Recent Maths chat.

[ColinJ]

You're 25 years too late for me to answer stuff like this...

That's exactly what I was going to say!

I wrestled with second order differential equations, boundary conditions, div, grad, curl etc. for my electrical engineering degree back in the 1980s and then promptly forgot all that malarkey after I graduated!

 

[beanzontoast]

I lost you in that bit where you started typing.

Has anyone seen my marbles? I can't seem to find them anywhere...

 

[MichaelM]

Use the two trigonometric identities Cos(2x)=cos^2(x)-sin^2(x) and 1=sin^2(x)+cos^2(x).
So

Cos(2x)=Cos^2(x)-(1-cos^2(x))
Cos(2x)=2Cos^2(x)-1

So
-1/4(Cos(2x)Sec(x)
=-1/4(2Cos^2(x)-1)sec(x)
=-1/4(2Cos^2(x)-1)/cos(x)
=-1/4(2Cos(x) -1/cos(x)
=-1/4(2Cos(x) +(1/4)Sec(x)

It took a while to follow, but yes

And so the general solution becomes:

y = CSec(x) - 1/2 Cos(x) + 1/4 Sec(x)

Apply the initial condition y(0)=1/2

The particular solution comes out as:

y = Sec(x) - 1/2 Cos(x) as required

I'm still at a loss as to why the general solution above is not in agreement with the given g.s. of :
y = C Sec(x) - 1/2 Cos(x)

Although I feel that if C is an arbitrary constant, then:

CSec(x)+1/4 Sec(x) = DSec(x) where D is now an arbitrary constant, trying to show it on paper is another matter!

Thanks for the help. Much appreciated.

Michael

 

[MichaelM]

Use the two trigonometric identities Cos(2x)=cos^2(x)-sin^2(x) and 1=sin^2(x)+cos^2(x).
So

Cos(2x)=Cos^2(x)-(1-cos^2(x))
Cos(2x)=2Cos^2(x)-1

So
-1/4(Cos(2x)Sec(x)
=-1/4(2Cos^2(x)-1)sec(x)
=-1/4(2Cos^2(x)-1)/cos(x)
=-1/4(2Cos(x) -1/cos(x)
=-1/4(2Cos(x) +(1/4)Sec(x)

Add this to the rest to get your 3/4Sec(x) +1/4Sec(x) to get Sec(x).

I've just noticed the time at which you posted that, and after being down the pub as well - most impressive !

 

[gratts]

What level is this Michael, for uni?

 

[MichaelM]

Gratts,

This particular question was taken from the revision material for an O.U. level 3 course (the revision material is online if you want a link). i.e. assumed prior knowledge. The proceedure for solving differential equations is level 2, but I found this particular question hard (very very!), due to the trig identities.

I do wonder whether I'm really suitable for maths at this level!

 

[User482]

10 years ago, I could do this stuff. I can only assume that my brain has poured out of my ears in the mean time, and I never noticed.

 

[marinyork]

Nice try User76 .

 

[MichaelM]

Well, I think it's lucky there are people in the world who do this type of thing. I am sure it is really useful. but what the hell is it for?

Applied maths can be used when modelling the effect of forces on bodies. Friction, air resistance, that kind of thing. It probably came in handy in stopping paras (and airborne donkey artillary) from going SPLAT.

As you can see I'm not particularly good at it so would have probably gone for the practical experimental approach myself !!

Jump, SPLAT, let's try a bigger one. etc etc

Luckily there are people in the world who do this type of thing !!!

 

[marinyork]

Mathematics is the science of patterns.

As for what it's useful for. Mechanics gives you a description of how firearms and projectiles will work. More advanced stuff gives an approximation how different materials will behave down to a fine detail, making advanced weaponry possible.

MichaelM you should try Schaum's D.E.s by Bronson for differential equations. Good to a fairly decent undergrad level of ODEs. If you want something higher level like Sturm-Louiville or Bessel functions more engineering books or special functions tends to meat it out a great deal.

 

[MichaelM]

MichaelM you should try Schaum's D.E.s by Bronson for differential equations...

I literally have a stack of textbooks. This is supposed to be revision before moving on to the new stuff. It's all I can manage to keep up with the coursework never mind doing even more for fun!

 

[marinyork]

What's the new stuff you're about to do?

 

[MichaelM]

What's the new stuff you're about to do?

Fluid mechanics, and Cosmology. And no, I can't even begin to picture a 4 dimensional warped space-time. But the alternative was Quantum mechanics, which scares me silly.

 

[marooncat]

All this thread has done is confirmed I have forgotton everything I ever learn at uni (or everything I learnt in regards to my degree anyhow!!)

 

[fossyant]

It's all rubbish anyway - you'll find this out when you have to work for a living.....