❖ Mixing Problems and Separable Differential Equations ❖
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- Опубліковано 28 вер 2024
- Mixing Problems and Separable Differential Equations.
In this video, I discuss how a basic type of mixing problem can be solved by recognizing that the situation is modeled by a separable differential equation.
You are the main reason why i passed calculus 1, 2 and 3. Whenever i have a classmate that is struggling, i'd always tell them to watch your videos. Thank you so much, patrick!
I like that
dude doing the same, from high school till college
Same, and now hes the reason i'm gonna pass DifEQ too
@@stephendavis1837 Read your book and understand the example problems, then work problems from the book until you feel comfortable. That's how I got an A by teaching myself Diff EQs. I know you're probably done with the class now though.
May I say that you are AMAZING, omg finally I found someone that talks in my language. Professors usually skip a lot of steps assuming we know them!!! but your videos makes a lot of sense, that a lot, SUBSCRIBED
I've always wanted to know why calculus textbooks always had this big hard-on for big tanks of brine. My textbook literally has a problem exactly like this... with brine. Anyways, you quite literally are the best math teacher on UA-cam in my opinion. You're the reason I get by in engineering. If I could, I would donate. Keep being awesome.
you and the khan academy guy should team up and be the kings of online education
professor leonard too ;)
don't forget professor dave, blackpenredpen and the organic chemistry tutor!
I've been struggling with the modelling of equations exactly like the one you explained in your video for quite a while. All thanks to your amazing teaching ability, I can now do mixing problems flawlessly. Thanks Patrick!
Thank you so much for filling in the gaps left by my Professor.
Your videos from 2010 are getting me grades in 2018. Can't thank you enough.
this was extremely helpful! We learned this in Diff. Eq today and i left class thinking it was so tough. You made it so much simpler. I swear im spending the rest of the semester studying your videos! Thanks!!
my professor completely blew through this stuff and my textbook is basically useless. Thanks for explaining it so clearly! you're a lifesaver =)
You're a great man!
I've watched these vids all the way through calculus and now I am in diff eq on my way for a degree in physics. You're a huge help, thanks!
Everybody kick in a few bucks to his Patreon, he deserves it more than most of our math professors!
@ermitz90 cause i am lazy and it is easier to write A instead of A(t).
it is the same reason people write: y = x - 3 instead of y(x) = x - 3
Thanks for making these vids patrickJMT. Keep it up!
I know it’s been 8 years but thank you so much for this video! Much clearer than my ODE class
you are most welcome!
you are an amazing human being
Thanks for explaining this in such a simple way . My DE exam is in 12 hrs and I'm confident now that I won't miss the tank problem 😆
this video is awesome still 13 years later thank you!
Can't imagine my math classes without u ! Thanks man
Wonderfully worked out example. I have terrible handwriting so my notes are often useless and the book skipped several steps including the part where I messed up, multiplying by e.
My prof only taught us to solve the resulting diff eq using an integrating factor, so I've never thought to use separation. That's gonna save soooo much time haha. Thanks man
thank you sir. your explanation is so helpful especially in online class. its funny how i didn't get this when my professor discuss but understand it well in your video. keep it up!
Could you do a problem where the volume of water in the tank changes?
you saved my day and I'm sure for many people as well. Thank you for the videos, they are very helpful!
Patrick could you also do circuits. (differential equation RL and RC circuits)
Great explanation
Thanks, you have made mixing problems a lot clearer to me.
Damn that sure is one mighty fine tank there, bud.
Brilliant!
@patrickJMT ...... How do benefit by making these videos?? It sure does benefit us, but how you??
hi
views=subscirbers=money
Thanks for this Patrick!
Sir, @05:25, it is clear that dA/dt=-A(t)/100; hence on integrating why doesn't the R.H.S. becomes (t^2)/200?
wow thanks!!! I have an exam today on this material and it really helped :D
good explanation, thank you! But can you expand your notes, I mean you write so much notes in little space
Make sure next video ( If it is a similar problem with same RATEin / RATEout ) that using the given volume is not always the case. If the rates are different then there will be a function for the volume
I have some question involving some mixture problems but I don't get it much: How many pounds of 35% salt solution and how many pounds of 14% salt solution should be combined so that 50lb of a 20% salt solution are obtained?
