Calc 2

It's been awhile since I've taken calc II, but for me the class was more of a test in pattern recognition than pure math skills. I felt like after I had done enough homework problems to recognize the patterns in the problems, I naturally remembered how to do the math anyway.

how about calc 3?

Ayy math major here. I'm going to be tutoring an engineer friend of mine calculus 2. What can I expect? Calc has always clicked for me so it is hard to understand why other people simply can't do it.

We are supposed to start on integration by parts and I made some notes I plan to use with him. I wrote a summary of the theory, including a proof of the integration by parts theorem, and I plan to show it to him and teach him the philosophy he should have in mind when applying it.

Then I made 6 categories of integrals, each with 3 problems. The categories are: Logarithm, exponential, trigonometric, hyperbolic, rational functions and interesting problems. The first 5 just mean the problems will use those kinds of functions. The last one is for interesting that have unexpected and non-trivial solutions. Also in the first 5 categories the 3 problems go up in difficulty like this: The first is a trivial routine problem to test if he knows how to use the theorem, the second is a more tedious/longer problem but still trivial to test his symbol manipulation skills, and the third is a problem that really makes you think and requires you to have an idea before you can do anything.

I have picked really good problems for him to notice the structure of the integration by parts technique. But hoping that many brainlets will congregate here I have to ask you to please reveal me how the mind of a brainlet works. What makes it hard for you to learn Calc 2? I need to get at the root of it.

Adopting a fixed mindset about your friend's abilities and potentially calling him a brainlet is a bad idea. Growth mindsets in tutors and teachers lead to growth mindsets in students.

You seem to really care about your tutoring so this should be a minor adjustment to not being an asshole mentally while working with him

I am not going to call him a brainlet or insult him in any way. He is my actual friend. I am just throwing some Veeky Forums banter here. Come on man. What are you, the respect police?

And I do care about my tutoring, I am just worried because I wrote my notes with the mentality of a "smart" person, which means that I understand it, but someone who is differently gifted may not. I just want to hear from past-brainlets who couldn't do Calc 2 but then fought through it and learned. How did they do it? I need to know.

Also, there is no shame in admitting you are a brainlet if you are one. That is how you were born. You should not think of it as an insult but as a descriptive term. It describes the differently gifted.

Math major here, I hope you neck yourself. You sound like an arrogant piece of shit, why in the fuck do you want to show him the (rigorous)proof of integration by parts? He will learn more for a class like CALC II by doing problems.

>You sound like an arrogant piece of shit
I am just having fun.

>why in the fuck do you want to show him the (rigorous)proof of integration by parts?

My idea to start from scratch and really make him understand why the technique works and why it is useful. I plan to focus on problems but as a quick introduction, I think I can get his attention by showing it to him. I mean, when I saw the proof way back then it impressed me, even though it is really simple and trivial. It is also pretty short, literally [math] duv = udv + vdu \implies uv = \int udv + \int vdu [/math] so it is a pretty short and interesting introduction before we start just going through the problems.

To be fair, you have to have a very high IQ to understand the product rule. The proof is extremely subtle, and without a solid grasp of real analysis most of the lemmas will go over a typical student's head. There's also Newton's ontological outlook, which is deftly woven into his writings - his personal philosophy draws heavily from Socrate's Meno Dialogue, for instance. The mathematicians understand this stuff; they have the intellectual capacity to truly appreciate the depths of these insights, to realize that they're not just clever- they say something deep about LIFE. As a consequence people who don't ace Calc I truly ARE idiots- of course they wouldn't appreciate, for instance, the profundity in Leibniz's existencial musing "Only geometry can hand us the thread which will lead us through the labyrinth of the continuum’s composition, the maximum and the minimum, the infinitesimal and the infinite; and no one will arrive at a truly solid metaphysic except he who has passed through this labyrinth," which itself is a cryptic reference to Descarte's seminal Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences. I'm smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as Gottfried Wilhelm's genius unfolds itself on their textbook pages. What fools... how I pity them. And yes by the way, I DO have an eπi=−1eπi=−1 tattoo. And no, you cannot see it. It's for the ladies' eyes only- And even they have to demonstrate that they're within 5 IQ points of my own (preferably lower) beforehand.

