Substitutions for Homogeneous First Order Differential Equations (Differential Equations 20)
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- เผยแพร่เมื่อ 1 ต.ค. 2024
- / professorleonard
Exploring Homogeneous First Order Differential Equations and a substitution technique that changes them into solvable separable equations.
Professor Leonard needs a Netflix original series
yesssss
I think he's in the first season of Altered Carbon (Joel Kinnaman)
[ASMR] Swole smart math boyfriend puts you to sleep while giving you a lecture about Homogeneous First Order Differential Equations.
hahahahahahahahahahah :'D
BHAHABAHAHHA PLZ-
LMFAOOOO
No matter how much i search for it
You are the only teacher i can understand calculus to
Even tho im not a native english
One great thing about Professor Leonard is that he always gives several straightforward example problems fairly early.
Most of my math teachers have stood and rambled on forever about proofs and theorems and confusing crap, and then they MIGHT have given one example problem - and it was always a very long, tedious problem, every single goddamn time.
Though I understand your pain, you should also be thanking your teachers. Many students dislike math because they don't know why they're doing it or where it comes from. Many teachers only give several examples and call it a day. When learning math, it's always important to know the derviation of the formulas you learn, and why certain concepts are the way they are. Any college student here would perhaps agree on this.
@@parinpatel5719 That's only useful when we can understand the proofs, and even then they're only really good for math majors. Professor leonard makes it clear what to do with it as a tool, and that's what engineers see math as.
@@pedrosantana3283 Leonard shows the derivation through his lectures. He spent an entire video explaining what exact solutions are and how they're derviaived. So I think hes a perfect blend of teaching theory and giving examples. Blessed we are to have this resource. I cannot find anything of this quality for real analysis or theoretical optimization. Im scared to attack abstract algebra and topology, since there isnt a professor leonard for those subjects... honestly.
Thank you for warning us about anger! This is the first math class that I really was infuriated by it. I'll take your advice and take a break when I feel angry. :)
ya I'm glad he said it too because my professor for this course seems to enjoy us getting frustrated and angry. He actively pursues it and without Professor Leonard I would have given up on this class by now.
The main thing I got from this video "When you get angry at your math, it's ok. Walk away, take a break and come back to it later." I felt this.
Same but I never come back
Jesus christ, those mathematical arms 😍
😂😂
i laughed way too hard at this
Looool
he is literally teaching me and give me motivation after the video to go gym. who needs more than that?
I like it when Henry Cavill is teaching me.
the gains on this math lad
Man this is so much simpler and more understandable than the way I was taught in class. I went from tearing my hair out, to solving these problems rather quickly. Thanks Leonard. ps As an extra benefit I find myself not just more motivated to do math but also to hit the gym, I wonder why that is.
Gym lectures
Yep, I'm still waiting for this guy to drop his training routine
when i listen to it in class, i think im the fish out of the sea. Here after watching i think i know kungfu
You deserve to pause my AdBlocker for you, you are a great man!
Do you work out, Professor?
*brofessor
Dominik B nah, he got that body by finding limits.
El Nieto PR lmao 😂
@@ElNietoPR lol
I got you , you are superman no more hiding clark
Leg day? More like math day #nodaysoff
For 1:05:08, you talk about domain. When you say x*y>0, why can't y=0?????
your teaching approach is so unique and wonderful. the last time I check no mathematics teacher would make this topic as easier has you have made it. I am so grateful professor keep doing this Good work for the world.
The most hated first order differential equation in my book.
I don't understand how you can do that x into the square root of x^2? why is that allowed?
Thank you always professor, always love the pep talks too ❤️❤️
Thank you professor. This lesson helped a lot.
my man you are built like a brick house, thanks for the lesson too
Wow this was so clear and helpful! I am very grateful for this excellent video!!!!
Finally I understood. Thank you so much professor Leonard :)
This channel may have saved me this semester, also why is no one commenting on how absolutely YOKED this man is?
