You are absolutely FANTASTIC!!! You taught me in less than 15min what my Phd professor with 40 years of teaching experience could not in 2 hr and 15min. I am beyond thankful for you to take the time to make these videos and post them here to help others.
your hard work in videos is really impressive and appreciable your videos are also very simple and giving more than two examples makes it really easy and clears the concepts you are doing well keep it up :)
Bonjour. Is there a way to visualize what this condition really means, please ? I get lost when I imagine a surface with its slopes and "concavities" across x or y directions. Can we say "doing this first and then that is the same as doing it in reverse order" ? And also, what can be said about the differences in shapes when the condition is met or not ? How does it translate into surface property ? Is there a kind of symetry involved somewhere ? I realize my question is fuzzy, but I hope it is still understandable. I'm trying to "see" things, and here I don't succeed.
So if the differential equation is exact, the cross derivatives are equal. But does it necessarily mean that if the cross derivatives are equal, the equation is exact? PS thank you for your great videos :)
Linear: dy/dx + P(x) y = Q(x) Exact: M(x,y) dx + N(x,y) dy = 0 dy + P(x) y dx = Q(x) dx P(x) y dx + dy = Q(x) dx If M(x,y) = P(x) y, N(x,y) = 1, and Q(x) = 0, is it Linear AND Exact?
Good question! :) I'd say, in that case, it could be rewritten/rearranged to be similar to both forms, but I also suspect that the differential equations satisfying all of the conditions you wrote could be solved similar to a separable differential equation . . . P(x) y dx + dy = 0 P(x) y dx = - dy . . . to solve this differential equation, I'm somewhat certain that you could just divide both sides by y . . . P(x) y dx = - dy P(x) dx = (-1/y) dy . . . this seems to separate the variables, allowing the one tasked to find the solutions to integrate on both sides! :) ∫ P(x) dx = ∫ (-1/y) dy ∫ P(x) dx = - Ln | y | + C1 Overall, if my deductions & steps were correct, we'd get the following general solution: y = C / [ e ^ ( ∫ P(x) dx ) ] Hope this helps! Sorry for seeing & answering this 6 years late; still, stay curious! :)
blackpenredpen It says: let f(x) = e^(bx) and g(x) = e^(ax) (a # b, 0, 1, -1). What is the value of b, expressed in terms of a, such that "the quotient of the derivatives of f(x) and g(x) is equal to the derivative of their quotient"? very fun problem, it gets hairy and then a lot cancels out.
Linear: dy/dx + P(x) y = Q(x) Exact: M(x,y) dx + N(x,y) dy = 0 dy + P(x) y dx = Q(x) dx P(x) y dx + dy = Q(x) dx If M(x,y) = P(x) y, N(x,y) = 1, and Q(x) = 0, is it Linear AND Exact?
You are absolutely FANTASTIC!!! You taught me in less than 15min what my Phd professor with 40 years of teaching experience could not in 2 hr and 15min. I am beyond thankful for you to take the time to make these videos and post them here to help others.
This is EXACTLY what I was looking for!! TYTY!
i realize I'm kinda randomly asking but does anybody know of a good site to watch new movies online ?
@Maximilian Julian lately I have been using FlixZone. You can find it by googling =)
@Maximilian Julian i would suggest Flixzone. Just google for it =)
your hard work in videos is really impressive and appreciable
your videos are also very simple
and giving more than two examples makes it really easy and clears the concepts
you are doing well keep it up :)
I'm from Egypt and I'm Studying my curriculum with you
best explanation on the internet by far
wow what a banger video! i learned so much!
Wow me too!
I've been struggling with this - it makes sense now. Thanks!!
rocking that supreme
Yup!!!
you are saving my test, thank you so much!
thank you sifu,so helpful
Showing Clairaut's Theorem holds true for the function coefficients on the differentials... Got it!
your videos are the best
So very clear!!!!!! Thank you!
Thank you for the help. Your video is easy to understand. keep it up!
amazing~! every DE student should be here lol
Very good
"exact" here what's it mean?
Thanku soo much sir 🙏🙏
How do solve “non-exact” ODEs, then?
