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File 163970052862.png - (27.85KB , 700x580 , 5afa4ffd353ce5f76f73155f2d41c72f.png )
2536 No. 2536 [Edit]
People have been doing calculus for hundreds of years, and yet there is still no place where you can easily find any kind of calculus problem, in any form, and how to solve it. Why?

This applies to pretty much any stem field except maaaaybe computer science. Finding problems is already hard enough because there's no simple, standard way of typing math notation, and which search engines would be able to understand. When you try searching for most problems, you often only get general tutorials as results. It's maddening.

Windows can be used to type Chinese, which has thousands of characters, yet there is no built-in math notation support.

Students have basically no choice but to pay for services which provide solutions to problems their customers post. And they find problems on those services(assuming they've been posted) by copying the part of the problem statement without any special notation. God help anybody trying to self-learn.

Why are we still stuck in the 90s when it comes to this stuff? How does nobody else have an issue with this state of affairs?

Post edited on 16th Dec 2021, 4:43pm
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>> No. 2537 [Edit]
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2537
>Why are we still stuck in the 90s when it comes to this stuff?
Luckily, there's a (16?)90s solution: get a book. These days, you can even get books filled with nothing but calculus problems if just a textbook isn't cutting it.

It's not clear to me what you're really upset about. Not being able to Google the solutions to your calculus homework?

>Students have basically no choice but to pay for services which provide solutions to problems their customers post.
People have been learning math for many years before these services were available. Arguably, people were even better at learning math back then. (Maybe these could be called disservices).

If you really need a tech solution that will solve any of your problems, you could always get a wolfram pro subscription---it's at least better than giving money to a site solely dedicated to helping students cheat. (There are reasons to avoid Wolfram's products, but there's no denying their convenience). The step-by-step solutions were good when I used them a bit eight years ago, and I imagine they've gotten better since.
>> No. 2538 [Edit]
>>2537
>Luckily, there's a (16?)90s solution: get a book.
People then and now rely on the help of teachers. For people without teachers, their next best option is begging for help on forums. I don't want to rely on either. Teachers should not be necessary.

>Not being able to Google the solutions to your calculus homework?
Wrong. There's a difference between copying answers and seeing a problem with the same format as one you can't figure out, and learning from it. If you can't solve a problem, you can't solve it. There's no benefit to making math a pay-walled secret.

Post edited on 16th Dec 2021, 7:42pm
>> No. 2539 [Edit]
>>2536
Just use libgen, friend.

>>2537
Grossly off-topic, but I will once again state my disappointment with Miki's route--or lack thereof.
>> No. 2540 [Edit]
No disrespect here OP, but have you considered making it yourself?
>> No. 2541 [Edit]
>>2536
> there is still no place where you can easily find any kind of calculus problem, in any form, and how to solve it. Why?
Er, aren't those called textbooks? Especially the soviet-era ones as >>2537 mentioned (not 1690s though, that's a bit too far back). Get the teacher's edition/solution manual if you want step by step solutions as well. I have a lot of rants about higher-math education, but a lack of calculus problems isn't really one of them in my opinion.

And besides, since you mention not being able to search via math notation it seems like you're referring to specific instances of derivative/integral problems? For lower-division calculus there are only a finite set of tricks that you learn: u-substitution, trig substitution, integration by parts, etc. Maybe once in a while there's a wildcard that requires a bit of thought, but even then unless you're dealing with obscure dilogarithms or hypergeometrics it's basically algorithmic enough that Wolfram has made a nice side-business providing step-by-step solutions to these as >>2537 mentioned.


>Students have basically no choice but to pay for services which provide solutions to problems their customers post
If your beef that there's no solution to the particular question in front of you, then isn't that basically working as intended since you are supposed to solve the problem, not just look up answers. Besides, there are only so many ways you can formulate calculus problems, you can easily find similar problems and just apply the same technique.

