@@aominetaiga343 probably a school with common exams. math department likely has a curriculum and material to teach/ adhere to but i agree, its kind of unheard of. there probably is a textbook tbh lol
@@aominetaiga343 It's kind of normal especially if you are doing an exam specific to a particular developing country and the curriculum isn't the same as the Western countries. You just don't know what textbooks to use. Like if you do SAT exams you know you can use SAT textbooks and if you do A-levels, there are A-level textbooks. Still, if you use other textbooks, it can be helpful.
the Grad student that teaches my calc class didn't go over defferentials at all in lecture and then proceeded to put it on the homework. Thank you for saving my grade.
So you said how a differential equation is made, and you showed proof of how the answer works, but you jumped straight to the answer. Thus confusing the audience. I know you said there are multiple answers, but not knowing how to get there makes it look like magic. Of course I could have missed something. But this felt like asume the answer and find the proof.
If you think of a tangent line, which is a line that touches a function at exactly one point, and is really just the limit, both the left side and right side of a secant line, has a rate of change, but is also the rate of change at that exact point. So all your doing is finding the rate of change or more simply rise over run. And these lines are based off of circles, and limits are based off the simple difference quotient, which in itself is just a way to think of rate or change. So all this is, is complex forms of math built off of circles and rate of change(rise over run). And a circle is just based off the idea of a closed loop, and is something people just drew, and rate of change is just the idea about how numbers change over time in a simple linear equation, which is based off of the ideas of numbers and variables, which in itself is based off of the idea of numbers.And a circle is just geometry, which is also based off of numbers. So when you get down to it. ITS ALL JUST NUMBERS! And differential equations are just ways to relate certain functions like derivatives, but actually can relate the world to numbers. ITS ALL JUST NUMBERS!
@@kinglaserna1533 Surely you've been introduced to some of the applications of calculus? There are a million ways it can be useful, very interesting stuff!!
They are very useful depending on what profession you'd like to take. Calculus is very crucial especially on probability, and there are a lot of professions that requires being good at probability. For example, being an actuary, or having a job at insurance companies
Sal: Here's a differential equation. Figure out if one of the solutions in this list of possible solutions is the solution. My professor: Here's a differential equation. Good luck idiot!
Don't worry, you've learned "how to learn" and that is extremely important. When you've learned something once, it's going to be easier to relearn it when you need it. Start from easier stuff when relearning :)
srmorales08 I know this is old, but I ran through it with a general e^ax. You end up with a quadratic who's solutions are 1 and negative three. I'm sure there's a more consistent way in another video you've probably already watched, but whatever.
I'm 3 years late but I'm just studying it now. He got it from l²+2l-3=0 Where l² is d²y/dx² l is dy/dx and y is just 1 From there you get -3 and 1 solutions for l.
Many people I know hate differential equations, idk I love them to bits, I find them fun. I thought I'd struggle understanding them cause I had struggled with calculus, but it was a surprisingly smooth ride. They really are pretty fun to deal with. _Unlike the spawn of Satan that is probabilities and statistics._
I’m currently a sophomore in algebra 2. All I wanted to do was take a sneak peek of what math would be like next. The only part I understood was when he showed the algebraic equation 🙃 what is math
Hey, not a bad idea, but you took a bit of a leap here :D You might want to look over (limits and) derivative calculus first, and then you'll understand this a bit.
The main thing that I like about the Khan Academy is that he makes advanced math that's usually difficult, a lot easier to understand to where anyone can learn and master what he's teaching.
My professor teaches for his first time ever, so his teaching is kinda awful and inefficient that I had to rely on teaching differential equations to myself.
A great video; I was highly recommended to watch your vids to improve my maths and I have to say you are great at explaining things. I look forward to the whole series of differential equations being this helpful! Many thanks
@@hahaha-zi1xf the order corresponds to the bigest derivative in the ecuation (if it has a second derivative then its a second order differential ecuation)
@@dxalrado He's just talking about differential equations. It's an introduction. We don't care about the order yet. The concept already difficult enough without it.