Parametrisation?
I think you should also say something about simple but important equation
y/(x^2+y^2) dx - x/(x^2+y^2) dy = 0
I think that's one of the HW questions that I actually have another vid for it.
Can you teach us Linear Algebra?
sorry, prob. not anytime soon
Are still exact even in opposite sign?
I loveeeed!!!!! Thanks
Hey, I was just wondering why the condition for exactness is ∂²/∂y∂x(N)=∂²/∂x∂y(M).
PS. LOVE your videos
i think ∂M/∂y=∂N/∂x means that F is a consevative function
Actually, checking the if the mixed second derivatives are equal or not is not enough to say that we are dealing with an exact differential.
Bonjour. Is there a way to visualize what this condition really means, please ? I get lost when I imagine a surface with its slopes and "concavities" across x or y directions. Can we say "doing this first and then that is the same as doing it in reverse order" ? And also, what can be said about the differences in shapes when the condition is met or not ? How does it translate into surface property ? Is there a kind of symetry involved somewhere ? I realize my question is fuzzy, but I hope it is still understandable. I'm trying to "see" things, and here I don't succeed.
hi, u visualize maths? i kinda just do the maths not knowing what is happening, rip
@@nandogouveia6904 go check 3b1b if u want to visualize it
So if the differential equation is exact, the cross derivatives are equal. But does it necessarily mean that if the cross derivatives are equal, the equation is exact?
PS thank you for your great videos :)
A differential equation is exact if and only if the cross derivatives are equal. Wikipedia has a proof.
Linear: dy/dx + P(x) y = Q(x)
Exact: M(x,y) dx + N(x,y) dy = 0
dy + P(x) y dx = Q(x) dx
P(x) y dx + dy = Q(x) dx
If
M(x,y) = P(x) y,
N(x,y) = 1, and
Q(x) = 0,
is it Linear AND Exact?
Good question! :)
I'd say, in that case, it could be rewritten/rearranged to be similar to both forms, but I also suspect that the differential equations satisfying all of the conditions you wrote could be solved similar to a separable differential equation . . .
P(x) y dx + dy = 0
P(x) y dx = - dy
. . . to solve this differential equation, I'm somewhat certain that you could just divide both sides by y . . .
P(x) y dx = - dy
P(x) dx = (-1/y) dy
. . . this seems to separate the variables, allowing the one tasked to find the solutions to integrate on both sides! :)
∫ P(x) dx = ∫ (-1/y) dy
∫ P(x) dx = - Ln | y | + C1
Overall, if my deductions & steps were correct, we'd get the following general solution:
y = C / [ e ^ ( ∫ P(x) dx ) ]
Hope this helps! Sorry for seeing & answering this 6 years late; still, stay curious! :)
Hi did you study in the MIT?
Erwin Rules Rojas I went to UC Berkeley for my undergrad.
Did you study applied math, physics or just pure math?
Love your videos btw.
Can I send in a math for fun question? I thought it was a fun question. I will write it tomorrow if I can
Sure. hopefully I know how to solve! = )
blackpenredpen It says:
let f(x) = e^(bx) and g(x) = e^(ax) (a # b, 0, 1, -1). What is the value of b, expressed in terms of a, such that "the quotient of the derivatives of f(x) and g(x) is equal to the derivative of their quotient"?
very fun problem, it gets hairy and then a lot cancels out.
Sighmaniac RotMG What does (a # b, 0, 1, -1) mean?
N0tY0ur4v3r4g3N0th1ng # is not equal to
Sighmaniac RotMG So f ' (x) / g ' (x) = [ f(x) / g(x) ] ' ?
Math 201 University of Alberta
superp
😂😂😂😂😂😂😂😂😂for me.......
Is he a Korean ?
His screen in the previous video suggest so!
chinese
Linear: dy/dx + P(x) y = Q(x)
Exact: M(x,y) dx + N(x,y) dy = 0
dy + P(x) y dx = Q(x) dx
P(x) y dx + dy = Q(x) dx
If
M(x,y) = P(x) y,
N(x,y) = 1, and
Q(x) = 0,
is it Linear AND Exact?