Any one good at Math, I mean really good

Bl8ckr0uter

Man I'm interwebbing and I came across this:

ei + 1 = 0

Eulers Formula. I have read this
http://www.geoffsquared.com/math/eulersformula.pdf

And done some googling. It ain't hitting me. Can someone explain this to me ? (I am not super great at math but I pick things up pretty well)

UnixGuy

Calculus 102 ??

I really forgot this stuff !

tell me which part of the proof you don't get ?

Bl8ckr0uter

UnixGuy wrote: »

Calculus 102 ??

I really forgot this stuff !

tell me which part of the proof you don't get ?

The entire thing . Honestly I am not sure what it exactly this is trying to prove or what its application is for real life (btw I have not taken my calc classes yet...)

Honestly I saw it on a Tee Shirt on Think Geek and I was curious. I pulled/am pulling a double a the NOC and I am seriously board. CCNA later today but honestly if I see another circle with arrows on it I WILL die.

UnixGuy

Ok, it's trying to prove that: ei + 1 equals to zero.

I went thro the wiki article to remember, and yeah I do remember now little.


It's important because it's one relations between "e" and trigonometric functions (sine, cosine,..etc).

The mathematical proof you linked us to is using Taylors series to substitute for "e" to the power x. He then substituted x for "i" times Pai. (i = the imaginary number, which is square root of -1).

Then he removed the "series" notation and substituted for the product of it.

Like when you the series y=1+x (for x=0...to infiniti)

you can substitute it by writing:

y = (1 + 0) + (1 +1 ) + (1+2) +.....


so the same idea he used here.

Then he factored the nominator: (i times pai) square.

you need to know all these equations, they're available in any calculus book. With proves. They're not difficult, you need to work out lot of problems, and you will be fine



Now the applications, don't ask. Plenty ! All these notations are used heavily in electrical engineering. They're used in computing electrical signals, and power machines. They're also heavily used in probabilities. These formulas are the basis for all the electrical engineering.

UnixGuy

knwminus wrote: »

Honestly I saw it on a Tee Shirt on Think Geek and I was curious. I pulled/am pulling a double a the NOC and I am seriously board. CCNA later today but honestly if I see another circle with arrows on it I WILL die.

Ok, you don't need that in for CCNA or anything of that sort.

you only need this in electrical engineering at college. Chances are you won't even use them on the job even if you work as an electrical engineer.


It's not difficult, if you started at college with calculus then you moved up, it's normal

Bl8ckr0uter

UnixGuy wrote: »

Ok, it's trying to prove that: ei + 1 equals to zero.

I went thro the wiki article to remember, and yeah I do remember now little.


It's important because it's one relations between "e" and trigonometric functions (sine, cosine,..etc).

The mathematical proof you linked us to is using Taylors series to substitute for "e" to the power x. He then substituted x for "i" times Pai. (i = the imaginary number, which is square root of -1).

Then he removed the "series" notation and substituted for the product of it.

Like when you the series y=1+x (for x=0...to infiniti)

you can substitute it by writing:

y = (1 + 0) + (1 +1 ) + (1+2) +.....


so the same idea he used here.

Then he factored the nominator: (i times pai) square.

you need to know all these equations, they're available in any calculus book. With proves. They're not difficult, you need to work out lot of problems, and you will be fine



Now the applications, don't ask. Plenty ! All these notations are used heavily in electrical engineering. They're used in computing electrical signals, and power machines. They're also heavily used in probabilities. These formulas are the basis for all the electrical engineering.

That actually makes a lot of sense. Still a bit over my head, but I have been working for going on 16hrs...

UnixGuy wrote: »

Ok, you don't need that in for CCNA or anything of that sort.

you only need this in electrical engineering at college. Chances are you won't even use them on the job even if you work as an electrical engineer.


It's not difficult, if you started at college with calculus then you moved up, it's normal

I have to do a trig class then a Stats class then technically I will have all math I need for by AAS. But since I want to transfer to a 4 year as soon as I am done, I will try to complete Cal I-III and do Dif Eqs at the 4 year.
My dad has his masters in Chemistry and a minor in math so he will be my tutor for that .

Honestly Calc I-IV were the reason why I was not going to do a CS degree, because I really don't care for math and at the 4 year I want to go to the failure rate for these classes is like 75% and I have a nice GPA But looking at a class on OS Structure really made me want to go CS.