Calculus 2 isn't hard except for the billions of difference convergence tests. Damn feels like a fucking art instead of a science. Everything else is beautiful and has aesthetic value.

The calculus usually isn't that hard for most people to grasp when it is taught right. i.e., the principles of functions, continuity, limits, differentiability, the meanings of derivatives and integration, the fundamental theorem of calculus, and how all of that leads to various applications. Teaching how to derive important stuff in calculus and getting people comfortable with the problem-solving mindset also helps with this.

The hardest parts are usually algebra tricks (since Amerilard algebra education sucks now), calculus "tricks" (i.e., dealing with cases that test for misconceptions of chain rule (composition of functions) or the FTOC (derivative of a definite integral), and being able to solve calculus problems quickly by drilling problems over and over. And if you're referring to calculus 2... well the best you can help with convergence tests (the hardest and most annoying part since it is more heuristics than reason) is to choose good practice problems.

Assume nothing about his prior knowledge. Teach it as if you're teaching a 5 year old. Highlight every important piece of logic. Reiterate important points. Clearly explain your rationale.

I finished it with an A and I barely did any homework. Laplace has got me nuttin in calc 3 though.

Do not, I repeat, DO NOT PROVE ANYTHING. AND I MEAN ANYTHING with an engineering student. He's not a math major. He's an engineering student. Show him how to work the equations. Give him the tools. That's it. Spending 20 minutes proving a derivative or an integral rule is just going to.confuse him.

t. Engineering student whose cal 1 professor decided to introduce the concept of the derivative by teaching how to write proofs with Delta and epsilon

10/10 copypasta havent seen it before

No dude you don't understand, I won't spend 20 minutes. It will maybe take a minute, I will just show him [math] duv = udv + vdu \implies uv = \int udv + \int vdu [/math].

My bigger plan is to use this as a starting point for a quick exposition of the way he should think about the theorem. I plan to tell him something along the lines of this:

You should not think of this as a formula but as a relationship between integrals. What this theorem is saying is that if you know what [math] \int udv [/math] is then immediately you also know what [math] \int vdu [/math] is. So if you have an integral of the form [math] \int udv [/math] which seems too hard you can instead study the integral [math] \int vdu [/math] to see if it is easier and if it is then you solve that and then use the theorem to find the answer to your original problem.

What do you think of that perspective? Do you think it will click? I feel like integration by parts is always presented as a formula to be "applied". I instead think of it as an identity all pairs of functions obey and as a tool to obtain an integral by studying another, perhaps simpler, integral.

What does calc 2 include. Integration by parts?
For none amerilards.

integral calculus with series and sequences

If the guys not an idiot , he will eventually understand the relationship of udv and vdu. IMO engineer students learn best by just doing a lot of problems with supervision of an instructor. Show him how to solve integral of x*e^x , then more complicated problems like with trig and natural logs. But keep the explanations to a minimum. He's not stupid. Hell make the connections eventually. The most important thing is to get him working problems.

If you explain and he doesn't understand at first he might feel stupid and discouraged. Get him working a bunch of easy problems , I know you wanna explain the concepts but really it will only make it harder for him.

People struggle with that? I consider myself a brainlet and I learned that shit in a week or two just using a textbook.

I have to admit that you make sense. I guess it would be risky to make him think he is too dumb to understand by showing him the theory. I'll think about it. But I am very confident in the problem set I have personally curated which includes a couple of the trivial ones to get him started like x e^x and it goes up to even a couple of really interesting integrals that will really make him think.

Extremely boring and therefore difficult to sit through, difficult to do the homework, difficult to study.

