What's a derivative?

[Anonymous No.11437065]

I've been studying electrical engineering for 4 years and I still don't know what is.

[Anonymous No.11437072]

The behavior of general functions is complicated, but the one of linear functions is simple. So if you want to investigate the behavior of a function f at a point x, you make the problem easier by looking for the best linear approximation of f at x. The best linear approximation is exactly the derivative. It gives you a lot of information about how the function behaves around the point, even though the information is local.
The connection between local and global is then given by the fundamental theorem of calculus - it says that you can stitch together the local information of the derivatives to reconstruct the actual function and exactly how to do that.

[Anonymous No.11437075]

>>11437072
In the case of real functions the viewpoint of the derivative as the best linear approximation can be overlooked just because the definition is so simple, but you can't avoid this viewpoint when you try to define derivatives in functions f: R^n -> R for n higher than 1. Technically speaking, in the case R->R the value of the derivative is the slope of the best linear approximation, not the linear map itself, but it could have just as well been defined as a linear map L:R->R such that
lim of (f(x+h)-f(x) - L(h))/h = 0
h->0
I'll leave it as an exercise to see that these two definitions are actually equivalent :)
The fundamental theorem of calculus is also remarkable in the following sense. When I was a child, I tried to think about what exactly the speed means. Sure you can take the ratio of distance with time between two distinct times, but that would be the average speed. What is the speed right now? Turns out the intuitive notion as taking the limit of the average speed as the future time point tends to the present time works out well. And then you might wonder, if you know the average time in the time interval, you know how far you traveled (by multiplying by the time), could you do a similar thing with instantaneous speeds? There are infinitely many speeds, because there are infinitely many time points at which you could have measured the speed, so what do you add and multiply? And what the FTC says is exactly that the intuitive thing to do: to consider instantaneous speeds as average speeds for small time intervals and calculating the distance in that way, while making the intervals smaller and smaller, the limit is remarkably the actual distance that you traveled! That seals the deal: derivatives are the right thing to look at and calculus is based!

[Anonymous No.11437076]

>>11437065
rate of change of some quantity
positive and big derivative = the quantity increases fast
positive and small derivative = the quantity slowly increases
negative and small derivative = the quantity slowly decreases
negative and big derivative = the quantity decreases fast

[Anonymous No.11437085]

>>11437065
The inverse function of the integral

[Anonymous No.11437091]

>>11437065
>>11437072
don't listen to this mumbo jumbo fancy word answer, the derivative is a formula for the slope of a line tangent to the graph at a given x value, for example, if the derivative of x^2 is 2x, the line tangent to the graph x^2 at x value 3 would have a gradient of 6(2*3). now, a line tangent to the graph at that point shares the same gradient as the graph at that point. WOAH WOAH WOAH!! BUT HOW DOES THIS MAKE SENSE!!??? GRADIENT AT A POINT??? by at a point i mean imagine the rise over run triangle becoming closer and closer to that point, its like an approximation, what the gradient converges to as you decrease the size of this triangle more and more

[Anonymous No.11437098]

>>11437085
not true

[Anonymous No.11437359]

>>11437065

dunno, probably some functor in the category or functions or something

[Anonymous No.11437363]

>>11437359
idiot

[Anonymous No.11437367]

>>11437065
The growth rate of a function.

[Anonymous No.11437369]

>>11437065
A derivativeis a contract thatderivesits value from the performance of an underlying entity. This underlying entity can be anasset,index, orinterest rate, and is often simply called the "underlying".Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives includeforwards,futures,options,swaps, and variations of these such as syntheticcollateralized debt obligationsandcredit default swaps. Most derivatives are tradedover-the-counter(off-exchange) or on an exchange such as theNew York Stock Exchange, while mostinsurancecontracts have developed into a separate industry. In theUnited States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the three main categories of financial instruments, the other two beingstocks(i.e., equities or shares) anddebt(i.e.,bondsand mortgages).

