>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
Funnily enough the only top tier US university most people know by initial is MIT, because it's globally recognised
Lincoln Murphy
>The only relevant UT The university of Tokyo?
Gabriel Garcia
>The only relevant UT The university of Toronto?
Brayden James
Well memed my friends
Carson Harris
What did you have to do in the test?
Camden Miller
Integrate e^(-x^2) and check continuity
John Young
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
Asher Garcia
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.
Jack Anderson
America everyone I did this in pre-kindergarten you shithead
Jeremiah Watson
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.
Nolan Nelson
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.
Jordan Price
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.
Luis Adams
>if they have a divisor that looks like the |v| I have no idea what you mean.
Kayden Hall
|v| = [math] \sqrt {a^2 + b^2 + c^2} [/math]
the length
Ian Cox
Just check the norm in your head it's instant
Dominic King
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.
Hunter Moore
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.
Jose Sanders
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) ?
Christian White
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.
Sebastian Thompson
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.
Dominic Hernandez
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.
James Jenkins
Calc 2 isn't hard. People are just brainlets.
>staring at obvious trig sub integral >can't think to trig sub
Jace Jones
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]
Blake Collins
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.
Juan Parker
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.
Thomas Myers
Use \langle and \rangle for angle brackets in LaTeX [eqn] \langle f , g \rangle [/eqn]
Caleb King
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.
John Jackson
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
Brayden Lee
well meme'd friend xD
Asher Martinez
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
Lucas Ortiz
I could swear Veeky Forums's latex had a problem with it, looks like I was wrong.
Landon Reed
Holy fuck american education
I did all that when I was 3
Kayden Clark
Why hasn't all the amerifat shitposters learned this by now? Obnoxious fags thinking everybody knows the initials of their universities.
Levi Reed
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?
James Gray
Stewart's, 7th edition
Jose Reed
Not user, but same here.
It's a shit book tho.
Michael Robinson
Why do you day that
Gabriel Rivera
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.
Nicholas Baker
stupidly enough there are two U of I's in Illinois. One in Champaign and one in Chicago unaffiliated.
Mason Collins
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.
Liam Cruz
>campus is liberal so it's shit
I bet you're voting for trump too
Samuel Robinson
Well man, profit then. Go get your A+ champ.
Sebastian Bennett
It's hard for brainlets like who spent their whole life learning math as a series of steps to memorize and follow.
Lucas Watson
>good uni >UT Pick one faggot.
Connor Richardson
University of Toronto is a more relevant school than some faggot UofT school in Austin.
Aaron Collins
Good one guys, gave me a hearty chuckle
Michael Smith
Texas is shit, your school is shit, you're shit. Deal w/ it.
Julian Jackson
We're higher up than toronto in terms of engineering :^)
Jason Jones
>being proud of being better at sucking dicks
Henry Garcia
>has to resort to stale memes to save face Pathetic tbqh
Easton White
It's not even true. Toronto is ranked 3 points higher in EE/CE (aka the only respectable discipline of engineering) :^)
Logan Foster
You're really grasping at straws now, aren't you?
Eli Richardson
Don't tell me you actually majored in something completely pleb like Chemical or Mech. You're not this pathetic, are you?
Matthew Nelson
>if I start flinging meaningless insults, it'll look like I have a point!
Cameron Harris
Chemical engineer confirmed
Enjoy your thermodynamics and process piping, KEK
Logan Roberts
This is just getting sad now, famalam.
Elijah Smith
enjoy staring at pipe flanges all day, autocad monkey
Landon Brooks
>a meme class
go stick your memes up your ass
Isaiah King
I did this when I was a fetus in my mothers womb.
American education everyone.
Caleb Kelly
Unreal Tournament?
Jose Lee
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.
Ethan Fisher
What are you,American? I did this before my great grandfather was conceived.
Thomas Russell
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
Jaxon Robinson
Third worlder detected
I did this 14 billion years ago, and my wave of understanding was such that it spawned a universe
Robert Flores
Kek
Gavin Russell
Once you "get" calculus, the rest is just extensions.
It only gets hard again when you have to do weird integrations
Gavin Allen
On a scale of one to assblasted, how mad are you that Cal killed your possible natty run?
Robert Edwards
I'm pretty salty, but we were overrated af after Norte Dame.
Jayden Turner
A typical "smart" person doesn't start to struggle until line/surface integrals (which is the latter half of Calc 3).
Jack Turner
>wow I did good in my first cal 2 test I'm a math god
Adam Brown
>The only relevant UT obviously. University of Turin?