One of the dumbest people I've ever encountered in my entire life got an A in Calc 2 when I was there. As with all of academia it requires zero intelligence to excel in, but rather a sheep-like obedience that retards call "work ethic."

>"heh, yeah, that's why I flunked Cal 2... Cause I'm not a sheep"

what the other user is trying to get at is that the material taught in calc 2 is not at all conceptually difficult, since it is usually taught to european brainlet students before even going to university, hinting at the fact that people struggling on said subjects are literally worse than said brainlets.

People struggling in calc 2 don't put the work in, it has nothing to do with intelligence.

Okay even if we assume all Europeans are doing integration by parts at 12th grade, so what? In the US, that's not the case and cal 2 has a high dropout rate. This is such an autistic thing to nitpick and the only reason to do so is to humble brag you learned calculus earlier than someone else. Congrats. I mean sure your colleges have worse accreditation but I'm sure that's irrelevant. :^)

Both of these things can be true. Europeans can all be enlightened by their own intelligence while in the US, cal 2 is the first barrier for entry since you can't skate by barely paying attention or studying 30 mins before the exams to get a B. Which is all my post fucking said.

But no we all have to get lectured on the american fucking education system because every European is required by law to harp on America every waking moment of their life, so it seems

>College kids always complain about calc 2
Whatever you say, Grandpa.

>Math is an art instead of a science
Surprise.

...

if this was OC, props dude

i promise you didn't teach yourself the entire calc II course in two weeks with a textbook

Sure you can "learn" all of it, but you won't have very well developed skills.

No shit, everyone I ever met who took Calc 3 said it was EASIER than Calc 2.

I took Calc 2 twice because I fucked iff the first time.

Honestly, Calc 2 is hard because the professors make it hard. The second time around the professor FUCKED the class multiple times, my favorite being after the first test of the semester that he admitted it was too strenuous of a test by the standards of his peers. By the end of the class, he noted that instead of ONE bell curve of grades, there were TWO. He constantly would say "this test should be easier" when the test averages kept going down. Of the 50 students to begin the class, MAYBE ten passed.

The last three tests of five for the semester, I got almost every question "right" but because I didn't go into the detail that he wanted, he marked me down, even though other students got full marks for THE SAME chain of reasoning. I failed the class by three points. Kids that I thought for SURE were going to pass the class did not.

Honest advice to anyone who worries about Calc 2 or who struggled a bit with Calc 1, take some time off and learn it ON YOUR OWN before you take the class; the same for Organic Chemistry. Both are not impossible classes to pass, but how the classes are rushed with so many students in one sitting, you're better off being exposed to and mastering the main ideas before paying to be rushed to understand them.

If he did, I want to see his textbook. If it's a James Stewart Calc book I'm calling bullshit.

>Both are not impossible classes to pass, but how the classes are rushed with so many students in one sitting
Yeah university is pretty ridiculous about rushing through content, especially when most of the students don't even need to know the information. I've always learned faster and more productively on the spot, when I knew what I needed to know and how to go about doing it, rather than being told I have to memorize information in a vacuum from an 800 page text book in 4 months.

Same. I'm a ChemE student, and I LOVE chemistry. Going from community college to the University was a punch in the gut though. I'm not kidding, but somehow in all my chemistry and math classes, the kids who have sat next to me have done better in the classes than me, even though I was FAR more knowledgeable than they were on the subject. They would ask me questions on the concepts, be totally lost and I would shake my head, but they would get the A/B and I would get the C. I honestly believe it's the fact that there are so many kids in the University classes and the content is so rushed that it fucks me up.

It's more frustrating when I've worked in the "real" world/industry before going to the University, and know most of these classes are BS considering all the engineering charts, manuals and data is already written.

I think the main reason most engineering grads don't STAY in engineering jobs for 20+ years is because they have an idea of what they'll be doing going into the field, only to find out once they graduate they need a PhD in engineering to do what they initially thought they were going to do. Anyway, there's my rant for what it's worth.