I tried to solve this using different equations but I'd come up with some negative answers...
hope it helps!
i am sending you brain waves right now just in case you are taking the quiz this very second....
my friend you are amazing as always
Great video with clear explanation. Thanks!
what do you do iffthe problem involves two tanks? the problem i have says that a tankA has say 200 L of water with 40 g of salt in it and tankB has 200L of water with 20g of salt in it. tankA drains into tank B at a rate of 16L per minute. tank B drains out of as spout at a rate of 12L per minute and out of a different spout, 4 L per minute, which this one feeds back to tank A. tank A is also filled by a seperate spout with pure water at a rate of 12L per minute. how do i work that out??
bless you patrick
i love your vids! they help soooo much! THANKS :)
imagine if patrick was your professor... every class could be 10 minutes
never!
thank you so much sir plz do another qestion same like qestion
Thanks man, really appreciate it! xoxoxoxo
this was really good thank you!
Awesome sir have enjoyed it
excellent
.
very helpful. Thank you
would you tell me if flow out is 5? how can i set up the ode? please answer me :) thanks you for good content.
thank you very much sir
Thank youuu!!!
What if the rate in and out is not the same?
Thanks Man. B
What happen to "t" why did you remove it? And what is the final answer? Why is it you final answer is an equation? No exact value? Please enlighten me.. I'm confused.
Thank you
Thank u so much Ppl i need help z there any 1 know a reference for deferential equations.! I neeed names
straight from my calc book. siiiick :D
thank you!!
You're elite!!!!!!!!!!
what about a parachutist or an iv drip? This makes zero sense to me and theres nothing other than these mixing problems on the internet
quiz on this tommorow
you are the best :)
greeeaaattt explanation !!
what about the rate in is not 0?
helps a lot
its good but i dont see the link? o.O
oh man... i had a quiz on this last night and i missed this vid...
no prize guessing how i did :(
I love you thank you
Can anyone explain why C can't also equal 15? Because technically if you 'e' both sides in order to solve for Q first, then c would equal 15. Thanks! @patrickjmt
lmao 1:58 its beautiful tank``
u know
problem was too simple to answer my question :(
20x easier
creepy...
10 years down the line and, your material is still relevant !
Great work, Patrick.
Calculus is 400 years old, and still relevant. His videos will likely be relevant for the next 500 years, assuming youtube remains for that long.
@@MrNukenin16 hahaha makes a lot of sense.
I love that the main ad you have is "That Tutor Guy". I haven't even followed the link! For YEARS I have had great success with your videos. Nothing against the other guy. No One on the internet explains with the same clarity and consistency as you.
Thank you!
I wish I had known about your tutorials sooner! So much easier to understand than my professor! Thanks a ton!
he makes it look so easy
what happened to your rate in (10L/min), it seems that you left that out, shouldn't it be dA/dt +A(t)/100= 10? Making this a first order linear diff eq instead of an easier separable equation?
i think it's pretty clear cuz it's pure water flow in, water has no concentration, so when you multiply concentration it cancels out. watch video carefully, if it's salty water flow in, then that's the case you are talking about.
great job MR. AMAZING
Amazing video!!!!!!!!!!!!!!!!!!!!!! :)
excuse me. Can u help me solve this problem? TQ
- A tank with capacity limit of 1000 gallons initially contains 200 liter of pure water. Then at time t = 0, brine containing 5 lb of salt per gallon is allowed to enter the tank at a rate of 20 gal/min and the mixed solution is drained off at a rate of 10 gal/min. How much salt is in the tank at the point of overflowing? (it says that the tank INITIALLY contains pure water, and at the same time, at t = 0,they pump the salt) so what should I do? )
I do some exercises of mixing problem like this, but the solutions write the denominator of rate out with the variable t. When the rate out part should have variable t? sorry for my poor english.
Nearly 10 years on, this video is still really helpful. Thanks bro!
This made a hell of a lot more sense than my textbook, thanks for the crystal clear explanations.
Thank you for your videos. I think it would be better if you talk a bit louder.
You're my hero.
Thank you
Fire!
Your explanation is very good. I'm only a sophomore in high school, and I understood you pretty well. Great video.
Thank you so much! You're so amazing!!!
Why your C(out) is Mass/Volume of the tank? In my class, my professor told that the volume of the tank would change as a linear function. so your volume should not be constant.
I feel like your fucked if you have an initial concentration. Then you have dA/dt = (x)(y) - A(t)*z which is now not separable.
i like math
you are the man!!!..best math teacher out there!!,,:D
Thank you!
I just came across these. So much easier to understand now.
You can also skip the separation of variables by using the characteristic polynomial.
A’ + 1/100 * A = 0
R + 1/100 =
Root = -1/100
Y = ce^(-1/100)
c = A naught = 15
15e^(-1/100)
If it weren’t homogenous you could also use undetermined coefficients to find y particular and add it to the homogenous solution.
Good video
mas madali pato kaysa sa prof ko
Thanks Patrick I was struggling substitute the initial condition but now I am ok many thanks please keep up can you also cover the complicated lakes problems please ? I could not understand them thanks