@@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.
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!
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.
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.
@@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
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
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!!!!
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.
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.
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.
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...
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!
@@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.
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._
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.
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!
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 :)
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)
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.
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
that silent chain rule you mentioned helped, i laughed 'cause indeed the derivative of e^x is "1" e^x and will repeat in the 2nd derivative. gonna stick around for some more khan videos, prep for college and first at math is differential geometry, this video is just 1% of the entire math146
Probably one of my hardest class during my second year of engineering. I thought I was pretty good with calculus but this one killed me. Dont know why I was so slow. Literally passed this class because of how nonchalant my prof was. Dude was super smart and taught great but dont give af about tests. 10% midterm 12% finals 20% attendance and the rest were just assignments 😂
just like me, from the first meeting until now it's almost close to the final exam, I still don't understand this and I'm worried if I don't pass this class lol
Subtract 1 from exponent only if the base is the variable (not e or other number) and if the exponent is a constant and not an expression having the variable in it.
He is using the chain rule, which doesn't include a subtraction of the exponent. f(x) = e^x and g(x) = -3x chain rule: D f(g(x)) = f'(g(x)) * g'(x) so... because f'(x) = e^x and g'(x) = -3 D e^(-3x) = e^(-3x) * (-3) = -3e^(-3x)
@@aryonugroho6690 He is using the chain rule, which doesn't include a subtraction of the exponent. f(x) = e^x and g(x) = -3x chain rule: D f(g(x)) = f'(g(x)) * g'(x) so... because f'(x) = e^x and g'(x) = -3 D e^(-3x) = e^(-3x) * (-3) = -3e^(-3x)
Thank you so much! My teacher seems to be in a rush all the time and he didn't take the time to explain us what DE's were like you just did. Thank you.
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".
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😭
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
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.
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.
"I'm assuming you've had a go at it"
Quite bold of you to assume that Sal
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
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
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
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!!!!
Finally! a new playlist for differential equations, I've been waiting for a year.
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.
After watching a truck load of introductions to differential equations... finally one that makes sense!
I used to watch these vids for GCSEs I'm now doing an undergraduate and I'm still here, who says RUclips is a waste of time smh
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.
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.
your videos are by far the most helpful!
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
You are doing a great stuff by spreading education!
Hats off!
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.
Love the way you explain each step
Easy to understand
Keep up the good work
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...
I really appreciate that these lectures explain everything in simple words, don't skip any steps, and do not talk down to you like you are stupid.
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
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.
Your handwriting is excellent.
This is an amazing introduction to differential equation. I am taking the course this year.
this guy`s sound is perfect to teach anything :)
you lost me at 0:01
THis is the BEST video explaining DE, it has finally made me understand them. Thanks a lot :)
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._
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 has been my best introduction to differential equations ever🙏
So simple and straight to the point. Thanks.
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!
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 :)
looks so hard, but actually so simple....*Mind blown!!!
Khan Academy knows everything
This discussion is so much live. I mean this discussion has a life to make us understand.
swear this is second order, not first
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)
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
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
Wow. Finally I know now that the solution of diff.eqs are functions. Gee! Good job! A math mystery finally lifts! Not that I can solve any, haha!!
I’m going to ace this class fr
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
Why is your voice oddly so good...
Ikr!
I rlly love this and i am actually understanding this... even tho im in year 6
thank you Mr kahan .. i cant do anything without your amazing channel ♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Here's an explanation of differential equations for people who already understand differential equations.
that silent chain rule you mentioned helped, i laughed 'cause indeed the derivative of e^x is "1" e^x and will repeat in the 2nd derivative. gonna stick around for some more khan videos, prep for college and first at math is differential geometry, this video is just 1% of the entire math146
hi bestie thanks for the help. love ur handwriting.
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
Thank you. I was so confused when my professor was teaching this because I thought the second derivative was an 11th power lol.
Thanks, done watching.
Probably one of my hardest class during my second year of engineering. I thought I was pretty good with calculus but this one killed me. Dont know why I was so slow.
Literally passed this class because of how nonchalant my prof was. Dude was super smart and taught great but dont give af about tests.
10% midterm
12% finals
20% attendance and the rest were just assignments 😂
just like me, from the first meeting until now it's almost close to the final exam, I still don't understand this and I'm worried if I don't pass this class lol
this is going to be a bumpy ride
This was a great introduction! Thanks!
6:01 why didnt he subtract 1 from 3x for the exponent of e^-3x when he took the derivative? Isnt it just the chain rule?
yeah i'm asking the same
Subtract 1 from exponent only if the base is the variable (not e or other number) and if the exponent is a constant and not an expression having the variable in it.
He is using the chain rule, which doesn't include a subtraction of the exponent.
f(x) = e^x and g(x) = -3x chain rule: D f(g(x)) = f'(g(x)) * g'(x)
so... because f'(x) = e^x and g'(x) = -3
D e^(-3x) = e^(-3x) * (-3) = -3e^(-3x)
@@aryonugroho6690 He is using the chain rule, which doesn't include a subtraction of the exponent.
f(x) = e^x and g(x) = -3x chain rule: D f(g(x)) = f'(g(x)) * g'(x)
so... because f'(x) = e^x and g'(x) = -3
D e^(-3x) = e^(-3x) * (-3) = -3e^(-3x)
what software and hardware are you using to write with? it looks nice
nice video sir..nice explaination
There exists a set of an infinite number of solutions to an ODE. Reply with an equation that satisfies the above statement .
Nicely explained!
Mistook this for ASMR for a bit there.
Straight to the point explanation. Good work..
Amazing explanation
yay a 7min video
Thanks bro. 🔥😎
that was really useful
here for my midterms, pls pray for me.
same
Amazing ❤
Thank you so much! My teacher seems to be in a rush all the time and he didn't take the time to explain us what DE's were like you just did. Thank you.
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?
Oop my bad I'm only here because I'm a huge SIMP for this man's voice...
Likeeeeee omg
I got it. thanks!
This is quite late question but at 4:52 shouldn't that exponent be 3x-1?
No, e^x is a special function. The derivative of e^x is e^x. E^-3x Requires chain rule
Yeah, learnt that few weeks ago and now afterwards that seems a very dumb question
Boom! Mind blown.
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.
what is the software is he using to write?
paint
@@TheRayll no... It's not.
Classic khan academy stuff its iconic right?
Thank you very much
thanks to make this video
Is it order 2 here isn't it ??
S
the derivative of e^x is e^x
Very clear and simple introduction of "Differential equations" 😊👌
Cool intro to DEs! 😂
Power series expansion method is my favorite way to solve a differential equation
good job, Thank you
I have a request.
Can you arrange the playlist by what order to watch these please?
Thank you very much.
he just said "that is the start"...hmmm i wounder how the end will look like!
Watching this for fun 😅 how did I become this way
in what job industry (or job title) are differential equations useful for?
+idknuttin as omar said but some specific examples are heat transfer (the movement of heat across a membrane) for chemical engineers
+idknuttin Circuit calculations for Electrical Engineering.
Trial SPM P7 or P8
SPM C6
Sealed.
My man Sal. Saved me from a breakdown just now.
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.
very good!
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 ؟؟؟
can u teach us how to function our brain like yours?
Learn the Feynman Technique pre. Repetition until you mastered it is really the key.
Thankyou sir
may god help us all
You can take -3x as x and it will be the same right
Thank you!