Sounds like you're a lazy student. Most universities design tests to benefit the "hard-worker," and by that I mean that you usually can't do well on a test unless you've seen the problem before and recognize because, I.e., not enough time is given on tests to produce original solutions

None of this shit adds up. You don't know the material as well as you think you do. I know exactly the kind of person who does this and they're not pleasant to be around. Go somewhere else to rant about your narcissist problems.

That's cute. Too bad none of the problems on the test were never seen before. And yes, ample time was given from the third to fifth tests.

>doesn't add up

One of the chica who was a 20 year old single mom constantly contacted me to study with me. I always helped her because I help people, yet she would say she got an exam score that was higher than my own. I took her word for it because she passed the class, even though she was always lost. She even saud she Christmas tree'd a test and still scored higher than me.

But hey man, blow me. I've moved on. I still study chemistry and do well for myself. I'm unpleasant to be around? You sound like one of the greek cunts that wouldn't have made it through a lab if I didn't carry you through.

>wouldn't make it in a lab
Yeah, I'm sure the person who takes no self-responsibility and lives in a delusional bubble where he magically knows chemistry is going to perform better in the lab. I'm sure of it.

Learn some social skills (because those people were fucking with you because you're clearly a dumbass) and learn to take personal responsibility for your grades.

That's it user! Eureka! Social skills lol. Nevermind that I tested to make sure I wasn't being fucked with. And I still know chemistry.

Tell me, no bullshit, specifically how much effort did you put into passing Calc 2? Did you pass it the first time?

Let me put it to you this way. If somebody did better than you on a test by christmas tree-ing, then you have NEGATIVE knowledge of chemistry. In fact, they effectively discarded your advice to try a strategy of randomly guessing answers, which made them do better than they otherwise would have. You don't know fucking anything. Get that through your skull so you don't fuck up when money and lives are on the line.

And yes, I took AP Calculus BC in high school and I aced the class. Convergence tests are tricky but the rest is elegant and beautiful, minus some of the more rote tasks like parametrics and polar coordinates. God you are a moron.

>because luck doesn't exist

Okay bud. I don't know chemistry. The shit I've made counts for nothing. The fact that I didn't program a raspberry pi to titrate a sample from my backyard pool to monitor chemical levels is bullshit right? Nevermind that I've made and played aroud with chemicals that are frowned upon, much less write my own "reports" on them that would raise eyebrows at my university. Nevermind I've made alcohol that I can drink while Greek fags like you pay for it.

>took AP calc BC in high school

Well aren't you a genius! That pat on the back must be so comforting! I wonder why I haven't heard of such an amazing individual doing anything great in the news lately for muh mankind lol. Congrats on going to a school that lacked common core.

>The fact that I didn't program a raspberry pi to titrate a sample from my backyard pool to monitor chemical levels is bullshit right?
Maybe you should be a programmer instead of a chemist, because if you can't perform simple titration calculations on an exam, then you sure as hell aren't going to be able to calibrate pH titrations in the field.

>much less write my own "reports" on them that would raise eyebrows at my university.
They raise eyebrows because people wonder if you're going to inadvertently kill yourself from your ignorance one day.

>Nevermind I've made alcohol that I can drink while Greek fags like you pay for it.
You can distill alcohol without knowing an inkling of chemistry. What, are all of the Appalachian hillbillies master chemists or something?

You're a fucking idiot who doesn't know how to admit when he knows nothing. Throw your delusions of understanding in the trash before you end up hurting somebody because of it.

Well aren't you a genius! That pat on the back must be so comforting! I wonder why I haven't heard of such an amazing individual doing anything great in the news lately for muh mankind lol. Congrats on going to a school that lacked common core.
Who even said that AP Calculus BC in high school is a big deal? It was a class of 30 people and most of us aced the exam.

