Read all over the internet how cal 2 is super hard and it's the hardest calculus

>read all over the internet how cal 2 is super hard and it's the hardest calculus
>take first cal 2 test today
>easy as shit
>all my friends thought so too
>I go to a good uni (UT) so it wasn't easy because it's a trash school

The fuck? Is cal 2 a meme class? Are people retarded? Does it get harder? Someone explain this shit to me

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We'll look into it. Could be a problem with our instruments.

>UT

What the fuck is it with plebs thinking anyone knows their shit tier university just from initials?

UT - University of Tampa? University of Tennessee? University of Texas at Austin?

Fucking ameriplebs
en.wikipedia.org/wiki/List_of_colloquial_names_for_universities_and_colleges_in_the_United_States

The only relevant UT obviously.

Funnily enough the only top tier US university most people know by initial is MIT, because it's globally recognised

>The only relevant UT
The university of Tokyo?

>The only relevant UT
The university of Toronto?

Well memed my friends

What did you have to do in the test?

Integrate e^(-x^2) and check continuity

Partial fraction decomp, series convergence/divergence, improper integrals, finding the nth term where the level of error will be less than .0000001, and that's probably it, there were only like 8 or 7 questions

Sounds pretty usual for calc II, it really isn't that hard.

From all the calc courses, the part that fucked me the most was triple integrals.
I just couldn't find the regions correctly and struggled a lot with it.

America everyone
I did this in pre-kindergarten you shithead

I'm guessing it depends on the teacher. I had a pre-calculus teacher that destroyed me and showed me that I would never major in Math. I had a Calculus II that was hard where the class average was a C, but I got a B on it. Of course, this was all at a community college known as Mt. San Jacinto.

Calc 2 is more difficult because, later in the semester, you'll have built up a large toolbox in terms of how to tackle series/various integrals. It will then be on you to use these tools on your own, without being told which ones to use, to solve integrals or evaluate series. Right now everything should be familiar and simple. You want to learn this stuff very well. Near the end when you have everything at once, people tend to get rocked because they forgot things like trig substitution, partial fractions, geometric series, etc. when it comes back.

It's like in Calc 3, people forget about how to parametrize a plane/curve and then get rocked when it comes time to do stokes/divergence theorem calculations or general surface line integrals.

Quick dumb question for calc bros

Can you only tell the difference between a unit vector and vector if they have a divisor that looks like the |v|?
for example: u = is unit vector
u = is not.
I'm just a bit surprised for the professor did not mention anything about unit vector conversions.
Or it may have slipped my mind.

>if they have a divisor that looks like the |v|
I have no idea what you mean.

|v| = [math] \sqrt {a^2 + b^2 + c^2} [/math]

the length

Just check the norm in your head it's instant

This is the information I was missing - I was unaware of norm until you mentioned it.

Thanks, that's a better way to verify whether the vector is normalized or not.

You mean the brackets around the vector?
Please don't use for a vector, that's the symbol for the inner product of vectors.

The usual notation for a unit vector is û, the vector with a ^ on top.

Otherwise you have to calculate the norm.

I'm not very familiar with proper vector notation, I don't mean to error.
Interesting enough is that's how my professor represents vectors when he does not put the arrow over the variable.

How would you write it then?
û = (5, 1, -2) ?

The most common notation in indeed writing the vector with (), like you did there.
v = (a,b,c), or in column format.

In your example, (5,1,-2), isn't a unit vector, so you'd just write it as u = (5,1,-2), since the norm is sqrt(30).

If it was instead, say u = (5/sqrt(30), 1/sqrt(30), -2/sqrt(30) ), then the norm is 1, and you can call u as û.