>>2538
>their next best option is begging for help on forums.
You can go through past MIT exam papers and solutions? Basically every university has past exams released online, that should be plenty of material.

Also you mention that you're self-learning, so in that case why be so focused on learning how to solve every type of integral? No one bothers with closed form solutions to anything but the most trivial ones anyway (unless your'e a soviet era scientist in a nuclear bunker without computers, in which case that thick soviet book of obscure tricks is just the thing for you). Focus on concepts and applications.
>> No. 2542 [Edit]
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2542
>>2541
>For lower-division calculus
I'm talking about shit like this.

If I NEED to know how to solve something like problem 8, and I don't know how to do it because z is on the right side of the second sphere's equation, finding an example of a problem just like that is basically impossible.

Looking at random textbooks will not help me in this situation. My ONLY option is asking a teacher, asking on a forum, paying for a step-by-step answer.

Maybe wolfram is the solution. Would it help me here?

Post edited on 16th Dec 2021, 11:48pm
>> No. 2544 [Edit]
>>2542
>and I don't know how to do it because z is on the right side of the second sphere's equation
Rewrite it to standard form? Then just integrate via spherical coordinates which should be part of any standard multivar calc textbook (find the points of interection, and use those to construct the triple integral. May have to split into two or more depending on how the intersecting region looks like.)

[Edit: You actually don't even need to rewrite it to canonical form since you only really care about the intersection points for the computation, and it's trivial to convert to spherical coordinates in the existing form. The rewriting is more so that you can get an image of what the intersecting region looks like.]

>Looking at random textbooks will not help me in this situation. My ONLY option is asking a teacher, asking on a forum, paying for a step-by-step answer.
In that case I really suggest you look at those "random" textbooks. I remember doing problems like these, so they must surely be in there. Same for the other two which are basically textbook applications of jacobian and line integrals.

I don't mean to come off as dismissive, but it seems like you're expecting textbooks to teach you how to apply the concepts in every possible permutation, which is basically impossible. You learn a basic set of concepts (in your problem, spherical coordinates and computing volume in that coordinate system) and then apply that to something you should have seen in calculus 1, which is taking a region of intersection and expressing it as sums of smaller integrals. The only difficulty here (which I'm not trivializing since I'm personally terrible at 3D visualization, I often just blindly "trust" that the numbers work out) is that you're working in a higher dimension so breaking up regions into smaller subregions and getting the limits of integration right might be tricky. But this is a well-known issue, so there are tons of practice problems online on how to set up these integrals for all sorts of whacky regions.

Post edited on 17th Dec 2021, 1:21am
>> No. 2545 [Edit]
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2545
>>2544
>Also you mention that you're self-learning
No, I'm a student. Today was the final exam of my class and I know for sure I didn't pass the class, a lot of that was due to my lack of motivation, but nonetheless I'm not in a great mood.

>there are tons of practice problems online
Assignments are problems chosen for the student. A student has to solve those specific problems. Homework is supposed to be the practice. You're suggesting practicing for the practice.

If some little thing trips you up, and you don't know how to proceed, there's no way around it. You need to know how somebody else handles the specific thing you don't know how to. I can't believe you've never had an experience like that. Even if the solution lies somewhere in the things covered previously, people forget, they don't have perfect recall of things they don't use anywhere outside of math class.

Post edited on 17th Dec 2021, 1:48am
>> No. 2546 [Edit]
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2546
>>2545
>No, I'm a student.
Then what did you mean with all your complaints like
>God help anybody trying to self-learn.
>Teachers should not be necessary.
>My ONLY option is asking a teacher, asking on a forum, paying for a step-by-step answer.
If you've got an instructor, may as well take advantage of that. That's what they're there for.