[Anonymous No.11437372]

>>11437098
The inverse function of the integral plus a constant

[Anonymous No.11437380]

>>11437065
how the fuck did you get through high school without knowing what derivative is?

[Anonymous No.11437398]

>>11437065
what have you tried?

[Anonymous No.11437411]

imagine that these people who answered actually visit universities in 2020
holy fucking shit
a function is differentiable at a point x if and only if:

[math] f'(x) = \lim_{x \rightarrow x_0}\frac{f(x)-f(x_{0})}{x-x_{0}} [/math]

exists, this is the most basic definition, the most important thing to prove is that every differentiable function is continuous but not vice versa, which isn't very difficult

[Anonymous No.11437419]

>>11437411
holy fucking shit you're retarded

[Anonymous No.11437444]

Simple animation to illustrate the concept.

[Anonymous No.11437476]

>>11437380
Im very good at applying calculus and actual doing it. But I can't explain must of the terms succinctly.
Essentially, it's a black box to me. I know what to expect and what to use it for, but not why it works.

[Anonymous No.11437478]

>>11437411
You should be aware that every single poster ITT, including OP, knows this definition very well but the point of the thread is to give a simpler explanation and the point of /sci/ is to shitpost about science. Not understanding this and thinking that you're the only one in the thread who gets it is the most reddit thing you can do.

[Anonymous No.11437500]

>>11437411
holy fucking shit I hope you're joking with this post

[Anonymous No.11437539]

>>11437476
this is some next level autism

[Anonymous No.11437548]

>>11437539
that's not autism that's just rote memorization

[Anonymous No.11437561]

>>11437411
>not using h in the limit deffiniton
>not using the sequence deffinition
Yikes, even OP was less of a faggot

[Anonymous No.11437569]

>>11437411
biggest joke is that the formula is actually wrong

[Anonymous No.11437617]

>>11437561

this IS the limit definition, the h definition is obtained by setting h:= x-x_0 ; it's kinda obvious if you arent a brainlet

>>11437569

no its not

[Anonymous No.11437620]

>>11437478

if you think derivative is some wordsy thing that must have a physical explanation you are wrong
it is no such thing, in its simplest form its just it is just the definition of differentiability

if you need to write an essay to understand that f'(x) only exists if the limit on the right side exists, then you clearly dont understand the formula

[Anonymous No.11437633]

>>11437065
its like when you copy art
"oh that painting has nothing original, its just derivative of other impressionist pieces"

[Anonymous No.11437637]

>>11437065
dea why dee ex

[Anonymous No.11437641]

>>11437098
Yes it is, that is how you can construct derivatives of any order, fractional, negative or complex.

https://en.wikipedia.org/wiki/Fractional_calculus

[Anonymous No.11437661]

>>11437617
I know, it looks better with the h tho

[Anonymous No.11437662]

>>11437617
>no its not
>x0 undefined

[Anonymous No.11437671]

>>11437617
Also it is wrong because you wrote f'(x) which has no meaning since x is the variable of the limit. What you meant was [math]f'(x_0)[/math]

[Anonymous No.11438117]

>>11437091
derivative is not always an linear function, is it?

[Anonymous No.11439262]

>>11437085
kind of

[Anonymous No.11439264]

>>11437411
yais. I agree. and the art of electronics agrees too. and there is a song about it.

[Anonymous No.11439270]

>>11437380
Yeah where did you go to school? I was suspended or had to spend certain lessons in the library from 15 years old cos I wuz bored but understood that stuff

[Anonymous No.11439274]

>>11437478
>the point of the thread is to give a simpler explanation
wrong, this is a thinly veiled EE hate thread. try again.

[Anonymous No.11439275]

>>11437065
I thought it was the rate of change if a function at a given time on the function

[Anonymous No.11439290]

>>11439275
yeah. thats it. how fast is the thing changing, or rate of change. you got it.

[Anonymous No.11439293]

>>11439275
read the art of electronics appendix: javascript:quote('11439264');

[Anonymous No.11439297]

>>11438117
What that idiot forgot is that you're supposed to take the value of the derivative at that point and then multiply by x. Basically a Taylor expansion up to the first order.

