/sci/ - Science & Math

>>11074538
Even if you don't ever want to evaluate one, you'd want to gain some understanding of how a differential equation (the base of most models) functions and produce the observable results it does

>>11074538
All universities understand that. Apart from some neat tricks to solve very specific integrands that rarely model adequately enough the actual reality, no university spends time teaching how to solve hard integrals. Derivatives are easy enough and you need an understanding of how it transforms functional space to get intuition on what you're doing when you're applying one. Engineering/real world problems rely on numerical solutions to all of these problems since it's easier and there exists a much better theory that covers a lot more cases on finding adequate enough solutions compared to analytically solving all of them. If you have no analytical understanding of what you're supposed to expect you'll never be able to troubleshoot or spot something that's off.

tldr: If anyone ever needed one of Cleo's integrals they would find a numerical solution.

>>11074591
>>11074557
I did A levels 9 years ago, since forgotten most of integration and recently I've been working on my own "engineering" startup. Up until now I've just been plugging and chugging any integrals that come up but it's basic shit like (5+(3cos(x))^3)tan(x) dx so I felt guilty and got a Schaums outlines book to do them by hand and while mildly fun it took up my entire day and I got no CAD done. So now I'm thinking of going back to Wolfram but that leaves me dissilusioned wondering why I bothered spending 2 years learning integration if I am just going to use a computer now that I finally have a reason to do it.

>>11074591
>tfw your third world uni focuses on making you derivate and integrate by hand a bunch of stuff rather than making you learn the shit behind it
I hate it. I passed differential calculus without even knowing what differentiation was truly about.

so guys should I relearn integration or just keep using wolfram? is there any alternative to wolfram that is free/cheap? Wolfram locks a lot of features unless you pay and I hate web apps anyway.

>>11074538

>>11074670
I personally don't bother integrating by hand anything that requires a trigonometric identity or worse. I think that's already fairly high level for the real world of numerics.

>>11074666
>I passed differential calculus without even knowing what differentiation was truly about.
literally everyone in my class. I still don't have a rigorous understanding of it just that derivatives are a rate of change and integrals are a sum but the rest of my class never even bothered learning that. I don't blame them though, all that mattered was passing the tests for which such knowledge was unimportant except for the few questions on water flowing out of a bathtub or whatever.

>>11074676
don't hate the player, hate the game.

>>11074670

I agree with:
>>11074683

I dont know about what you're job is like: I am a physics grad student who has been doing it for a while. If I am doing analytic work, and the integrals are simple (polynomials, dirac-deltas), I do it by hand, otherwise I use either wolfram or python depending if I need a symbolic solution.

Imo if you are paying for wolfram, you are a sucker, but thats my ego

>>11074709
OP here I don't pay for wolfram.

>>11074670
Learn mathematica and download a cracked version. It's the backend of wolframalpha and basically wolframalpha on steroids. I'm a math bachelor and when I need integrals(I rarely do, most of the stuff I do are optimizations so I mainly use differentials) if I can't do them on my head I plug them in a CAS. Can't remember the last time I actually solved an integral by hand.

>>11074666
>>11074687
You do need to learn how to take a derivative before understanding that taking the derivative of a function is basically applying a linear transformation, namely the differential operator on your function. The real problem would be your uni making you differentiate an expression that would require i.e using 12 times the chain rule or some shit like that. Also, there is simply no way you're gonna use everything you learn in university, it's too broad. You have to learn how to find material and study on the field you're interested in by yourself.

>>11074763
Adding to the last part, this is what most undergrads get wrong. When you get your degree and want to work on something specific, you'll have to cram on the fly or at least along the way of your project all the information needed. Real life work is not a standarized test. You'll miss a lot of theory needed. But that's okay. You managed to get a degree, you know how to find and learn that theory, right?

>>11074763
>Learn mathematica and download a cracked version. It's the backend of wolframalpha and basically wolframalpha on steroids
Ok thanks, I hope it works on Mac

>>11074538
NNNNNNNNNRRRGGHHAAAAAAHHHH PICTURE OF SEXXXY LADY I"M GONNA DO IT I'M CCCCCOOOOOOOOOOOMMMMMMMMMMIIIIIIIIIIINNNNNNNNNNNNGGGGGGGGGG

>>11074591
>If you have no analytical understanding of what you're supposed to expect you'll never be able to troubleshoot or spot something that's off.

Speaking as an engineer, this really.
You would be amazed at how much shit out there that is peddled that is just wrong.

If you can't test the output of a program, function, method or other 'tool' against known analytical solutions and the intuit variations on those analytical solutions then you can NEVER trust what your 'tool' is telling you.