You can always obtain a unit vector by diving a vector by the norm, which is how i got that example. so for some vector v
[math]\hat{v} = \frac{v}{\|v\|}[/math]

Well, if you aren't going to see the inner product in your class then that notation doesn't make much difference, but it just creates needless habits for later (chances are you're already seen it, since you're dealing with vectors, the dot product or scalar product is simply a special case of the inner product, and you normally define the norm in terms of the inner product, [math]||v|| = \sqrt{} [/math]).
If you are working if you vectors in 2 dimensions for example, and you're going to take their inner product you'd write the inner prodct as , so you can already see the problem if you're also writing your 2D vectors v = too for example;
Quantum mechanics though, normally uses the notation for the inner product, but that's besides the point.

Thanks for the clarification. I was bothered when my professor sometimes chose and others (). We already are on scalar products and such but he chose to write out instead of using proper notation. I'll probably have to follow his rules for labeling with the upcoming test. I'm curious though, What's the difference in writing [math] | v | [/math] and [math] || v || [/math]? Do they both mean the same thing? I only know that [math] | v | [/math] is defined as the length of the vector.

After searching around I found that [math] | v | [/math] is in fact absolute value/length and [math] || v || [/math] is norm.

I still have a lot to learn I guess. For I'm a bit uncertain as to what a norm is, and wondering why we didn't go over it.

Calc 2 isn't hard. People are just brainlets.

>staring at obvious trig sub integral
>can't think to trig sub

You can say that absolute value by itself is something that is only applicable to numbers (ie 1D vectors)
You can have something called the absolute value norm when dealing with 1D vectors (ie, simply numbers), so you have that ||v|| = |v|.

The actual term is the norm, the reason some use |v| to denote the norm in some cases is an abuse of notation, which comes from the concept of a norm being a generalized concept of length of a vector.

Its most common in physics, like when dealing with the euclidean norm (||v|| = sqrt(a^2 + b^2 + c^2) ) or say the minkowski norm in relativity (||v|| = sqrt(t^2 - x^2 - y^2 - z^2))
As I mentioned above, the only case they're actually equal is the 1D case, where you define your norm as being the absolute value of the number, for other cases it's just an abuse of notation.

The concept really expands when you look at other types of norms, these are just specific cases of the p-norms, which you can easily associate with numbers.
You get other interesting norms when considering functions as vectors (yes, you read that right) or matrices as vectors for example.
The first one is used widely in quantum mechanics where you have the hilbert spaces, which are vector spaces of functions (hence, functions as vectors), and you define inner products on it as well as norms (here is an example of a generalised inner product).
And is denoted as
[eqn] = \int_0^1 f(t)g(t)dt[/eqn]

I went to a big 10 uni.
Calc 2 prof is head of math department. Made us memorize trig subs without explaining where they come from.

Years later.
Tutoring.
See a blip about trig sub in students text. Instantly recognize why it is and makes it 1000x easier to do them.

Naturally, you might notice that we're playing with the notion of length (and with the notion of angle if you look at the inner product, where you can indeed define angles between functions for example), so you might realize that we're playing with the notion of distance, which is where something called the metric comes in, where the metric is what gives the distance, and we can generalize it too, like creating the concept of distance between functions, or being able to deal with curved spaces (like in general relativity), since the euclidean metric (the euclidean distance we're all familiar with) is only valid for flat spaces.

Use \langle and \rangle for angle brackets in LaTeX
[eqn] \langle f , g \rangle [/eqn]

Calculus 2 isn't that hard. I got a C in calculus 1, but top marks in Calculus 2.

I think people say Calc2 is hard because of Series and Sequences, which isn't super intuitive the first time you look at it, and it will give you something like 11 different tools you will need to use in order to check if a series diverges or converges. Having all the tools available and being required to think a little messes up people who don't study hard or absorb abstract concepts really quickly.

But, really. It's not that hard.

kek freshmanlets confusing hard with tedious again

no calculus course is objectively hard, they just get progressively more tedious

rote application of all the memorized formulas is all you'll be doing

in calc I you learn how to think like an autist

in integral you learn 5000 more ways to be autistic

in DE you will learn how to ascend to turboautism and spend 15 minutes and 2 pages on a single question, taking double and triple derivatives, and double integrals, all for a 2 line long final solution.

if you werent autistic before calc 1-3 + DE, i guarantee you will be at the end.