Listen dude, I get that your trying to trigger me, but I'd be more than willing to stomp your maggot ass. You Eurocucks on Veeky Forums are just that. I wonder, what have YOU made. WHO are you? I've had setbacks, but again, WHO are you, and what have YOU done for muh humanity?

I don't know of any Europeans who take AP classes lol. You're beyond helpless.

And you're a beta faggot that never saw poon beyond the crack of your ass. See ya femboi

>getting a C in general chemistry
>writing pseudo-reports on controlled/ hazardous substances
>thinking titrations and distilling alcohol means you know chemistry

You're not fucking Walter White. That said, ChemEs need only a minimal understanding of chemistry itself; they are more concerned with macroscale effects like mass transfer. Having skill in programming and hands-on stuff like you seem to is way more useful than knowing the details of every reaction.

Get good at programming, learn multiple languages for multiple applications.

t. 3rd year ChemE student

It's not cute that you claim to know the material well but do poorly. C =/= average - it's dumb. I agree with other user - I know your type. You pretend to be super smart, but aren't. I'm sure you correct the teacher, too

>trig subs, integration by parts, improper integrals, partial fractions, calculus of parametric eqns & polar coords(arc length and surface area), series & sequences: AST, radius of convergence, ratio & root tests, power series, taylor series, binomial series.
It's definitely 'harder' than calc I and calc III, but it's not bad at all if you do homework and pay attention to the lectures.

I always wondered what Americans were complaining about with "Calc 1" and stuff. I thought shit, do they all have to take some super advanced math in uni ?

Turns out you guys do in uni what we do in highschool, ayyy lmao.

You guys should study that shit sooner, srsly.

waaaah waaah

You're a dumbass. In American highschools they teach differential and integral calculus if you want.
And I know for a fact studying calculus in European highschools is about as common as it is in America. And less common elsewhere.

That's the pissing in the pool longterm strategy to scare away potential competitors

Disregard

do they teach you theory in these "calc" courses ? like, are you supposed to be able to rigorously prove the fundamental theorem of calculus after completing "calc I" ?

>some countries
America does. Calc BC covers more advanced integration techniques, polar shit, sequences and series, etcetera. It's the EZPZ version but you can take it when you're 15 if you just skip precalculus.

>engineering students end up with even harder classes down the line
I'm seriously surprised no physics or methhead have made some faggy joke about engie students considering most think engie students only take 1 calc.

>why do people find it so hard?
I don't know. Shit is pretty easy.

>Because it has no real world use that a computer isn't better at handling.
Just because "subject x" has no real world use doesn't automatically mean it will be hard or easy.

Also, just because a computer can do the math really quickly and easily doesn't mean that the ideas behind the math should be tossed to the side.

Not at all. They just throw a bunch of formulas at you and then test your memory later. Subject comprehension certainly helps but it not required or expected.

Short answer: no.
I remember being absolutely frustrated in all of my calc courses because we were expected to just memorize the formulas and techniques. One of the reasons I loved Real Analysis is that we actually derived and explained most of that stuff.

In terms of difficulty for me, Calc 2 was the hardest, followed by Calc 1 and then Calc 3 being the easiest.

>Do not, I repeat, DO NOT PROVE ANYTHING. AND I MEAN ANYTHING with an engineering student. He's not a math major. He's an engineering student. Show him how to work the equations. Give him the tools. That's it. Spending 20 minutes proving a derivative or an integral rule is just going to.confuse him.
Nigga I'm a computer science major and even I refuse to believe math if I can't see and grasp the proof.

calc 1, 2 and 3 are literally all memorization, though, especially 2.

are you telling me that integration techniques, convergence tests, series representations, parametrics, and area problem methods aren't memorization?

Yeah fuck those with a sheeplike obedience to objective reality and reasoning skills

Memorization isn't the hard part of convergence tests and integration techniques, it's pulling the right "tricks" at the right times.

when people say they are bad at Calculus, what they mean is they are bad at Trig and Algebra. Calc is one new concept wrapped up in a bunch of high speed algebra and trig techniques. more importantly, the teacher is going to expect you to know all that shit like the back of your hand and is going to skip obvious algebraic operations and generally zoom through proofs.

basically, shitters half ass the entirety of their mathematical education and get BTFO by calc because its the first course that expects you to recall previous courses material.