When I hear Sal's voice, I automatically listen. I automatically want to learn and understand the lesson. From the years I've spent on khanacademy, he has become my everyday professor/coach when learning. I'm studying electrical engineering right now. Khan academy has its own professor in that department, but when whenever I go back to whatever Sal's teaching, it makes me feel happy to hear his voice.
The point is to show some examples, and to showcase how taking derivatives and adding them isn't anything too scary. It's an introduction, not a full explanation of the subject.
Why are Math teachers so bad at explaining things? Not you, Sir. You seem intent on conveying something. I was literally abused by my math teachers. Not a word about what "this " might be good for in the "real world". Bad teachers are "baaaaad news"!
I just figured out a great way to study math at school: Watch videos on the topic to get more insight, intuition and curiousity. This is definitely one of the elements that modern educational systems lack, namely recommending great youtube videos!!!!
All it’s about is dealing with derivatives of a composition of functions, i.e. functions wrapped inside other functions. If you’ve got a function of x like f(g(x)) then the derivative is f’(g(x))*g’(x) Example: Derivative of (sinx)^2 = 2(sinx)(cosx)
One thing that annoys me about differential equations as they are often presented is that they omit specifying what's a function of what. What helps me keep the eye on the ball is this idea: When solving a number equation, like x^2 = 4, you're really describing the set { x in R | x^2 = 4 }. One description is to list all the elements: { x in R | x^2 = 4 } = {-2, 2}. When solving a differential equation, you're describing a different set, such as the following: { f: R -> R | f'(x) = f(x) for all x in the intersection of the domains of f and f' } or { f: R -> R | f''(x) + 2f'(x) = 3f(x) for all x in the intersection of the domains of f, f' and f'' } and so on. I have a proof using only ideas from my one-semester real analysis course, without Taylor series, that if f' = f (where f: R -> R) then f(x) = f(0) * e_x where e_x := lim (1+x/n)^n as n -> oo. In other words, { f: R -> R | f' = f } is a subset of { f: R -> R | f(x) = f(0) * e_x for all x }. I have only proven that f(x) = f(0) * e_x is a constraint that can be satisfied if f(0) = 0 [implying f(x) = 0 for all x]: I have not proven that non-zero solutions exist, only how they must look _if_ they exist. This is a less precise description of the set { f: R -> R | f' = f } than I would like, but it's a start.
This is a good refresher so far. Took diff eq ages ago in college and always felt depressed that it was one of those use it or lose it things and wanted to try and get it back.
A question, are there any lectures/materials that I should look at before I look at this? At 4:08 I have no idea what he is asking me and how I am supposed to do it.
You should look into derivatives. He y' is the first order derivative of y, and y'' is the second order derivative of y. y in this case is e^(-3x). To learn how to find the first and second order derivative of e^(-3x) make sure that you learn the chain rule part of derivatives as well :)
Iam about to take this subject next sem! wish me goodluck! just starting to learn... Imma update you guys how I did after this incoming sem. BTW, Im a CE student from Ph. Best of luck also to those engineering students! we can do this!
Could someone recommend a path from algebra to here? I am good at algebra, like in school I could graph in my head. Not kidding. But I want to understand this and I’m a wee bit ill equipped
Thank you for this. I managed to get all the way thru university and get my math degree without taking a single course in Differential Equations. At the time I didn't care because my work only involved theory, but now I regret it because I'm more interested in applied math and physics...
What you do not get? Oh where does he get the y = e^(3x) from? He forgot to said: it is given? And then to said oh the solution is equals to itself is not correct?
This isn’t true. Exponential functions just happen to be the type of solutions to the DE examples Sal gave in this video, which are second order constant coefficient DEs.
marian mortada A differential equations class will teach you the derivations for all sorts of methods to solving different types of differential equations. Most DEs cannot be solved by simple separation of variables as taught in your first calculus class.
Its summer time yet here i am hoping id learn something so i can even have 30% chance of passing. Coz rn my chance of passing is 2.5%. Hopefully, id make it.
From what I've heard from upperclassmen, Calculus II is by far the hardest math class so far much easier than I and III. They also refer to Calculus II as "Learning Witchcraft" or "This is Fake Math".
