/sci/ - Science & Math

>>7115618
Professional math and physics is almost entirely made up of solving triple integrals.

Its important to know the theory. Really calc b is just for teaching critical thinking

>>7115618
I think working mathematicians hardly ever actually solve integrals. Physicists probably just guesstimate.

>>7115618
Even worse: they just do numerical integration and call it a day in most cases.

>>7115626
>>7115629
>>7115631
Don't listen to these trolls OP.

>>7115626
you call it critical thinking but it seems more like basic pattern matching.

once you understand that the fundamental theory of calculus is there really a reason to do all these messy trig integrals? what's the point?

>>7115618
Youre stupid op, its important to know the underlying theories if you want to deveolop new ones. If everyone just kept using fucking calculators, everyone would be like you

Complex contour integration is another method you'll learn. If you don't care about the fundamentals wiki generalized cauchy integral formula and you can apply it basically immediately, but I highly recommend a complex variables class. One of the most fun I've taken

Integrals are fun. It's like sudoku.

the point is that only the most trivial integrals can be solved analytically. approximations are extremely important, anyone working in an applied field pretty much has to give up on closed-form solutions. of course it's important to know the stuff you learn in calculus B, but i'm assuming your teacher just meant that there really aren't that many techniques for analytically solving integrals. you learn integration by parts, substitution, and a handful of other tricks and that's pretty much what you have to work with.

>>7115658
>it seems more like basic pattern matching.
welcome to math. math is about patterns.

>>7115618
He was right, as an engineer I just integrate it numerically using Matlab

>>7116794
>only the most trivial integrals can be solved analytically
How is f(x)=x^x integrated?

>>7116983
this post gave me aids

>>7115618
It doesn't make much sense to memorize a whole lot when you'll in real situations always have references, but I recommend meditating as much as possible on the underlying meaning and logic of integrals and derivatives.

>>7116983
numerically
but that integral never uesful

>>7115618
The whole point of integral calculus courses is not to make you really good at solving integrals. They just want you to be as familiar with the operation and the underlying concepts as you are when it comes to addition and multiplication.

The idea is that if somebody says something like "it's a sum of line integrals" in conversation, you instantly know exactly what they mean. Not that you can sit there and actually evaluate the integral in your head like an autistic number cruncher.

>>7115618
>Calc
>hard
not to sound like an ass, but Calc is the easiest math course you'll ever take. That's sad if you can't even do a simple triple integral.

>>7117421
you do not know if he is a math major
but i'd agree for physics and electrical engineering and mechanical engineering

>>7117421
who the fuck are you quoting you retard? i never said it was hard.

>>7116983
logarithmic differentiation

>>7117232
sum of the line integral
What's that?

>>7117627
it means to connect the lines, I guess

>>7115658
because trig integrals are like fun little puzzles that can take up 3 pages of your notebook in the worst cases

but honestly trig integrals rammed the trig identities into my head, and that helped in physics a ton. it also came in handy in vector calc sometimes.

regardless think of this way: if you can't solve trig integrals, you aren't doing to be able to some many much much harder problems. the lower division stem courses are there to scare off people who are either stupid or not serious enough about their subject.

>>7115618
>so what's the point of the class

To learn how to integrate common classes of tricky integrals, series methods, and coordinate changes.

>"you'll get as good as you're going to get at solving integrals in calculus b, and that won't even be very good"

Because most functions can't be integrated in terms of common functions. Not because we never integrate.

>do working mathematicians and physicists solve their own integrals or do they just do them in mathematica or maple

Mathematicians invent and study special functions which are the functions (or inverses of functions) of unsolvable integrals:

ln(y)=<span class="math">∫_1^y dx/x[/spoiler]
J_n(y)=∫cos(n*x-y*sin(x))dx "Bessel function"
gd(x)=∫sech(x)dx "Gudermannian function"
erf(x)=<span class="math">2/√π∫_0^x e^{-t^2}dt[/spoiler] "error function"
Γ(t)=<span class="math">∫_0^∞ x^{t-1}e^{-x}dx[/spoiler] "gamma function aka (t-1)!"

>>7117964
pls write out your math more pretty

<span class="math">
ln(y) = \int\limits_{y}^{1}dx/x
[/spoiler]
<span class="math">
J_{n}(y) = \int cos(nx - ysin(x))dx
[/spoiler]
<span class="math">
gd(x) = \int sech(x) dx
[/spoiler]
<span class="math">
erf(x) = \frac{2}{\sqrt{\pi} \int e^{-t^{2}} dt}
[/spoiler]
<span class="math">
\Gamma (t) = \int\limits_{0}^{\infty} x^{t - 1}e^{-x}dx
[/spoiler]

>>7118020
i'd rather write by hand and take a photo lel

>>7115623

>Professional math and physics

WTF is that? Is there a secret pro-circuit for math and physics, like some kind of fight club?

STFU anon, OP check this out: http://www.amazon.com/Inside-Interesting-Integrals-Substitutions-Undergraduate/dp/1493912763

>>7118075
got a pdf?

>>7118075
you can't seriously not know about this maymay of ebic proportions
https://www.youtube.com/watch?v=FOZO0WWULLA

>>7118020
functions like log or cos etc. are all TeX function, e.g. there is \cos.

Compare

<span class="math">cos[/spoiler]

and

<span class="math">\cos[/spoiler]

>>7118110
compare

<span class="math">
\int\int\int benis \: :-DDDDDD
[/spoiler]

and

<span class="math">
c====8
[/spoiler]

trick question, they're algebraic isomorphisms.