Thanks especially for the final segment concerning domain restrictions. It's not just nit-picking; over the years I've seen many practical cases where lack of attention to this detail have produced incorrect or incomplete results.
Absolutely, and I'm glad you enjoyed it. Lately, I've been of the mind to get the technique understood first and then, once that's mastered, to explain the finer points of what's really going on "behind the scenes" so to speak. Students seem to grasp the domain restrictions better once they have mastered what they are actually doing and why the are doing it. Thanks for watching!
Your approach does seem like the most effective plan. Even a quick mention early on that there are details to be examined later is enough to damp down a tendency to ignore them. Thanks again!
come teach at CSU PLEASE!!! my professor is so hard to follow that I watch your videos during class time rather than go to class and I gain SOOO much more comprehension. THANKYOU!!!
He never tells us what is implied by the term "Homogeneous".
Hey professor,
First, I would like to thank you for teaching us.
Second, I have only one problem with this method (I know I am the problem, not you).
For example, the following problem is really difficult to solve using the method I learned from you. Or maybe I am doing something wrong? But when I searched for a solution, all the solutions I have found are using different methods for the specific problem I am facing.
x dx + (y -2x) dy = 0
Would love to be able to solve it using the method I learned from you.
I think every professor should tell their students your speech about getting angry. I have noticed time and time again when I get angry, I am no longer taking in any information. I have to walk away!!! Thank you for always being so awesome Professor Leonard. I wish you'd come back and make more videos. I really could have used your help with Eulers method and then the improved Eulers method!
You can have a square root of 0 (which gives you 0). The only problem is with a square root of a negative number. Therefor you do need both x != 0 and xy >= 0.
Man, what pen do you use? I wanna get bulky arms too 😯
sir please discuss linear programming in your future video lectures and also linear regression.
This dude looking like a smart Jonny Bravo
Oh my gosh. Spot on.
Johnny Bravo's smarter younger brother.
PLEASE HELP ME UNDERSTAND.
Why is his definition of Homogenous D.E. different than everyone else's. That definition being f(tx,ty) = f(x,y).
I can't thank you enough for explaining things step by step. I wish all teachers were like you!
Then all the gyms in the world would be constantly crowded.
eipi plusone lol you what I mean. I am talking about his teaching strategies here.
If power of x and y and the term xy is same in nominator and the denominator, it will be homogenous equation.
Those biceps are out of this world
A major zoo reported that a couple of their massive pythons were missing. Seeing Professor Leonard's arms and biceps, it is obvious where those pythons are hiding.
Wow
Just simplified this problem for me...
Never understood this in class 😊
I wonder what he thinks about the comments about his appearance. If it were a woman people might be more apt to call it objectification.
44:34 wow just when i was wondering if i skipped something or was at the wrong video a problem very similar to the one on my hw shows up lol, you're a god
Hello Professor Leonard, I know I'm late to the party, but I was wondering why you didn't completely solve for y (left it as y^2) during the first homogeneous example (somewhere around 33:00). If anyone wants to tune in and provide an explanation it would be greatly appreciated.
square root would make it + and -; we dont know if its positive or negative. Leaving it as y^2 is better when you have no values. He also kinda explains it 32:28
It's implicit
Thanks for another great lecture, Professor Leonard!
guys my prof told when x and y,s largest powers are equal then homogeneous can be used
At 36:55 I did the same technique but using property of square roots then exponents. Right away, I noticed \sqrt{xy}=\sqrt{x}\sqrt{y} since it was all over x I then used the property of exponents to simplify. Super cool to see how different brains process and think when working through problems. I am almost done with my BS in Pure math just going back to previous classes to not lose the skills. Thank you so much!
These examples are so neat and tidy compared to the monsters we used to get on exams.