UnixGuy

knwminus wrote: »

Honestly Calc I-IV were the reason why I was not going to do a CS degree, because I really don't care for math and at the 4 year I want to go to the failure rate for these classes is like 75% and I have a nice GPA But looking at a class on OS Structure really made me want to go CS.

I wouldn't change my major because of one class or two. While the failure rate is high, there are lot of people who can get full marks. Anybody can do it, and it doesn't really need super brains. It's just about working out problems in books, period !

I recommend CS, you will enjoy it. And for the math classes, just invest your time in working out those problems at the end of each chapter, and you will be just fine Same goes for Electrical/Mechanical engineering courses, IMHO.

Bl8ckr0uter

UnixGuy wrote: »

I wouldn't change my major because of one class or two.

Or 4....

UnixGuy wrote: »

While the failure rate is high, there are lot of people who can get full marks. Anybody can do it, and it doesn't really need super brains. It's just about working out problems in books, period !

I recommend CS, you will enjoy it. And for the math classes, just invest your time in working out those problems at the end of each chapter, and you will be just fine Same goes for Electrical/Mechanical engineering courses, IMHO.

Hopefully. Since it is a BSCS w/ a concentration in Business, I think it blends my interests perfectly. Plus BSCSB sounds really bad ass to say.

UnixGuy

knwminus wrote: »

Or 4....




Hopefully. Since it is a BSCS w/ a concentration in Business, I think it blends my interests perfectly. Plus BSCSB sounds really bad ass to say.

lool @ BSCSB sounds bad ass


It won't matter a lot, few classes difference. Personally I'd choose computer engineering or science.

Good luck

Bl8ckr0uter

UnixGuy wrote: »

lool @ BSCSB sounds bad ass


It won't matter a lot, few classes difference. Personally I'd choose computer engineering or science.

Good luck

Thanks. I passed the CCNA and after I do S+/L+ I am going right for SCSA/SCNA so watch out

hypnotoad

The PDF of the proof you linked to is basically a neat calculus trick -- in the proof they don't use the actual number zero, but both sides of the equation approach zero at i = infinite.

The PDF says..."Assume that Euler's Formula is true, then Assume the Taylor Series is true (which it is) and show that they are equal in the limit i->infinite."

Yes, the equation has actual use in trig.

dynamik

knwminus wrote: »

Plus BSCSB sounds really bad ass to say.

Palindromes are cute

Sepiraph

The proof uses infinite Taylor series expansion to show the equivalence of for both side (e^ix & cos x + i sin x), basically if you re-arrange the terms (and provided the series convergences) you can see that the two sides are equal.

Another way you can see this is through complex analysis in which you map e^ix and you can see it is just a circular function on the complex plane. And you can map out the same function using cos x + i sin x, which is valid for -infinity to +infinity.

(So when you substitute pi for x, you get the shown result)

Btw that equation is frequently voted as one of the most beautiful equations by mathematicians.

Bl8ckr0uter

Sepiraph wrote: »

The proof uses infinite Taylor series expansion to show the equivalence of for both side (e^ix & cos x + i sin x), basically if you re-arrange the terms (and provided the series convergences) you can see that the two sides are equal.

Another way you can see this is through complex analysis in which you map e^ix and you can see it is just a circular function on the complex plane. And you can map out the same function using cos x + i sin x, which is valid for -infinity to +infinity.

(So when you substitute pi for x, you get the shown result)

Btw that equation is frequently voted as one of the most beautiful equations by mathematicians.

I got with my dad this weekend and he explained it. Although he didn't know why it is so beautiful. He has a Masters in Chemistry and a minor in Math but he was telling me it has been about 20 years since he has seen this thing.

Sepiraph

knwminus wrote: »

I got with my dad this weekend and he explained it. Although he didn't know why it is so beautiful. He has a Masters in Chemistry and a minor in Math but he was telling me it has been about 20 years since he has seen this thing.

Well it is subjective but IMHO it is because that equation illustrates some fundamental concepts in mathematics, yet shown in a simple, elegant equation:

- e (transcendental number)
- i (imagery/complex number)
- pi (transcendental number)
- 0
- 1 (Unity)