>Assignments are problems chosen for the student. A student has to solve those specific problems. Homework is supposed to be the practice. You're suggesting practicing for the practice.
If you can't do the homework straight away, then you should study until you can. So, yes, you should "practice for the practice". But your assertion that "homework is supposed to be the practice" is not really true. Don't think of the homework as practice, think of it as a description of expectations. That is, as though the instructor is saying "you need to understand the material well enough to be able to do these problems", rather than "after doing these problems, you will understand the material well enough". (How exactly the instructor views the role of homework depends on their individual teaching philosophy, but nobody who has taught before would mean the latter). You're in for a rude awakening if you can always succeed by doing exactly what is assigned in a course and refusing to look at anything else. The fact of the matter is: math is hard, and you will need to work hard to master it. There's really no avoiding that.
>> No. 2547 [Edit]
>>2546
>Then what did you mean with all your complaints
Teachers have their own schedule. You have to wait for them to be available, wait for them be free from helping other students and wait for them to respond to your emails.

Then, you have to hope they'll be willing to help you in a meaningful way, which isn't a given. I want immediate, 24/7 help.

>but nobody who has taught before would mean the latter
How about every single grade school teacher?
>> No. 2548 [Edit]
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2548
>>2547
Anyway, I know it's annoying when somebody complains like this and I probably come across as a lazy person. I've posted about my problems before and how I'm changing majors.

I'm considering going back on my own to the beginning and reading Lang's Basic Mathematics, a linear algebra book, and then trying calculus again.
>> No. 2549 [Edit]
> Students have basically no choice but to pay for services
There's your answer.
>> No. 2550 [Edit]
>>2549
Only the middling or failing ones pay for these services. After all, they're exchanging money for shortcuts.
>> No. 2551 [Edit]
>>2550
That's a false statement if I've ever seen one. Not every student who gets good grades acts like a zen buddhist monk.

Post edited on 17th Dec 2021, 1:24pm
>> No. 2552 [Edit]
>>2551
Universally? Perhaps. But in my experience, it's very true.
>> No. 2553 [Edit]
>>2552
Why are you saging and being cagey? It comes across as elitist. Am I not right about k-12 teachers presenting homework as THE practice?

I guess you could argue they don't really teach.
>> No. 2554 [Edit]
>>2547
Math in grade school is very different from university level math/ In the latter, homework (which is never actually called homework, it's almost always called "problem sets") is where you actually do the learning. And unlike grade school where collaboration is frowned upon, professors will usually explicitly allow collaboartion/discussion when solving these psets, because that is where the learning happens. And that is indeed the ultimate reality: like it or not, I'd bet almost every engineering/math major everywhere has done the bulk of their learning on their own. What professors teach in class is more of an outline: they introduce the topics, introduce the basic concepts, and then expect you to to put in the effort to dive deeper in order to internalize these.
>> No. 2556 [Edit]
>>2553
>Why are you saging and being cagey? It comes across as elitist.
One sages when his post isn't pertinent to a thread's topic, or his post is unsubstantiated. It has nothing to do with being cagey, nor should you infer it as elitist behavior.

>I guess you could argue they don't really teach.
They don't teach well, because if they did, homework wouldn't be assigned. Instead, it would be optional. I agree on this point. My original posts pertained to those paid services and their userbase.
>> No. 2557 [Edit]
>>2556
Unrelated but it's disappointing that people (read: the current crop of users from 4chan) have forgotten sage etiquette and treat a sage as some sort of mark of disapproval.
>> No. 2728 [Edit]
>>2557
Whether properly or not, most of those users don't use sage. Some even improperly state it's not enabled on 4chan, and that was years ago. I'm sure it's gotten worse.
>> No. 2729 [Edit]
>>2728
>Some even improperly state it's not enabled on 4chan, and that was years ago. I'm sure it's gotten worse.
I guess that only means no one ever read the rules. I checked again and to my surprise it even mentions the proper intended usage (I don't know if that addendum was always there)
>What is "sage"? Entering "sage" (by itself) into the [Options] field while replying will cause the thread not to bump to the top of the page. Contrary to popular belief, a sage is not a downvote, and should not be used as one. "sage-bombing" or announcing that you've saged a thread may result in a ban.

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