Why does the derivative of y=vx is dy=vdx+xdv in our book(dx is included). Tried solving the first problem with same approach on our book but i cant get it. Welp
i spent hours trying to understand the book but you made it better
I'm lost in the first ten minutes.Using "function of.." I have no idea what you mean. While I understand what a function is, I can make no relation from what you're saying to what you've written on the board.
wham
I am confused. My teacher told me when I was doing the question x-y/x+y that the numerator and denominator have the same power, hence it's a homogeneous equation. Can anyone plz tell me if this approach is correct?
At 55:00 would it be wrong if you accidentally left the absolute value lines? Don't think it would really affect things, but can anyone confirm?
love this guy so much. I always feel dumb in my math lectures because all these professors have nothing on leonard... This is what education looks like^^
Leonard looking jacked. Never thought i'd still be watching you after 4 years of college
4 weeks from now? haha nice one, my final is tomorrow
When we are creating the y/x substitution don't we have the potential to be dividing by zero ? If how do we handle it ? just say x cannot = 0 ?
Do you even lift professor?
Homogeneous Leonard differential equation
1:03:43 but y could be zero so shouldn't we have the restrictions xy>0 n xy=0 n x not equal to 0 ?
At 53:00 Im a little confused with that split professor. Isn’t it ilegal to separate it since there’s more than one term in the denominator?
Sir ...God bless you and keep you, may He make his face shine upon you and your family.
dont even attend lectures in uni for diff. eqs. just watch these videos. Thank you so much for them!
Your reminder to not get angry about math (around minute 15) came at a perfect time!! :) Thank you!
I love him
Hocam kaslar fena ;)
professor would be great if you please start a trig series too!
What are you supposed to do if you get dv +v? How do you solve this.
Henry Cavill can teach diff eq?
for the second example problem, can you use a substitution v = y-x?
@ 17:10 when he says "is it linear ----- NO... kills me every single time
Man if my math professor is buff like him id prolly get A for all my midterms.
Every video, this man keeps getting buffer. Soon he will be the hulk
is this variation of parameters?
i learned this as derivative+func of deriv*x= x then let the rhs equal zero to find its solution.....that constant that the homogenous equation comes with is treated as a parameter ito x again and..."varied" i guess xD but i was shown this algebraically and also this was the first thing i learned after learning about vector fileds in chapter 3....wtf XD these videos are so useful man they relay more humanity to the super-optomised jargon in the textbooks.....uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
jesus dude i just properly thought of the implications of this.....if that first constant i find from the homogenous equation is just randomly set equal to y/x isnt that weird??
wait they say "a sepcial case of a method called variation of parameters"
wait dude so this is a method for y/x? or x/y but ur definition of homogenous is way different from mine
stilll learned how to tell if something is a function of something else>>v is functiuon of x cause v=y/x therefore divide by x? makes function of x
it nice explanation but it takes lot time
It’s hard to concentrate on the math! 😍
You're a wonderful online lecturer, which is hard to do. Thanks for teaching me DE Professor Leonard
Elegant solution! So simple yet so useful! Thank you!
thanks from Brasil
What if you squared at the begining prof plzz respond
شكرا لك
Here’s a John Bravo for you
You’re the best!
didnt know magic mike needed a math sequel but zayum
I'll bet his classes fill quickly. He's the best I've seen.
man looking like clark kent
Blast from the past! 😎
I am from india
homie is YOLKED!
To my book this is art not math ! Thanks professor!!!
Biceps lookin' extra swole today
you are very handsome
the move at 46:00 when you divide by x, doesnt (dy/dx) get divided by x as well?
No
You divide the numerator and denominator by x on the right hand side... no change needs to happen on the left side because (1/x ÷ 1/x) equals 1
you are a godsend.
clark Kent always does it or me ...from south africa
There is a homogenous diffy q that is dy/dx =x+y that is very difficult to rewrite in that form. Do you have any examples of how to do that?
just a linear DE: y' - y = x
Big bisep
I owe you my degree
1:04:20 About domain issues, should we not also include y/x != 1?
And one minute later, I realized that it is given by the x-y != 0. Always nice when I answer my own questions on youtube. No one else ever does it:-)