[Anonymous No.11439473]

>>11437091
Best retarded answer in the thread

Stay away from teaching

[Anonymous No.11440867]

>>11437065
I thought people went in to EE to make a shit load of money. I guess not?
>A derivative is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset (like a security) or set of assets (like an index). Common underlying instruments include bonds, commodities, currencies, interest rates, market indexes, and stocks.

[Anonymous No.11440888]

Derivative is the slope of a tangent line at that point

[Anonymous No.11440936]

>>11437065
If you restrict a function's domain to integers, it effectively becomes a bar graph. The delta function can then be considered the difference between sequential bar heights.
The difference between any two sequential integers is 1, right? So, whatever the difference in the y axis is between sequential bars, it's equal to the difference in the y axis divided by the difference in the x axis, because anything divided by 1 is itself.
From this observation, we can generalize the delta function to other step sizes than just 1. Let's say we increment the x axis by 0.5 each time, and compare sequential bar heights in the resulting bar graph. We'd divide each difference between 0.5, since that's our new step size. So if one bar has height 12, and the next has height 18, the raw difference would be 6, and since our step size is halved, the scaled difference would be 6/(1/2) = 12.
The derivative, then, is the continuous function you get when you generalize the delta function to an infinitesimal step size. It's the limit of scaled delta as step size approaches 0.
Hence the notation: dy/dx.
For any other step size, the generalized delta function would be discrete, just like the function you're calculating the deltas of. But a "discrete" function with a fixed infinitesimal step size is by definition a continuous function.

[Anonymous No.11440938]

>>11437561
>>not using h in the limit deffiniton
>>not using the sequence deffinition
???

[Anonymous No.11440944]

>>11437065
The slope of the graph of a function at a given point.

[Anonymous No.11441612]

>>11437476
The engineer

[Anonymous No.11441647]

>>11437072
>>11437075
>>11440936
>OP doesn't know what a derivative is
>Instead of just replying in simple tearms you type out some ultra pretntious reply to look smart on logchan
>Not even using TeX
Brainlets like you should be killed
>>11437369
reddit

>>11437065
If you still don't understand what a derivative is after 4 years of school than you are beyond help

[Anonymous No.11441648]

>>11437617
>no its not
Yes, it is. Left side is dependent of x, right side isn't.
In fact the formula doesn't make any sense at all.

[Anonymous No.11441658]

Rofl, so called first world universities have shit engineering programs. In my country for electrical engineering you are expected to get past complex analysis and vector analysis (same courses math majors have to go through) and not some watered down versions of the courses. Can´t believe an electrical engineer can´t properly explain what a derivative is, specially when you have to learn the complete functioning of electromagnetic interactions in a simple circuit. It is just not possible to not understand a derivative and study more complex circuits. Has no one ever told you that the electric current is the derivative of charge with respect of time?. Basic concepts that explain basic physics and therefore should be second nature for an engineer.

[Anonymous No.11441662]

>>11441658
>In my country for electrical engineering you are expected to get past complex analysis and vector analysis (same courses math majors have to go through)
That probably only speaks ill of the math majors, imagine taking a math course engineers also take...

[Anonymous No.11441668]

>>11441662
It´s not about that. Engineers have to take advanced math classes to be able to understand physics on a deep level. Las exam i had to take was complex analysis and I had to prove the residue theorem using lorentz series. What i´m saying is that mathematical reasoning used to come up with proofs and definitions is intrinsic to an engineer´s thought process.

[Anonymous No.11441673]

>>11441668
>Engineers have to take advanced math classes to be able to understand physics on a deep level.
Not really.
Especially since here taking the basic analysis and linear algebra courses of the first year is already 18/30 ETCS per semester, if you want EE students to actually learn EE then you can't put them in with the math majors.
Because either they don't learn anything about EE or the math majors get a shot tier education.