>pic related

well meme'd friend xD

calculus 3 was the hardest for me

not because i didn't understand the material, but because i'd always miss a fucking minus sign or something, and get the wrong answer

because the textbook i used insisted on having excessively long problems, i almost lost a whole letter grade because of stupid mistakes like this in my homework

i guess, in a way, basic arithmetic was harder than calculus for me

I could swear Veeky Forums's latex had a problem with it, looks like I was wrong.

Holy fuck american education

I did all that when I was 3

Why hasn't all the amerifat shitposters learned this by now? Obnoxious fags thinking everybody knows the initials of their universities.

It gets mildly harder, but if you study and aren't a total dumbass, it shouldn't be too challenging. The concepts are, in general, pretty basic.

What curriculum are you guys using?

Stewart's, 7th edition

Not user, but same here.

It's a shit book tho.

Why do you day that

I feel that it doesn't explain any of the lessons thoroughly, and is missing information.

For example, today in class we started a new chapter learning integration by parts, and my professor went through stuff like LIPTE/LIATE, as well as cases when it doesn't really work, and tabular integration. The book didn't have any of that. It just tells you to set [math]u[/math] to the one thats muh simpler to differentiate. Check the book for yourself.

It could be just a few of the lessons that do this, but then again, I never read the book much anyways besides spending almost $200 on it.

stupidly enough there are two U of I's in Illinois. One in Champaign and one in Chicago unaffiliated.

UT Texas is actually a shit school. UT progress has kind of stagnated because the good faculty left for other universities as Austin/UT got more and more left leaning.

>campus is liberal so it's shit

I bet you're voting for trump too

Well man, profit then. Go get your A+ champ.

It's hard for brainlets like who spent their whole life learning math as a series of steps to memorize and follow.

>good uni
>UT
Pick one faggot.

University of Toronto is a more relevant school than some faggot UofT school in Austin.

Good one guys, gave me a hearty chuckle

Texas is shit, your school is shit, you're shit. Deal w/ it.

We're higher up than toronto in terms of engineering :^)

>being proud of being better at sucking dicks

>has to resort to stale memes to save face
Pathetic tbqh

It's not even true. Toronto is ranked 3 points higher in EE/CE (aka the only respectable discipline of engineering) :^)

You're really grasping at straws now, aren't you?

Don't tell me you actually majored in something completely pleb like Chemical or Mech. You're not this pathetic, are you?

>if I start flinging meaningless insults, it'll look like I have a point!

Chemical engineer confirmed

Enjoy your thermodynamics and process piping, KEK

This is just getting sad now, famalam.

enjoy staring at pipe flanges all day, autocad monkey

>a meme class

go stick your memes up your ass

I did this when I was a fetus in my mothers womb.

American education everyone.

Unreal Tournament?

I've taught calculus and honestly believe integral Calc is the easiest bit. I'd give the hardest to sequences and series, which takes a bit of getting used to.

What are you,American?
I did this before my great grandfather was conceived.

For your first test? We barely had a test on inverse functions, hyperbolic functions, and exponential/logarithmic functions. You must've covered a lot of material in calc 1

Third worlder detected

I did this 14 billion years ago, and my wave of understanding was such that it spawned a universe

Kek

Once you "get" calculus, the rest is just extensions.

It only gets hard again when you have to do weird integrations

On a scale of one to assblasted, how mad are you that Cal killed your possible natty run?

I'm pretty salty, but we were overrated af after Norte Dame.

A typical "smart" person doesn't start to struggle until line/surface integrals (which is the latter half of Calc 3).

>wow I did good in my first cal 2 test I'm a math god

>The only relevant UT obviously.
University of Turin?

Which UT?