Integration

[twentysix by twentyfive]

Don't worry 650 - you haven't missed anything interesting...

Oh - I don't know about that. I did have a bit of a giggle reading thro all above.

But I do hope I'm not an "ivory tower elitist/intellectual". I would not do these things if it wasn't fun. I'm perfectly happy to understand those who say it's boring. Just don't ask me to understand Football - that's Bor ing in my book

 

[rich p]

.

So I'm off to brush up on contours.

I think I might start up a cycling holiday rip-off company - contours is a good name

 

[threebikesmcginty]

I think I might start up a cycling holiday rip-off company - contours is a good name

I was thinking of starting a small holiday company for people who swear - I'm calling it Tourettes you ****!

 

[rich p]

I was thinking of starting a small holiday company for people who swear - I'm calling it Tourettes you ****!

I'm thinking of asking Hushovd if he'll front up my new cycling holiday company taking punters round a French town -

I'm calling it Thor's Tours tours

 

[twentysix by twentyfive]

Righty Ho.

I draw my contour in the upper half of the complex plane as a semicircle centred at z=0 and the diameter along the real axis. I draw a little semicircle around z=0 in the upper half plane so that pole isn't enclosed by the contour. The only pole included is at z=I. The residue at z=I is Ln/2I. Ln=Pi/2 so the integral is (2Pi I * Pi/2)/2I =( Pi^2)/2 which is not zero. So where have I erred? Presumably at z=0? As Limit z->Infinity is zero but Limit z->0 is -Infinity.

marinyork help..........

 

[marinyork]

You missed out an i. The principal value of ln(i) is πI/2.

 

[twentysix by twentyfive]

You missed out an i. The principal value of ln(i) is πI/2.

Ah right indeed. So the answer is Imaginary and the real integral is Zero.

Thanks for all that.

 

[longers]

Out of interest, what would that sort of maths be used for?

I've been trying to get my head round simple trigonometry today for the first time in a while so am just curious.

 

[dan_bo]

Oooooh here we go- real world applications of things that don't exist.

 

[twentysix by twentyfive]

Out of interest, what would that sort of maths be used for?

I've been trying to get my head round simple trigonometry today for the first time in a while so am just curious.

I've used this contour integration (well a colleague on my behalf) in solving problems related to weak shock wave propagation in gases. The shock waves messed up the amplifying medium in a gas laser and transferred the "mess" to the optical beam.

In general it is a very common need to be able to add up things and integration is the methosd used to add up continuously varying stuff - any stuff in the real world. Technology and knowledge would be very poor indeed without integration. There are sevveral ways of getting answers to integration problems. This complex number method is very powerful for otherwise intractable problems (until we all got lazy and just chuck it at a computer)

 

[twentysix by twentyfive]

Oooooh here we go- real world applications of things that don't exist.

Sorry dan but you wouldn't own anything engineered or technical let alone the computer you are currently using without these mathematical tools being used.

It's fine to not want to know stuff but it's not fair to decry it when you depend on it so much. How about the medics and all that chemistry/biology - would you sneer at that when you get ill?

 

[longers]

I've used this contour integration (well a colleague on my behalf) in solving problems related to weak shock wave propagation in gases. The shock waves messed up the amplifying medium in a gas laser and transferred the "mess" to the optical beam.

Thanks, that'll do for me. I really was just being nosey as it is way beyond my comprehension.

 

[twentysix by twentyfive]

Thanks, that'll do for me. I really was just being nosey as it is way beyond my comprehension.

Happy to help longers. Be as nosey as you want

 

[threebikesmcginty]

I use trig. every day at work!

 

[dan_bo]

Not sneering 26, just a maths wimp engineer/ technician.

I work in a rich field of optical physics, microelectronics and applied chemistry, I just leave the maffs to the brains.....I've done OK lasting more than a decade without having to rely on it myself.