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A Summer of Maths (ASoM) 2016

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Original post by krishdesai7
Sorry if I'm wrong but shouldn't it be sin(x)cosh(y) — icos(x)sinh(y)


No?

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Just out of curiosity, how regularly and for how long do you mathmos exercise?
Original post by MathsCoder
Just out of curiosity, how regularly and for how long do you mathmos exercise?


I'm in my job(gym) around 5 times a week, somewhat serious powerlifter


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Original post by drandy76
I'm in my job(gym) around 5 times a week, somewhat serious powerlifter


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Quite cool!
Original post by MathsCoder
Just out of curiosity, how regularly and for how long do you mathmos exercise?


2x/week gym
Original post by MathsCoder
Just out of curiosity, how regularly and for how long do you mathmos exercise?


never

fat ****
Original post by krishdesai7
Sorry if I'm wrong but shouldn't it be sin(x)cosh(y) — icos(x)sinh(y)


Nope. Take a look at this entry in the DLMF for all the identities.
Original post by Insight314
All right, gonna try that, after I finish eating though. However, is it possible to show that it has infinite solutions using my method?


I can't say, as I don't see how you're going to proceed from where you got :biggrin:
Original post by MathsCoder
Just out of curiosity, how regularly and for how long do you mathmos exercise?


I get up from my desk and walk over to the coffee machine at least twice a day.
Original post by Gregorius
I can't say, as I don't see how you're going to proceed from where you got :biggrin:


Using your method, I got up to having to show that sin⁡xcoshy=2 \sin x cosh y = 2 where x,yx, y satisfy z=x+iyz = x+iy, has infinitely many solutions. :/
(edited 7 years ago)
Original post by Insight314
Using your method, I got up to having to show that sin⁡xsechy=2 \sin x sech y = 2 where x,yx, y satisfy z=x+iyz = x+iy, has infinitely many solutions. :/


Easier than that. Think about sin⁡xcosh⁡y=2\sin{x}\cosh{y} = 2. Choose x so that sin⁡(x+nπ)=1\sin(x + n \pi) = 1. Now work out what y must be,
Original post by Gregorius
Easier than that. Think about sin⁡xcosh⁡y=2\sin{x}\cosh{y} = 2. Choose x so that sin⁡(x+nπ)=1\sin(x + n \pi) = 1. Now work out what y must be,


Whoops, I meant sin x cosh y in my reply, but you saw that. :smile:
Reply 172
Avatar for wlog54
wlog54
Can I use the fact that sinx = (e^ix-e^-ix)/2i and solve directly for sinx = 2 to prove that it has infinite solutions
Original post by Mathemagicien
I do exercise papers every day, for a few hours :biggrin:



A powerlifting mathematician? :eyeball:


Probably a better powerlifter tbh


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Original post by wlog54
Can I use the fact that sinx = (e^ix-e^-ix)/2i and solve directly for sinx = 2 to prove that it has infinite solutions


You can certainly set off in this direction - the equation turns into a quadratic in eiz e^{iz} , which you can solve so show you get a solution. But the difficulty then is to show that you get an infinity of them (using periodicity). I suspect that you end up going in circles proving the periodicity.

The advantage of the method I suggested is that it gets you the infinity of solutions due to the periodicity of the real function sin(x), which I assume you are allowed to quote.

Take a look at this plot of sin(z) in the complex plane to get your intuitions fired up!
Original post by Gregorius
You can certainly set off in this direction - the equation turns into a quadratic in eiz e^{iz} , which you can solve so show you get a solution. But the difficulty then is to show that you get an infinity of them (using periodicity). I suspect that you end up going in circles proving the periodicity.

The advantage of the method I suggested is that it gets you the infinity of solutions due to the periodicity of the real function sin(x), which I assume you are allowed to quote.

Take a look at this plot of sin(z) in the complex plane to get your intuitions fired up!


I see where your avatar comes from!
Original post by Insight314
I see where your avatar comes from!


:colondollar:

The book that goes with that website is pretty special!
More than 5 hours of maths are done for today, gonna chill with some GoT until sleep. Continuing with V&M tomorrow.

I hope Beardon's textbook arrives tomorrow so I can start working through it. Probably not gonna look at lecture notes at all, unless I want to revise the material I have learnt. Also, I am gonna try and finish question 5 of the example sheet tomorrow since I attempted it with @Gregorius's hint but couldn't get through it as much (or my headache didn't allow me to).
Original post by Insight314
More than 5 hours of maths are done for today, gonna chill with some GoT until sleep. Continuing with V&M tomorrow.

I hope Beardon's textbook arrives tomorrow so I can start working through it. Probably not gonna look at lecture notes at all, unless I want to revise the material I have learnt. Also, I am gonna try and finish question 5 of the example sheet tomorrow since I attempted it with @Gregorius's hint but couldn't get through it as much (or my headache didn't allow me to).


This thread should be renamed "Insight314's diary"
Original post by gasfxekl
This thread should be renamed "Insight314's diary"


Lol.

Sorry, won't happen again. :hide:

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