>Las exam i had to take was complex analysis and I had to prove the residue theorem using lorentz series.
Memorization isn't mathematics, exams are nothing more than a necessary idiocy anyway.

>What i´m saying is that mathematical reasoning used to come up with proofs and definitions is intrinsic to an engineer´s thought process.
Why?
Seems totally counter intuitive.
I mean I HAVE taken some serious PDE classes and a lecture on theoretical EE at the same time.
I know that the Helmholtz equation is just an Eigenvalues problem for the Laplacian and I know some existence and uniqueness theory about it, but why would an engineer need that?

[Anonymous No.11441675]

>>11441668
>It´s not about that. Engineers have to take advanced math classes to be able to understand physics on a deep level.
no they don't

[Anonymous No.11441680]

>>11441673
You know to need this stuff to be able to be an engineer. You can get by without knowing this stuff but you can only reach a 'technician' level, your vision of engineering is just not real. You HAVE to know math, you HAVE to know physics extremely well. How can you learn electromagnetism without being able to operate with vector functions as easily as real functions? You get to this point by studying math. Alot. The thing is engineering career is 6 years long in many places. Which is more than adecuate.

[Anonymous No.11441690]

>>11441680
>You know to need this stuff to be able to be an engineer
Why?
Why do you need to know the proof that Laplace operator has countably many Eigenvalues in order to do some simulation for your wave guide.
Where is the connection.

>How can you learn electromagnetism without being able to operate with vector functions as easily as real functions?
"Operating with vector functions" isn't "higher mathematics" any engineer everywhere in the world learns that and practices it. Do you know who doesn't, though? Mathematics majors.
Your view of mathematics seems to be delusional.

[Anonymous No.11441693]

>>11441675
How can you study relative movement in 3 dimensions without knowing how to differentiate vectors? how can you understand rotational movement in three dimensions without knowing what a tensor is?. How can you study complex charge distributions without knowing how to expand potential up to the multipole term without using complex mathematical tools?

[Anonymous No.11441696]

>>11441690
Mathematicians do that and much more. Which has nothing to do with the fact that you need to know this stuff to be a true engineer. Thing is universities in the US particularly have shit engineering programs due to the fact that the sole purpose of these programs is to have 'semi-qualified' workforce for the industry(excluding high tier private universities)

[Anonymous No.11441699]

>>11441693
>How can you study relative movement in 3 dimensions without knowing how to differentiate vectors?
That isn't higher mathematics. That is very basic mathematics and if your math students spend their time doing that then they are getting a shot education.
Every engineer learns that, but it shouldn't be a significant part of any mathematics curriculum.

Your view of what happens in math classes is very weird.
Mathematicians learn proofs, engineers learn applications and tools.
All you are doing is naming these applications and tools, which have little to do with mathematics students should learn.

>>11441696
Why do you refuse to answer my question.
Why do engineers need to understand involved proofs EVERYTHING you name that engineers need is unrelated to proofs. It's just tools.

[Anonymous No.11441700]

>>11441690
>Eigenvalues
On this, the laplace operator is fundamental to calculate potential in any area, including distributions that are not geometrically symmetric, for example in a given problem you have to use Dirichlet eigenvalues to define potential in a certain area. If you can´t prove it has many eigenvalues how can you particularly use Dirichlet or Neumann eigenvalues to solve an electromagnetic problem?

[Anonymous No.11441703]

>>11441700
>If you can´t prove it has many eigenvalues how can you particularly use Dirichlet or Neumann eigenvalues to solve an electromagnetic problem?
Because a mathematician TOLD YOU it has finitely many eigenvalues.
Why do you need to know the proof. Seems a waste of everybodies time.

[Anonymous No.11441705]

>>11441699
Deeper understanding of tools makes better engineering. Therefore knowing proofs about what you are using is essential. Higher physics means higher mathematics to describe it. Engineering is physics. Your view of engineering is wrong. You share the same view your universities have, you practically think engineering is understanding machines which is not. Engineering is understanding physics in such a deep level that you understand how everything works.