That's how solution works, you basically try and try and try till it works, the assumed y= to e-3x is just a result of experimenting and in differential equations you don't necessarily "solve" u simply try to prove that this Y NEED to be this (=). SO u can substitute whatever u want and in the end u'll reach e-3x is the most suitable substitute, u can try anything from negative infinity to the infinity of null
i wish there was highschool college where you would take college courses on a highschool schedule. so like an hour- 2hours a day, everyday, for a year. i would be so good at differential equations. i wish i had the time to love math the way i did in highschool
It is just an example, so he prepared it beforehand. But I assume he explains the process of finding such solutions later. I will try to explain how I'm thinking about this, but I'm just starting with differential equations myself. It is quite analogous to the algebraic equation of the form x^2 + 2x = 3... which we can rewrite as x(x+2) = 3. The solutions to it are -3 and 1. So we can place those into the function e^x in front of x. Because of how the "chain rule" works (especially with e^x), we effectively just add another "times -3" whenever we take the next derivative. I hope this was at least somewhat helpful to someone!
What i love about math is that the learning is recursive. I wanted to understand differential equations. Now im trying to figure ot how y becomes e and what are first and secon derivatives. F* me.
My dude if you don’t know what derivatives are you shouldn’t be in a diff eq class. This isn’t an insult- you really should have zero way of getting into diff eq without taking at least two calculus classes first
@@richardgarrison8328 I'm not in any class. I just took a weekend project implementing a neural network backpropagation algorithm. The problem is that english is not my native language and I went to school long time ago. So I'm facing the issue wrapping my head around the logic here and re-educating myself in english :D The local resources have not been too helpful. But Here I'm not trying to disrespect anyone. I was just in a low point where I had been watching videos and searching up on diff eq's, etc for few days already and just didnt find the "beginning" node of this journey. And here I realized again that I need to go an find some primer to this video. All good :)
This stuff is way after derivatives. It is assumed that you can handle derivatives quite easily by the point you come to differential equations. Imagine if we were learning about exponents, right? When teaching it, you assume that the students already know multiplication and addition. This is the same sort of case here. Don't be scared by this, if you haven't gone through derivatives. Differential equations should come later, when you are more comfortable with them. :)
My college algebra teacher has us trying to learn this almost right at the start of the semester. I signed up for algebra.. why are we starting with calculus :(
To be honest not very insightful nor explanatory in nature. The lesson should explain why and how rather than stating names of things written on the screen
As a student learning differential equation but no textbooks provided in the class, these set of videos means everything
No offense but how in the world can your professor lecture differential equations without providing texts?
@@aominetaiga343 probably a school with common exams. math department likely has a curriculum and material to teach/ adhere to but i agree, its kind of unheard of. there probably is a textbook tbh lol
z-lib
@@aominetaiga343 It's kind of normal especially if you are doing an exam specific to a particular developing country and the curriculum isn't the same as the Western countries. You just don't know what textbooks to use. Like if you do SAT exams you know you can use SAT textbooks and if you do A-levels, there are A-level textbooks. Still, if you use other textbooks, it can be helpful.
@@aominetaiga343 mine just gives us exercises but we have no theory about it😭
you lost me at 0:01
the Grad student that teaches my calc class didn't go over defferentials at all in lecture and then proceeded to put it on the homework. Thank you for saving my grade.
here for my midterms, pls pray for me.
same
swear this is second order, not first
civil engineering student here studying differential equations from scratch! will let you guys know how everything goes for me
you didn't
@@kevindemeulenaere1459 on my 3rd year of college and i still dont know jackshit
@@kevindemeulenaere1459real
I rlly love this and i am actually understanding this... even tho im in year 6
So you said how a differential equation is made, and you showed proof of how the answer works, but you jumped straight to the answer. Thus confusing the audience. I know you said there are multiple answers, but not knowing how to get there makes it look like magic. Of course I could have missed something. But this felt like asume the answer and find the proof.
Is it order 2 here isn't it ??
S
the derivative of e^x is e^x
Trial SPM P7 or P8
SPM C6
Sealed.
3e^x [dne] 3e^-3x. I'm confused.
Sal: So I'm assuming you had a go at it...
Me: What's a derivative again???
