converse...


Proof of onto-ness:

If

is one-to-one if for every
there is a
s.t.
.

err... not sure where to go from here rolleyes

#38 Help Me ! » bijective inverse function » 2010-03-05 03:32:37

Identity
Replies: 5

Let

be one-one and onto. Then show that the inverse function
is one-one and onto.

Could someone please help me with writing out a rigorous proof of this? I need practice writing proofs and I'm not sure how to set it out
Thanks smile

#39 Re: Maths Is Fun - Suggestions and Comments » Spelling? » 2010-02-27 21:12:12

Identity

Your browser language setting is en-au

So these are the spellings we will use:

Maths, metre, litre, colour, organisation.


Correct!

#40 Re: Introductions » Hi there - I am new to forums so please be gentle! » 2010-02-26 03:11:17

Identity

Hi EmilyW!
Wow, World Maths Day, sounds exciting, I might just join in the fun smile

#41 Re: Help Me ! » integration help please » 2010-02-26 02:58:41

Identity

Multiply the top and bottom by "sin(x)+cos(x)"


Hopefully you can go from there. If you're having trouble then

#42 Re: Help Me ! » physics questios » 2010-02-24 02:22:02

Identity

4) What is at the edge of the universe?

If there were an 'edge' to our universe, that would imply that there was something outside of our universe. But our 'universe' IS space and time, so there isn't an 'outside'.
Some theories say that the universe is analogous to a 'curled' up sphere. Imagine walking on the surface of a sphere, there is no edge. No matter which way you walk you will still be on the sphere. However, if you go to a higher dimension (beyond the 4 space-time dimensions), you may be able to enter a parallel universe, which is 'layered' on top of our own.

6) Is the universe moving? If yes, then would this imply that there would have to be an object with a greater mass than the universe, causing it to move due to gravitational pull?

There is no evidence to show that the universe is moving. Even if it were moving, what would it be moving 'into'? (there is no space outside our universe)

11) Extra question -- why is the lowest temperature possible -273 degrees celsius?

Take a gas and put it in a container. Then heat the container, measuring the Pressure inside the container at specific temperatures.

If you draw a graph of Pressure vs. Temperature, you'll find that it's linear, and if you continue the graph to the T-axis intercept (where pressure is zero), the value you will get is -273 degrees celcius.

In other words, -273 degrees celcius is the temperature at which the molecules in a gas have no kinetic energy (thus exerting no pressure on the walls).

We aren't able to cool something down to absolute zero (it's very hard to keep a molecule absolutely still), but we have gotten very, very, very close.


By the way, the links to Q10 seem to be broken, I can't access them

#43 Re: Dark Discussions at Cafe Infinity » Other Forums, are they rude? » 2010-02-12 00:20:03

Identity

I've also been a bit surprised by how some forums seem polite and others seem rude. Even with excellent site administration and moderation (which this site has too), other sites can still appear very rude to outsiders. I don't know what attracts certain types of people to certain sites, but it seems that Maths Is Fun Forum has been blessed.

#44 Re: Coder's Corner » I have devised an uncrackable substitution cypher code » 2010-02-11 15:04:24

Identity

Couldn't some of the filling words or letters pollute the message so that it decrypts not how you intended it?

#45 Re: Help Me ! » Inequality » 2010-01-29 01:33:45

Identity

Fully expanding:

Factoring nicely:

AM-GM

AM-HM

Therefore, putting it all together,

#46 Re: Dark Discussions at Cafe Infinity » Why to not strive for being safe » 2010-01-24 23:04:51

Identity

lol, that is... interesting  o.O

#47 Re: Dark Discussions at Cafe Infinity » Why to not strive for being safe » 2010-01-23 15:35:09

Identity

bobbym, what do you think the person meant by "you live here and you don't know"? Who helped?

#48 Re: Help Me ! » surface integral with stokes » 2010-01-16 16:50:48

Identity

Thankyou rzaidan, tha helped smile

#49 Re: This is Cool » Pi to a Million Decimal Places! » 2010-01-13 12:33:01

Identity

3.1415926535897932384626433832795028841971693993751058209749445923078[1]640628620899862803[482]534211706798214808

dang I got 4 wrong xD

#50 Re: Help Me ! » Simplifying » 2010-01-13 10:14:30

Identity

For any numbers a,b,c

a(b+c) = a*b+a*c

Applying that formula,

5(x+3) = 5*x+5*3 = 5x+15

7(2x-4) = 7*2x+7*(-4) = 14x-28

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