Sometimes YOU have to develop that tool and if you don't test it properly it will lie to you and you will lose your job because the company you work for went of business because your customer sued you and yours for all everyone was worth.

Don't be a pussy. Learn your fucking math.

>>11074811
boomers used to give this as an excuse for not using calculators

U need to use physics in engineering, and u need to use calculus in physics don't get it?

>>11074822
If I code a calculator in a new language I'm not an absolute expert in, screw that, even if I am, do you really think I won't cross validate 1042^7 * 19111^19 using an existing calculator? Or start by testing if it outputs 71*6122 correctly by multiplying it by hand?

>>11074836
reread the thread

>>11074822
Algorithms are man-made. Machines are man-made. They're prone to errors, mostly stupid ones. Overlooking an overflow error in a bank software can make them go bankrupt. I'm the math bachelor, the engineer should be able to better explain this, but this is common sense. Not some boomer bullshit.

>>11074822
I will grant that it is typical of an older generation to neglect more modern advances in a kind of baby duck syndrome. However, if you carefully review what was said, it was explicitly pointed out that it is used in the interrogation of new tools not the refusal of new tools.

I like your agest ad hominem attack slant assuming I am much older than I am. I may be wisened, but I am not aged. I have seen first hand the hubris of fools, at one time myself among them, who placed their trust in things they do not properly understand.

I imagine you also think that modern deep learning AI will soon be making life or death decisions as well.

I fear the pain of experience, and only this, will bring you to understanding.

Good luck.

Also a physics graduate like >>11074709

Would just like to add that that I pretty much do the same, together with some exponentials IF it seems easy enough (I assume the poster just forgot to mention it).

>>11074851
Read this instead.

OP here I've decided to do the integrals by hand wherever possible, the reason is in case i ever want to get a real qualification in engineering I'll be prepared.

>>11074538
>why learn anything, the machines can do the work!
Way to make yourself expendable come automation time. You don't think it's important to at least tease your brain into problem solving advanced concepts? You don't think a boss is going to hire someone who's well rounded and might use one of the concepts one day up help a customer? You don't think someone other firm will come in and say help us make this and they bust out the drawings and your engineering division looks dumbfounded and can't follow the conversation and theyll just quit on you?
Dude half the stuff you learn, ever, will never be used. I'm surprised you wasted a thread on this question rather than about art electives. At least your learning common concepts and language to other engineers in calculus.

I'm honestly thinking your a Chinese shill trying to dishearten Western students and engineers and this isn't your first thread today.

>>11074591
>>11074811
>>11074945
really it's just nice not being a retard amongst your peers

>>11074538
Maybe because you need to understand what are you doing. Integrals are basic calculus course.

>>11074637
Don't equate the understanding of integration with the particular ways to solve integrals. It is the set-up that is important, not the number crunching part. If you understand the problem at hand and have a clear idea of what integration is and how to apply it to solve the problem, thats all you need. Solving integrals by hand is a waste of time. That said, I can see how it can be fun similar to solving a random puzzle. So yeah you can refresh your memory and look up stuff like integration techniques and trig identities etc. So if you see it as an intellectual challenge then by all means do it. Schaums is actually good for that, it has a bunch of problems with solutions, straight to the point.

>>11074855
>Overlooking an overflow error in a bank software can make them go bankrupt.
That's why they need to write their software in Rust instead of C

what are the best books for a first timer that teaches setting up differential equations instead of just applying formulas?

>>11077588
No one needs to write anything in trannyware, you fucking faggot

>>11074538
What is the point of teaching addition of a simple calculator can do that for you?
What's the point of learning to write off most people just use keyboards nowadays?
What's the point of teaching reading if you can simply use text2speech engines?

>>11074538
Unfortunately, this is what engineering majors believe after 2 years of suffering through basic math courses. While it’s true that you don’t have to be the best at any of these things to do a job well, you need to understand what’s going on in order to succeed in engineering. Even on the most practical level, it’s mandatory you understand what your mathematical tools are giving you, even if your own abilities aren’t that great. Nobody is asking you to do any hard derivation or prove anything difficult. The most you need is some sophisticated ideas to handle the physical computations - you should be able to do that as an engineering student.

>>11074822
Calculators don’t do math. They calculate. You use calculations to do math, not the other way around

>>11074538
Based

>>11074538
>>11074709
t. retards that can't integrate

>>11076671
>Dude half the stuff you learn, ever, will never be used
And you are okay with spending $40k tuition on this?

>>11077149
Thanks.