/sci/ - Science & Math

>>6490602
Sure they are. I proved it. If you don't believe me, post a counter-example.

>>6490623
Construct an algorithm that makes a machine learn how to come up with new BSc thesis topics for CS students.

>>6490634
derivations in differential Galois theory

>>6490650
about tree fiddy

>>6490567
"Trivial" is subjective. With an IQ as high as mine finding all the zeros is trivial. For an undergrad student it might be harder.

>>6490577
Nobody can. Triple integrals are currently being researched by the most talented mathematicians and the new tools we develop to tackle the problem are inspiring new and exciting areas of math. A solution to triple integrals however hasn't been found yet.

Math PhD here taking your calculus questions.

>>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

>>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!

>>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.

Taking your calculus questions.

Precalc is fine too.

>>6286920
No difference. The definitions stay the same.

>>6286888
I could if you tell me the domain.

>>6286863
There are very few calculus PhDs. When I received my doctorate, I got offers from several investment banks.

>>6286881
Very hard. If your IQ is lower than 200, you'll stand no chance.

Sorry for the late reply. I was busy finding the derivative of a quadratic equation.

>>6286808
Any job you want, 300k starting.

>>6286815
Because of multiculturalism.

>>6286850
Plug it in. The function has no singularity at x=3.

>>6286862
Did you write a PhD thesis on calculus?

>>6286749
>>6286760
The limit is 1.

>>6286752
Logic is philosophy. Set theory is only a tool, like functions or variables are not fields on their own. Algebra comes before calculus.

>>6286776
Nobody knows how to do it. The best PhDs are researching solutions to very simple triple integrals. A general theory does not exist yet.

>>6286737
Calculus is god tier. There is no topic of math more beautiful and profound than calculus. All the other math wouldn't exist without calculus.

>>6286713
I'd give it to my students as a homework assignment ;)

The unique solution is 1/x.
Set g(x) = x * f(x) and then show g(x) = 1.

>>6286682
Calculus is a very complex field of math and demands a lot of prerequisite knowledge in higher math. Are you proficient in algebra and precalculus?

>>6286684
I'm making 300k per month.

>>6286700
pi/2

>>6286667
Because sin is an odd function. The area from -pi to 0 cancels the area from 0 to pi.

>>6286670
Triple integrals are subject of cutting edge research and not fully understood. Maybe in 100 years we will have a complete theory of triple integration.

Ask an expert on calculus anything.

My PhD thesis involved triple integrals and quadratic equations. What made it even harder was the problem that I got constantly distracted by all the incoming offers from various investment banks to start working for them at a minimum entry salary of 300k.

>>6040243
Use the same proof by virtue of the fact that it only involves the property <span class="math">\int_a^b = \int_a^c + \int_c^b[/spoiler] which holds true for HK integral as well as R integral.

A circle is always finite. Pi is always infinite. The paradoxical nature of pi reflects the dissimilitude between perfect mathemacial circles as abstract objects and the imperfect quality of reality.

>>6039973
By defining a local connection on the tensor bundle.

>>6039992
Hyperbolic trig functions often arise in the theory of differential equations and integrals. They are of utmost importance in many approaches to the unsolved problem of triple integrals. HTF's allow mathematicians to dismiss the inconsistent notion of complex numbers by using split-complex numbers instead. <span class="math">e^{jx}=\cosh(x)+j\sinh(x)[/spoiler] is more powerful than Euler's identity and accounts better for the geometry of non-cubic spacetime.

>>6040051
I was busy solving a quadratic equation.

Ask an expert on calculus anything.

>>6012806
Imaginary numbers are a very controversial idea and I would even call them crackpottery. Advocates of imaginery numbers claim they can square root negative numbers. That sounds ridiculous, doesn't it? What they don't want to see is that they are paying the price of having to break several axioms of math. Many mathematicians - including myself - do not believe that imaginary numbers will lead to any practical applications.

>>6012795
>Are you doing your postdoc in calculus?
After publishing my PhD thesis in calculus I am now doing research in trigonometry.

>What do you see as the next big breakthrough in calculus?
Triple integrals are one of the big unsolved problems. Personally I don't believe we will see a solution within this century. The next big breakthrough could be finding the derivative of e^x.

>>6012799
By convention the solution is defined to be positive. Think of square roots which are also defined to be positive.