/sci/ - Science & Math

>>6345033
how do we prove that zeta(3) is irrational in less than 6 lines ?

How do I find the remainder term for a taylor series. I know the formula I just want to know how to find the specific value instead of a range of where the value should be.

>>6345042
not op , but there is an integral form of the remainder . Google it you fucktard2

I am starting calc and anal geom next semester, what are some good places to start textbook wise to try and teach myself so that i am not completely blindsides? Thanks OP

>>6345061
>anal geometry

ooookaaaay...

integrate integrate integrate diff integrate e^e

I need a closed-form antiderivative of exp(-x^2). It's urgent.

>>6345033
Quadruply Intergrate f(x)=x

Does the Lagrange multiplier method for maximizing a function have any real purpose?

>>6345040
Please no homework questions. I'm only answering serious calculus questions.

>>6345042
Plug in one value and then solve for x.

>>6345061
Try to practice IQ test problems. They will prepare you for mathematical challenges. Remember: All you need in math is a high IQ.

>>6345091
Triple integrals are still an open and unsolved conjecture. Maybe in 100 years we will know how to do them.

>>6345033
I want to get a better handling on topology, but not spend too much time on it. I read the Baby Rudin and I feel like it was not really enough, or let's say I haven't fully taken up all the information from the chapter yet.

I'd just love to be able to state certain theorems just as the theorem of continuity in terms of open sets etc and get a better handling with compactness and so on

any book you could recommend?

>>6345104
>triple integral unsolved conjecture
op confirmed for faggot troll unaware of differential forms

>>6345083
>not using the integral of the rotated cross sectional area of the colon to find the volume of poop that can be stored

>>6345110
the inverse image of an open set under a continuous function is open
any open cover of a compact set can be reduced to a finite cover

it can be proven that the image of a compact set under a continuous function is itself compact

>>6345098
<span class="math">\int_{-\infty}^x e^{-t^2}\mathrm{d}t[/spoiler]

>>6345101
1/2 * x^2 * y * z * w

>>6345102
It has a very important purpose: making your homework harder!

>>6345091
So...
<span class="math">\displaystyle \int \int \int \frac{d}{dx}\left[\int e^e dx\right]dx dx dx[/spoiler]

So...

<span class="math">\displaystyle \frac{1}{6}x^3e^e+\frac{1}{2}C_1x^2+C_2x+C_3[/spoiler]

>>6345115
cool, now recommend me a book so I can do this magic, too

>>6345116
closed form, faggot

>>6345119
Real Analysis by Royden

>>6345110
>better handling on topology
>not spend too much time on it
How much time do you have?

>>6345111
>implying differential forms can solve triple integrals

>>6345123
>anti-derivative
>closed form
gr8 b8 m8

a quick proof that compact sets are closed in Hausdorff spaces

>>6345133
How much time do you have?
Well, let's say it this way
I have 3 more weeks of holidays and then I have two major exams, one on Linear Algebra and one on Physics

I wanted to work through about 500 pages of stuff related to those subjects in the next 3 weeks

Then 2 weeks after thsoe exams I have an Analysis exam, but since I study physics we barely covered topology (we proceed real fast anyway) so it won't even help me for that and I don't need it as an end in itself, just to solidify my understanding of what I already know

Maybe 50 pages about topology would be enough, but I planned on reading Spivak's Calculus anyway, but I'm not sure of that will have me covered

Problem 8?

You have a cube with side lengths of 2 feet
you will fill this box with spheres of radius 6inches,
what is the number of spheres you fit into this box?, what will the angle be which the spheres touch one another?

How do i get better at series? Everything from the test, to taylor and maclaurin series. Im getting my ass kicked. . Ive already watched videos on the youtube. And while i might grasp some concepts for 1 problem i get owned another. Anyone have tips? Currently working on representing a function as a power series.

>>6345552
This is what I do. Make a column of derivatives, then make a column where they are evaluated. Make a column of polynomials. Make a column of factorials. Find the pattern. Make the series by plugging the pattern into a sum formula.


Eulers Identity as an example.