Calculus II (as per the typical American course) is a complete waste of time. I'm not a disgruntled student in calculus II. I just graduated with a math degree and did the baby analysis and so on.
Why on Earth do we waste so many people's time teaching them how to calculate obscure integrals? All they really need is to be able to integrate polynomials, integration by parts, sin/cos, maybe a few other tricks here and there.
They will likely never encounter integrals like these; if they do they can easily reference a text .
This is precious effort and time that could be much better spent learning some basic properties of real numbers (Archimedean property, basic proofs of Cauchy convergence) which would in turn provide a much better preparation for the study of limits and series convergence/divergence typically covered towards the end of a Calculus II course. They could also introduce students to the idea of elementary and transcendental functions so that they recognize that most of the functions one might conjure up can only be approximated as definite integrals.
Who the hell designs this stuff?
>>8169673
How little math did you do in your degree that some difficult integrals NEVER showed up?
>>8169704
I think OP just doesn't realize he's Autistic.
>math notation makes sense to me so its good for everyone
>>8169704
I didn't have to look up an integral a single time. I also didn't need a calculator after freshman year.
Which is not to brag: I've forgotten all those clunky integration methods and I'm no number cruncher. As far as I can tell this is typical for a math major.
>>8169710
notation is literally designed to make sense
naturally there's a bit of a barrier if you've not seen it before; learning new notation is something one begins to get used to if they're steadfast, something one always recoils from if they're not.
(You)
>>8169673
the trig subs were useless, everything else was cool
Because sometimes knowing a few techniques helps. Sometimes you do have to work on complicated integrals (if you do anything related to differential geometry, analysis or probability) and need to apply transformations to it in order to extract information (not necessarily compute it but at least estimate it).
I'm a math PhD who specialized in triple integrals. Sorry OP, you're just a brainlet who cannot appreciate the true beauty of math.
>>8169768
Kek
>>8169768
So you're nothing more than a calculator. I see.
>>8171538
Dont judge him for his passion dickhead
>>8171538
hownew.ru
>>8169673
For things like engineering and maybe physics I totally agree, everything is plug, no chug at the job level so what the hell is the point? But for pure maths how are you supposed to solve new integrals if you can't already solve the ones that are already known?
>>8171548
truthhurts.jp
>>8171538
The art of triple integrals is far more than mere calculation, oaf.
>>8169704
I finished a MSc in math in germany and never had to integrate something harder than exp(-x^2) by hand.
Wolfram alpha exists for a reason you know? And if that doesn't help you can just ask some autist on math exchange for solutions without showing steps
>>8169673
to weed out the weak
>>8172142
This makes a lot of sense.
>>8169673
Calc II is not for math majors. It supports other majors such as engineering, physics, chemistry, etc.
When modeling complicated systems, complicated integrals pop up all the time. Just think how complicated solving Maxwells equations is for simple configurations.
The advantage we have today is computer modeling which can basically come up with a discrete approximate solution, just pick a small enough mesh for your model..
>>8172002
An was für einer Pleb-Uni hast du denn deinen Abschluss gemacht?
>>8169673
It's a catch all weed out course for Physics/Engineers/Business(good ones at least)/Non-Honors Math students.
It's like that by design.
>>8172142
Weed out what? Calculus II is easy as fuck. Any person that applies to the subject can pass it.
>>8169673
You got a math degree and you're this clueless? Typical mathematician.
>>8172288
Not OP but I made a post saying its a weed out course.
It's not a weed-out course because it's hard. It's hard because there's a lot of techniques that you have to know along with identities. So that already weeds out people who don't remember them. A second thing is the entirety of sequences and series. It's completely "different" than what has been done during calculus before because it requires a bit of thinking instead of pure computation.
>>8172273
One that values actual math over rote memorization and busywork for their students I'd guess.
>>8172372
>actual math
>never involves any integrals
Anon, you are delusional.
>>8172303
dude weed lmao
>>8172398
>involves integrals
>requires to solve integrals by hand
this might shock you, but those concepts are not the same.
Why are there so many people in this thread who think that OP's statement is wrong? The random integrals one learns in Calc II won't appear again if you're a math major. Even in real analysis, you just prove that the standard techniques for integration are valid, you never compute the integral of any function. You're more likely to think about functions which are integrable, but do not have an integral which can be written in terms of elementary functions.
Course which do use these techniques are applied courses, like an application based class in differential equations.
>>8172411
Have to agree with this anon.
>>8169673
it is for physicists, who go on to use all this rote memorization garbage in their physics classes, thinking that their ability to cipher is 'being good at math'
>>8172399
I think I know who you are lel. Have fun at CSTAT it'll be lit.
>>8172411
How the fuck are you gonna do any higher math if you can't even properly transform an integral involving gamma functions, Bessel functions or zeta functions? You know, in analytic number theory, analysis of PDEs or stochastic processes you get that shit all the time and you need to derive strict upper bounds or establish convergence. But you're just a high school moron who thinks he's a genius for doing calculus 1, so you probably never even heard of those special functions.
>>8169673
The idea is to break High School notation and intimidate you while not teaching proofs and consistency.
School is designed to contradict itself in order to create Dependence: what you learn in kids school is oversimplified and just plain inconsistent with what you learn in high school, and what you learn in high school is wrong and inconsistent with college material. Guess what, same goes on in Masters and PhD. The dependence is created because everything you learned can thrown into the trash at any moment.
The intimidation aspect raises school profits. You will see there is a arbitrarily complex bullshit that you have to take in, Common Core is not a new method. You will get used with this arbitrary complexity and will be mentally impaired until you realize how retarded you were. Let me remind you that you are rewarded to be like this: to spend a lot of energy to take simple steps.
Without proofs, consistency, your real intelligence gets stuck: Soft sciences are created, disciplines become independent and mystified: ideally teachers should know each other subjects well, because while an student ideally gets out of school knowing all his teachers have taught him, each of his teachers don't care about what their colleagues taught that year.
There isn't really an interest in ever raising your intelligence in academia, my friend. These people don't want you motivated and independent, they want you happy and enslaved.
>>8172480
Well transforming integrals to get upper bounds is not exactly computing an integral, but you got a point there.
>>8169768
Are you this guy?
http://arxiv.org/pdf/1603.04910.pdf
talking about integrals. Does anyone collaborates with this integral?
>>8172526
fuck me did this make it past peer review?
>>8172904
I dunno, but I was introduced to integration w.r.t. spectral measures this past spring and they're pretty neat
>>8171559
>Thinks mathematicians spend their time solving new integrals
wew lad
>>8172480
I sure as shit didn't do that in my calculus 2
>>8171559
You don't know what pure maths really is do you
>>8172480
>learning bessel, gamma, and zeta functions in calc II
I'm pretty sure you've forgotten what undergrad was like. You'll learn bessel in DE's, gamma and zeta in real and complex analysis and for everything else you're an idiot.
>>8172970
he's a freshman drop out, what do you think?
>>8172974
Not him but I actually learned what a bessel function was in Calc II. It was used as an example for a power series.
