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/sci/ - Science & Math

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10548867 No.10548867 [Reply] [Original]

Hi /b/ I'm struggling with calculus 2, specifically infinite series and sequences. Basically i can do all the computational stuff but i can't understand WHY. This class is fucking retarded it's just "here take these series tests to get meaningless answer to continue with your meaningless life" i mean the nigga prof just said let the proofs for the math majors, you guys just have to compute stuff. Which is somewhat understandable

Anyway I'm just not satisfied. I wanted to read a real analysis book with the class but i just didn't have time. Can i at least read WHY the computation works? Like i want to look at the ratio test and say hmm the answer makes 100% sense to me. Or when i found out why the harmonic series diverges (proving why it's not bounded by looking at the graph)

>> No.10548872

lol not even my university's math tutors knew how to do that shit

>> No.10548874

You're looking at it backwards,, but you should be looking at it sideways

>> No.10548875

>>10548867
>Hi /b/
You had one job.
Here's your new assignment: stop smoking weed.

>> No.10548877

my advice is to talk to your prof about showing you the proofs so you understand them
imo your curiosity is not a brainlet thing and your prof is catering to brainlets who dont want to learn or care about the class

>> No.10548897

>>10548875
Oh, i spent 2 min trying to notice why /b/ is wrong lmao. Mb

>> No.10548906

>>10548877
Thx for the advice, I'll try to talk to him next time. Not sure whether he's gonna help or not tho. He's kind of "annoying" because he's too old desu

>> No.10548998

An analytic function is a function that has some series representation, by definition.

The problem then becomes, given some smooth-seeming function, if it were actually an infinite polynomial, what would the coefficients of that polynomial be? Because once you have the coefficients, you have all the information you need. Well whatever those coefficients are, you need to be able to plug in a value and guarantee that it's the same. Plugging in 0, provided that this function is smooth at 0, solves for the constant term because all of the x's cancel out at 0. Next, you should be able to plug in a value into their derivative and guarantee that it's the same. Well even without knowing the rest of the coefficients, you can take the derivative of the polynomial and plug in 0, and what you're left with is a single linear term. Keep repeating with the nth derivative and you get the Taylor series representation for your analytic function.

>> No.10549772

>>10548867
>why series tests work
to be fair, it should be obvious "why" it works: if you have bigger stronger infinity on the denominator and a weak ass infinity on the numerator then after enough L'hopital's rules you will git limit =0.
>calculus 2
> nigga prof just said let the proofs for the math majors, you guys just have to compute stuff
It's really unfortunate that the students who are actually more mathematically inclined than the rest are all lumped in together with the engineers, cs majors and other remedial math students for the purposes of calculus. You don't get to learn "why" until the very end of semester, when they teach you epsilon delta. And even then that doesn't explain why. Next you have to learn about abstract algebra and analysis to find out where numbers come from and "why" all these proofs work, and how Taylor figured out all the Taylor series.

>> No.10550112

>>10549772
>to be fair, it should be obvious "why" it works: if you have bigger stronger infinity on the denominator and a weak ass infinity on the numerator then after enough L'hopital's rules you will git limit =0.
Hmm ye i guess that make sense thx

>It's really unfortunate that the students who are actually more mathematically inclined than the rest are all lumped in together with the engineers, cs majors and other remedial math students for the purposes of calculus. You don't get to learn "why" until the very end of semester, when they teach you epsilon delta. And even then that doesn't explain why. Next you have to learn about abstract algebra and analysis to find out where numbers come from and "why" all these proofs work, and how Taylor figured out all the Taylor series.

It's really unfortunate, but hey at least i can learn all the other stuff on my own

>> No.10550114

>>10548867
Just take a real analysis book and read the proofs of the ratio test, etc.

>> No.10550118

>>10549772
>It's really unfortunate that the students who are actually more mathematically inclined than the rest are all lumped in together with the engineers
Imagine not going to a school with two separate calculus tracks -- a proof-based one for mathematicians and another more computational track for scientists and engineers.

(for what it's worth, CS majors can take either track. I'm a lazy CS major so I went with the less rigorous one)

>> No.10550520

>>10548867
Where the fuck are you studying?
I'm a math/CS freshman and our calculus is done in two parts - proof-driven theory and practice. Can't imagine not being able to prove those basic things I use.
Go to a better school I guess

>> No.10550752

>>10550520
>Go to a better school i guess

Too bad I'm studying in the best university in the country, going to a better one means studying overboard

>> No.10550862

>>10550752
Unimelb?