It's a lot of work. Memes aside. Especially for people who aren't mathematically inclined. There's a lot of material, and most people got through calc 1 without actually learning it.

Typically it's the first class that students encounter where they actually need to study to not fail. And it's the crossroad of a lot of different disciplines so you get a variety of students. Many of whom are weak in or outrightly intimidated by mathematics.

>sheep-like obedience that retards call "work ethic."
haha yeah unlike those other "productive members of society" or whatever, i'm useless and can't pass a calc 2 class
i am enlightened by my intelligence

so where do you learn the theory of differentation and integration ? I thought that the "real analysis" was supposed to be more like a measure theory course. I'm eurofag, everything's different here.

If I had a formula sheet for tests and quizzes, I would have gotten an A in calc II easy. I suck at memorization, like bad. I try to write trig formulas over and over and over and over and over, to no avail. As soon as I got the test, I freak out and completely forgot what csc x would equal, etc. More than half of calc II is you remember what your trig shit is so you can properly substitute and manipulate the integral to make it easier to solve. However, sequences and series was the part where you had to understand and actually think outside the box. sequences and series still haunts me today.

I challenge anyone here to name all the chapters of Calc 1 2 or 3 as they can.. let alone how to solve the problems

Human random access memory last about 2 weeks nevermore

Math is golf for nerds, tinkering and mental wanking with numbers approaching infinity. I think all of math is a shirt test.. it explains why Stacies and chads fail

i just switched my major to engineering and im way behind my math, currently taking precalc and all these replies are making me nervous when i take all my calculus but one thing is for sure the more i study the most easily i understand the concepts

>You should not think of this as a formula but as a relationship between integrals.
so, a formula

what were your grades for precalc - calc 3, Veeky Forums?

precalc: B
calc 1: D the first time, B the second time
calc 2: C, if I did literally one more homework assignment, I would have gotten a B, im so fucking upset about this still
calc 3: A

Precalc: C-
Calc 1: B-
Calc 2: A
Calc 3: A

Fucking this, had to take Calc III for CE

The real shit part is the vast majority of formulas used only require algebra

Precalc- A
Trig - A
Calc 1- A (took in HS, didn't take AP exam, took the course again at Uni)
Calc II - C
Calc III - C

The amount of time I devoted studying Calc II and III and consistently being unable to score higher than a C or low B on exams humbled the crap out of me.
It also drained all confidence I had during those semesters

Skipped precalc, calc I-III were A, A-, B-. Fucked up with calc III because I realized too late that taking 4 math courses in a single semester (including 2 pure math) is the worst mistake one could ever make.

>where do you learn the theory of differentation and integration
Real Analysis I, mostly. Depending on your curriculum, some part of it is covered in Real Analysis II.
>I thought that the "real analysis" was supposed to be more like a measure theory course
It honestly depends on a professor and the department. For example, the prof I took RA II from quickly went through the basics and then most of the semester was devoted to measure theory and Lebesgue integration. Also a bit of linear algebra.

That's still "Calculus 1" in my country (called "Mathematical analysis 1").
Now I'm taking Analysis 2, which is function with more than 2 variables, double and triple integrals and so on. What's is that called?
Calculus 3?

matfyz?

impressive

I had to take ODE and linear algebra with proofs. Idk where you think engineers can get proofs.

t Engineering student minoring in math

What is calc II? t: europoor

Integrals, sequences and series. How do you call it?

In Poland we have real analysis course, where two first semesters cover sequences, limits, real series, convergence tests, derivatives, continuous, convex, concave real functions of one variable, integrals, series and sequences of functions, pointwise and uniform convergence of these, Taylor series