[Anonymous No.11441707]

>>11441703
Knowledge is never a waste of time.

[Anonymous No.11441709]

>>11441647
>>Instead of just replying in simple tearms you type out some ultra pretntious reply to look smart on logchan
Which part of my explanation did you find pretentious?

[Anonymous No.11441710]

>>11441705
>Deeper understanding of tools makes better engineering
That is insane and doesn't answer the question. WHY does knowing a very abstract proof, which probably takes years of unnecessary education make you a better engineer?

>Engineering is physics
No.
It isn't.
Engineers try to make things work and physicist search for truth.
There is a reason Newton's laws have been discarded for over a hundred years in physics, but are highly relevant to engineers.

>Engineering is understanding physics in such a deep level that you understand how everything works.
Why does Engineering exist?
Why not get rid of it and tell everyone to study physics?

>>11441707
By that standard you can justify every engineer spending 3 entire years on learning the history of interpretative dancing.

[Anonymous No.11441722]

>>11441710
Engineering is physics + understanding the applications of physical phenomena. Everyone knows Newtons laws apply under certain restrictions(which happen to be around every day on the real world)
Engineers don't try to make things work, they invent things ( this is why if you do not have a lot of knowledge of mathematics and physics to study and describe prototypes you are nothing but an industry pawn, which is what most engineers are in 1rst world countries)
Why? To make better engineers..knowing lots of proofs will give a strong command of mathematics
Why not get rid of it and tell everyone to study physics?
Well, this question is just a product of being immersed in today's educational system. Take a look at the past? People in the past didn't have to choose a major therefore studied what they wanted. This is the core of engineering (just personal opinion here) people in the past studied our world vigorously, which lead them to be physicist mathematicians and also engineers, what i'm trying to say is most scientists in the past where a combination of all the disciplines that are in our day and age, all separate into different 'majors'.

[Anonymous No.11441834]

>>11437065
i literally didn't do shit but play games during my entire college and i know what a derivative is kys

[Anonymous No.11441863]

>>11441722
>To make better engineers..knowing lots of proofs will give a strong command of mathematics
You are refusing to answer the question.
Tell me a specific example where an engineer gained significant knowledge about an engineering problem by doing a proof HIMSELF.

>Engineering is physics + understanding the applications of physical phenomena.
So get rid of engineering. And if you got a physics master do an engineering degree.
But that is totally absurd.

>what i'm trying to say is most scientists in the past where a combination of all the disciplines that are in our day and age, all separate into different 'majors'.
Please don't appeal to the past to justify the current.
All fields have become more specialized, almost no mathematician can be relevant in multiple fields and only the best of the best will have any chance in multiple areas of study.
Your proposition makes sense in a time where a single book could contain most significant things we know about physics, or mathematics.
That time is over.

[Anonymous No.11441879]

>>11441863
Not doing a proof himself, but rather understading how to reach those mathematical concepts. This is achieved by learning how to prove stuff ergo learning mathematics. How is an engineer supposed to find applications for abstract mathematical concepts without understanding them properly?

[Anonymous No.11441947]

>>11441879
For the love of god, answer my question.
If you can't answer it then please don't bother responding.

>How is an engineer supposed to find applications for abstract mathematical concepts without understanding them properly?
He isn't.
Finding Application for abstract mathematics has absolutely nothing to do with being an engineer.
An engineer is supposed to solve concrete Problems using mathematical tools.
And just like a mechanic doesn't need to understand the material science, chemistry and engineer that was used to create his tools an engineer doesn't need to know how his tools were derived.

Seriously. Your notion of both engineering and mathematics are absurd and quite frankly so are your arguments, so just answer my fucking question and be concrete for once.