😭
If you think of a tangent line, which is a line that touches a function at exactly one point, and is really just the limit, both the left side and right side of a secant line, has a rate of change, but is also the rate of change at that exact point. So all your doing is finding the rate of change or more simply rise over run. And these lines are based off of circles, and limits are based off the simple difference quotient, which in itself is just a way to think of rate or change. So all this is, is complex forms of math built off of circles and rate of change(rise over run). And a circle is just based off the idea of a closed loop, and is something people just drew, and rate of change is just the idea about how numbers change over time in a simple linear equation, which is based off of the ideas of numbers and variables, which in itself is based off of the idea of numbers.And a circle is just geometry, which is also based off of numbers. So when you get down to it. ITS ALL JUST NUMBERS! And differential equations are just ways to relate certain functions like derivatives, but actually can relate the world to numbers. ITS ALL JUST NUMBERS!
@@kornelkr6639 I got you.
just exactly what I'm experiencing rn
its also important to understand the anti-derivative
He says "differential equations are super..." My brain is like "EASY??" ^_^ then he says "Useful" -_- Useful stuff is hard bruh
Ikr 😂
Useful? I’ve been learning Calculus since August of 2019 and still have yet to use out side of school
King La Serna When you get a job in STEM them you will.
@@kinglaserna1533 Surely you've been introduced to some of the applications of calculus? There are a million ways it can be useful, very interesting stuff!!
They are very useful depending on what profession you'd like to take. Calculus is very crucial especially on probability, and there are a lot of professions that requires being good at probability. For example, being an actuary, or having a job at insurance companies
Sal: Here's a differential equation. Figure out if one of the solutions in this list of possible solutions is the solution.
My professor: Here's a differential equation. Good luck idiot!
I'm starting my new years resolution a few months early : watch Khan Academy every day.
How are you doing with that?
@@buddychumpalfriendhomiebud9242 hmm... started strong, then forgot. Good timing!
@@fusion9619 good luck man
Why?
Mine this year
Did calc and aced it 5 years ago and can't remember anything. What is the point of my brain anymore.
Don't worry, you've learned "how to learn" and that is extremely important. When you've learned something once, it's going to be easier to relearn it when you need it. Start from easier stuff when relearning :)
I feel dumber since I started college 😂
WHERE DID HE GET e^-3x FROM???????????
srmorales08 I know this is old, but I ran through it with a general e^ax. You end up with a quadratic who's solutions are 1 and negative three. I'm sure there's a more consistent way in another video you've probably already watched, but whatever.
from Arab
I'm 3 years late but I'm just studying it now.
He got it from l²+2l-3=0
Where l² is d²y/dx²
l is dy/dx and y is just 1
From there you get -3 and 1 solutions for l.
@@elenav1210 Yes just realised you're right. He's used the auxiliary equation
Many people I know hate differential equations, idk I love them to bits, I find them fun. I thought I'd struggle understanding them cause I had struggled with calculus, but it was a surprisingly smooth ride. They really are pretty fun to deal with.
_Unlike the spawn of Satan that is probabilities and statistics._
I used to watch these vids for GCSEs I'm now doing an undergraduate and I'm still here, who says UA-cam is a waste of time smh
I’m currently a sophomore in algebra 2. All I wanted to do was take a sneak peek of what math would be like next. The only part I understood was when he showed the algebraic equation 🙃 what is math
Hey, not a bad idea, but you took a bit of a leap here :D You might want to look over (limits and) derivative calculus first, and then you'll understand this a bit.
hahaha I have a calc AP test in 6 days and I don't even know what this is.
In addition to derivatives, you will need integrals and limits to understand differentials. Without them differentials cannot be understood.
CE student here, and I'm also taking a sneak peek of what's coming.. :'>
WHAT IS MATH?! TEACHER DONT HURT MEEEE DONT HURT MEEE NO MOREEEEE DUN DUNDUN DUNDUN DUH DUH
The main thing that I like about the Khan Academy is that he makes advanced math that's usually difficult, a lot easier to understand to where anyone can learn and master what he's teaching.