[Anonymous No.11441957]

>>11437065
It's the opposite of an anti derivative bro

>>11437637
Kek

>>11437065
It's just the rate of change
The derivative of a linear equation will have a "smaller/slower" equation the the derivative of a parabolic

[Anonymous No.11442081]

>>11441947
Okay im sorry its the first time i am being trolled wasn't sure how to react.
I have answered all of your questions so far... You have answered mine by showcasing a mislead conception of engineering

[Anonymous No.11442085]

>>11442081
>I have answered all of your questions so far
No, you still haven't shown a single explicit example where advanced mathematics benefits engineering.
The best thing you gave was "differentiating vector functions" which obviously is VERY BASIC mathematics.

[Anonymous No.11442109]

>>11442085
Please define 'advanced mathematics'

[Anonymous No.11442129]

>>11441647
My explanation (>>11440936) wasn't intended to be pretentious or make me look smart, it just looks that way because explaining concepts in more digestible terms than initially postulated is hard. I, for one, often wind up slipping into bullshit land -- not because I want to look smart, but because I want to help the other person understand, but am not doing a good job at it.

[Anonymous No.11442142]

>>11437065
Instantaneous rate of change
Integral is the sum of numerous rates of change
Integrating a derivative makes the function (with some caveats) so a function is essentially the sum of the rates of change over a continuous interval

[Anonymous No.11442198]

>>11441947
>to solve concrete Problems

thanks to Internet most "easy" problems were solved by someone else

[Anonymous No.11442233]

>>11437411
What is limit tho? Limit is number right by how can it be number if argument x0 can be arbitrary large?

[Anonymous No.11442279]

The derivative f' of a function f is the slope of the function at that point. For example, if f(x)=6x, f'(x)=6 because for each increment of 1 to x, f'(x), or the y axis, increments in 6.

[Anonymous No.11442359]

>>11442109
The mathematics that are necessary to advance mathematics itself.

[Anonymous No.11442379]

>>11437065
Describing a mathematical operation in tangible terms requires synesthesia or a really shitty analogy.

[Anonymous No.11442399]

>>11437065

f(x) = secx
f'(x) = MB(p)

[Anonymous No.11442427]

>>11442359
Great, i have never encountered such level of mathematics in my work, Im an electrical engineer and currently im studying a masters in applied mathematics, however i teach college level calculus to business students (which is very basic) and also do consulting jobs for private companies, therefore im far away from being related to any of these topics. A collegue of mine works as a research engineer and he is constantly reading thesis papers and publications regarding various subjects of mathematics and physics to further his own research which is actually his job.
Is thesis level mathematics/physics enough?

[Anonymous No.11442481]

>>11442427
>Great, i have never encountered such level of mathematics in my work
So why do you claim any engineer needs them?
Because there is no point of putting engineers in with math majors if one is literally never going to use most of the course because it is required for advanced mathematics.

>Im an electrical engineer and currently im studying a masters in applied mathematics, however i teach college level calculus to business students (which is very basic) and also do consulting jobs for private companies, therefore im far away from being related to any of these topics.
A master's is LITERALLY a degree that should prepare you to be able to do research. If you are doing a master's in applied mathematics and don't know advanced mathematics, consider dropping out or switching Unis, because that is absurd.

>A collegue of mine works as a research engineer and he is constantly reading thesis papers and publications regarding various subjects of mathematics and physics to further his own research which is actually his job.
Be specific. "He uses these kinds of mathematics" is neither specific nor helpful. Say what particular area the math is involved in, eg. he needs to prove things about X to do Y.

>Is thesis level mathematics/physics enough?
A master's thesis in mathematics is literally "advanced mathematics" at least that is how it is supposed to be.

[Anonymous No.11442584]

>>11442481
First of all you are nit picking just for the sake of the argument and I get but I have to admit it is getting pretty annoying. I´m doing my masters because i am qualified for it, hence having to go through various tests and a 1 year course/lecture.
I only do know of one particular example in where he was working with fluids and part of his research referenced a paper involving the molecular dynamics and rheology of polymer
melts near the flat surface which is a common subject of study among mathematicians (particularly regarding modeling of fluids) while adding molecular simulations to his research and experimental study.

[Anonymous No.11442648]

>killeveryoneinthisthread.jpg

[Anonymous No.11442670]

>>11442584
>you are nit picking
What?
What the fuck am I nitpicking?

>I´m doing my masters because i am qualified for it, hence having to go through various tests and a 1 year course/lecture.
So?
I am starting to think that you can't read English.
I said that the point of doing a master's is to do and understand advanced mathematics.
If you are doing a master's and learning about those topics, great, if not, you are doing something wrong.
This wasn't meant to be a personal attack, it was meant to relate what I am talking about to what you are doing.

>molecular simulations to his research and experimental study.
So it has nothing to do with what I asked for. He read about a paper and used it's result to do some simulations.
Great, but where did HE USE ADVANCED MATHEMATICS? What did he need to prove?

So, my question still stands. Name a situation in which an engineer had to use advanced mathematics.

[Anonymous No.11442696]

>>11442670
He had to understand everything in these papers thus knowing 'advanced mathematics'.

Ill see you around

[Anonymous No.11442707]

>>11442696
>He had to understand everything in these papers
Why?
You don't need to understand an entire paper to use their results.

And even if he understood it entirely, which I doubt, he still neither did or had to use advanced mathematics.
He proved nothing, as it seems, so advanced mathematics is irrelevant.

[Anonymous No.11442716]

>>11437065
>engineer
>what is a derivative
imagine my shock

[Anonymous No.11442717]

>>11442707
Wow.
He furthered research on the topic thus making his own conjectures and proving them through mathematical analysis and expanding on experimental methods to support the theory.
It does not get easier than that.

[Anonymous No.11442727]

The measure of the rate of change of a function as it undergoes an infinitesimally small change.

Daily reminder that if you can't sum up a topic quickly and concisely then you're a brainlet who doesn't understand the topic at hand.

[Anonymous No.11442731]

>>11442717
So he did, I assume, PDE research?
What was his background in mathematics, did he take some courses on measure theory, sobolev spaces, etc., all the necessary prerequisites which takes a math student about 5 years to come up with?
Is that normal for engineers who do research?

And why would an engineer do mathematics research? It has nothing to do with his job, your friend should consider switching to mathematics if he is interested in it.

Also I start to think you actually do not understand what I say.

[Anonymous No.11442737]

>>11437065
it tells you the rate of change of some variable with respect to the change in some other variable

for example, current is the rate of change of electric charge at a given point with respect to some period of (i.e. change in) time.

[Anonymous No.11442740]

>>11442727
>infinitesimally
You didn't understand the subject either.

[Anonymous No.11442758]

>>11442740
Fuck you Calculus is the study of infinitesimals.

The Integral is adding up an infinite amount of infinitesimals over a range and the derivative is the rate of the change of dy over dx both of which represent an infinitesimally small change of the input and the output respectively.

[Anonymous No.11442769]

>>11442758
>Fuck you Calculus is the study of infinitesimals.
Maybe it was 300 years ago.

>The Integral is adding up an infinite amount of infinitesimals over a range and the derivative is the rate of the change of dy over dx both of which represent an infinitesimally small change of the input and the output respectively.
Are you time traveling from the 1850s?
No mathematician uses infitesimals, they have been replaced very long ago by something actually rigorous. Limits.

[Anonymous No.11443305]

>>11437411
>not even using the full delta-epsilon-didn't kill himself formalism

[Anonymous No.11443307]

>>11437411
I came here to laugh at you.

[Anonymous No.11443317]

>>11441668
>Engineers have to take advanced math classes to be able to understand physics on a deep level. Las exam i had to take was complex analysis and I had to prove the residue theorem using lorentz series.
What a bunch of useless bullshit.

I don't even remember what a differential is and I'm making good money in control systems, didn't even have to job hunt, jusr got approached while presenting my capstone project. You see, US engineering programs actually focus on important things, like building useful systems and getting jobs.

[Anonymous No.11443321]

>>11441680
i know literally nothing that you've mentioned and am a field engineer

lmao