My professor teaches for his first time ever, so his teaching is kinda awful and inefficient that I had to rely on teaching differential equations to myself.
thanks for the video! I'm taking a differential equation class, and my teacher skips all steps. Now I know what's going on lol
Teacher skipping steps? I guess it's time to skip your teacher's class.
A great video; I was highly recommended to watch your vids to improve my maths and I have to say you are great at explaining things. I look forward to the whole series of differential equations being this helpful! Many thanks
This is the second order differential equation
what is the difference between the first order and second order?
@@hahaha-zi1xf the order corresponds to the bigest derivative in the ecuation (if it has a second derivative then its a second order differential ecuation)
Sure, but he was just talking about what a differential equation is.
@@austinpundit6321 look at the title and say that again
@@dxalrado He's just talking about differential equations. It's an introduction. We don't care about the order yet. The concept already difficult enough without it.
"I'm assuming you've had a go at it"
Quite bold of you to assume that Sal
Too bad you picked "e" as the first example. "e" in itself is a more abstract idea.
I'm pretty sure I'm going to fail this class.
mikemustmurder pretty sure that i just failed my final exam in three months :')
did you fail?
@@darnelross6357 i guess so
did u fail ..??
I'm curious. Did you fail?
I’m cooked 🫶
When I hear Sal's voice, I automatically listen. I automatically want to learn and understand the lesson. From the years I've spent on khanacademy, he has become my everyday professor/coach when learning. I'm studying electrical engineering right now. Khan academy has its own professor in that department, but when whenever I go back to whatever Sal's teaching, it makes me feel happy to hear his voice.
Mistook this for ASMR for a bit there.
Why bro sound like DJ Vlad?😂
I have no idea what's going on here or how I got here.
What's the point? You gave 2 examples for functions that would work, but didn't actually explain how we get to those said functions in the first place
The point is to show some examples, and to showcase how taking derivatives and adding them isn't anything too scary. It's an introduction, not a full explanation of the subject.
Why are Math teachers so bad at explaining things? Not you, Sir. You seem intent on conveying something.
I was literally abused by my math teachers. Not a word about what "this " might be good for in the "real world".
Bad teachers are "baaaaad news"!
I just figured out a great way to study math at school: Watch videos on the topic to get more insight, intuition and curiousity. This is definitely one of the elements that modern educational systems lack, namely recommending great youtube videos!!!!
Why is your voice oddly so good...
Ikr!
I need to review the chain rule of derivative to understand the calculation.
All it’s about is dealing with derivatives of a composition of functions, i.e. functions wrapped inside other functions.
If you’ve got a function of x like
f(g(x)) then the derivative is f’(g(x))*g’(x)
Example:
Derivative of (sinx)^2
= 2(sinx)(cosx)
Finally! a new playlist for differential equations, I've been waiting for a year.
Love the way you explain each step
Easy to understand
Keep up the good work
I still need to watch this again a couple of times. Because the information just easily flew out of my mind the first time i watched this.
Here's an explanation of differential equations for people who already understand differential equations.
One thing that annoys me about differential equations as they are often presented is that they omit specifying what's a function of what.
What helps me keep the eye on the ball is this idea:
When solving a number equation, like x^2 = 4, you're really describing the set { x in R | x^2 = 4 }. One description is to list all the elements: { x in R | x^2 = 4 } = {-2, 2}.
When solving a differential equation, you're describing a different set, such as the following:
{ f: R -> R | f'(x) = f(x) for all x in the intersection of the domains of f and f' }
or
{ f: R -> R | f''(x) + 2f'(x) = 3f(x) for all x in the intersection of the domains of f, f' and f'' }
and so on.
I have a proof using only ideas from my one-semester real analysis course, without Taylor series, that if f' = f (where f: R -> R) then f(x) = f(0) * e_x where e_x := lim (1+x/n)^n as n -> oo.
In other words, { f: R -> R | f' = f } is a subset of { f: R -> R | f(x) = f(0) * e_x for all x }. I have only proven that f(x) = f(0) * e_x is a constraint that can be satisfied if f(0) = 0 [implying f(x) = 0 for all x]: I have not proven that non-zero solutions exist, only how they must look _if_ they exist.
This is a less precise description of the set { f: R -> R | f' = f } than I would like, but it's a start.
Yes it checks out, but how did you arrive to the solutions?
you divide the digit that has the y or x by that number and then simplify both sides
you understand 5x means (5× x)
eg 3z=6 so
3 3
then simplify ,then you will be left with z=2 so that means 3×z which is 2 is 6
Oop my bad I'm only here because I'm a huge SIMP for this man's voice...
Likeeeeee omg
This is a good refresher so far. Took diff eq ages ago in college and always felt depressed that it was one of those use it or lose it things and wanted to try and get it back.
After watching a truck load of introductions to differential equations... finally one that makes sense!
A question, are there any lectures/materials that I should look at before I look at this?
At 4:08 I have no idea what he is asking me and how I am supposed to do it.
You should look into derivatives. He y' is the first order derivative of y, and y'' is the second order derivative of y. y in this case is e^(-3x). To learn how to find the first and second order derivative of e^(-3x) make sure that you learn the chain rule part of derivatives as well :)
You are doing a great stuff by spreading education!
Hats off!
Iam about to take this subject next sem! wish me goodluck! just starting to learn... Imma update you guys how I did after this incoming sem. BTW, Im a CE student from Ph. Best of luck also to those engineering students! we can do this!
Best of luck. Im gonna take this subject too. IE student from ph.
Bruh i’m grade 12, and planning to take ece, we have De this sem uwuuu from philippines too
so, how is the course? I also consider taking DE next semester...
Im an ME student from Philippines. I have my Calculus 1 this semester.
Same wd you bruh, God Bless Us
your videos are by far the most helpful!
Could someone recommend a path from algebra to here? I am good at algebra, like in school I could graph in my head. Not kidding. But I want to understand this and I’m a wee bit ill equipped
Thank you for this. I managed to get all the way thru university and get my math degree without taking a single course in Differential Equations. At the time I didn't care because my work only involved theory, but now I regret it because I'm more interested in applied math and physics...
BAKIT AKO NAG ENGINEERING? 😭😭😭😭
he just said "that is the start"...hmmm i wounder how the end will look like!
what is the software is he using to write?
paint
@@TheRayll no... It's not.
Classic khan academy stuff its iconic right?
man, it never really clicked til you said it but of course the solution would be a function... just like for x's it'd be numbers.
Please I need help in this problem
Y"*Y^2=-K^2
WHEN :t=0,Y=A,Y'=B,Y"=C
Thank you. This is great and helps me understand . Can you let me know what tool you are using to draw and illustrate in your presentation?
What you do not get? Oh where does he get the y = e^(3x) from? He forgot to said: it is given? And then to said oh the solution is equals to itself is not correct?
wow ican finLLY WATCH A STUDY VIDEO WITH LIGHTS OFF ALSO
Ummm for the quadratic x is being used as a derivative version so....
Engineering brought everybody here
Me: Economics brought me here😮
why all genral solutions of diff equestion contain e to the power some thing interms of x
This isn’t true. Exponential functions just happen to be the type of solutions to the DE examples Sal gave in this video, which are second order constant coefficient DEs.
what software and hardware are you using to write with? it looks nice
where general solution of diff equetions come from
marian mortada
A differential equations class will teach you the derivations for all sorts of methods to solving different types of differential equations. Most DEs cannot be solved by simple separation of variables as taught in your first calculus class.
thank you Mr kahan .. i cant do anything without your amazing channel ♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Your handwriting is excellent.
Lopez Maria Brown Richard Garcia Anthony
Bruh why you fundraising you make money off UA-cam
Brown Robert Hernandez Sandra Lewis Thomas
Its summer time yet here i am hoping id learn something so i can even have 30% chance of passing. Coz rn my chance of passing is 2.5%. Hopefully, id make it.
i don't learn anything :(
Why
@@letoheeo3970 why not?
@@Sibearian_ what degree you had or have u been studying?
Didn't understand a single thing. Waste of time.
Taylor Maria Lee Kimberly Davis Matthew
hey guys who has taken it before hows this class overall? how u compare it to calc 1,2,3
From what I've heard from upperclassmen, Calculus II is by far the hardest math class so far much easier than I and III. They also refer to Calculus II as "Learning Witchcraft" or "This is Fake Math".
KzDM I’m taking it now turned out that is a sweet math man ..diff eq is so much fun!
هذي معادلات تفاصليه اخذتها كيف ؟؟؟
how did you come up with the value of y that would satisfy the equation? i wanna know how exactly it is to find the solution.
That's how solution works, you basically try and try and try till it works, the assumed y= to e-3x is just a result of experimenting and in differential equations you don't necessarily "solve" u simply try to prove that this Y NEED to be this (=). SO u can substitute whatever u want and in the end u'll reach e-3x is the most suitable substitute, u can try anything from negative infinity to the infinity of null
I hate maths 😭
But you've come this far???
i wish there was highschool college where you would take college courses on a highschool schedule. so like an hour- 2hours a day, everyday, for a year. i would be so good at differential equations. i wish i had the time to love math the way i did in highschool
Wait how does he know that y=e^-3x is a solution to the problem? How did he come up with it?
It is just an example, so he prepared it beforehand. But I assume he explains the process of finding such solutions later. I will try to explain how I'm thinking about this, but I'm just starting with differential equations myself.
It is quite analogous to the algebraic equation of the form x^2 + 2x = 3... which we can rewrite as x(x+2) = 3. The solutions to it are -3 and 1. So we can place those into the function e^x in front of x. Because of how the "chain rule" works (especially with e^x), we effectively just add another "times -3" whenever we take the next derivative.
I hope this was at least somewhat helpful to someone!
I founded it useful in modeling and spreadsheet?
❤
This is an amazing introduction to differential equation. I am taking the course this year.
I could’ve taken this in HS…
What i love about math is that the learning is recursive. I wanted to understand differential equations. Now im trying to figure ot how y becomes e and what are first and secon derivatives. F* me.
My dude if you don’t know what derivatives are you shouldn’t be in a diff eq class. This isn’t an insult- you really should have zero way of getting into diff eq without taking at least two calculus classes first
@@richardgarrison8328 I'm not in any class. I just took a weekend project implementing a neural network backpropagation algorithm. The problem is that english is not my native language and I went to school long time ago. So I'm facing the issue wrapping my head around the logic here and re-educating myself in english :D
The local resources have not been too helpful.
But Here I'm not trying to disrespect anyone. I was just in a low point where I had been watching videos and searching up on diff eq's, etc for few days already and just didnt find the "beginning" node of this journey. And here I realized again that I need to go an find some primer to this video.
All good :)
How is this an introduction without explaining what a derivative is?? Isn't that like the core concept which this describes? Idk imma look further.
This stuff is way after derivatives. It is assumed that you can handle derivatives quite easily by the point you come to differential equations.
Imagine if we were learning about exponents, right? When teaching it, you assume that the students already know multiplication and addition. This is the same sort of case here.
Don't be scared by this, if you haven't gone through derivatives. Differential equations should come later, when you are more comfortable with them. :)
@@vez3834 Thank you for the explanation.
My college algebra teacher has us trying to learn this almost right at the start of the semester. I signed up for algebra.. why are we starting with calculus :(
And I thought computer programming was hard. You lost me a derivative, and yes, I'm Asian, just not the math-smarts kind.
you're probably not asian
True, I don't think he knows he's actually a cat.
Haha, being lost at derivative... you got a looooong way to go.
Better be a good Karate student if you are not smart.
Why am I paying for college again?
Thank you. I was so confused when my professor was teaching this because I thought the second derivative was an 11th power lol.
Z y z
Not a al zebra
Know straight cut.
I’d be lying if I said any of this made sense to me.
Power series expansion method is my favorite way to solve a differential equation
THis is the BEST video explaining DE, it has finally made me understand them. Thanks a lot :)
To be honest not very insightful nor explanatory in nature. The lesson should explain why and how rather than stating names of things written on the screen
Okay .... What is a samential equation?
So, newbie question, how/why did e just suddenly and magically appear??
Because, i'm from Indonesia..
I THOUGHT I WOULD NEVER UNDERSTAND THIS