Newton's Law of Cooling // Separable ODE Example

How can we model the change in temperature of an object, like a cup of tea? In this video we explore Newton's Law of Cooling, which is a separable differential equation. We are going to do a bit of experimental data collection (measuring the temps of my coffee mug) along the way to see how good the model is. To solve this ODE we use the method of separation of variables. However, because there are multiple constants involved, we need to record temperatures at at least two different times to be able to solve for them.

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[NuclearPhysix]

I left university some decades ago. I do not recall anyone giving a practical use case for differential equations as you have just done Dr Trefor. You are amazing

[question_chaser]

Sir, you made more sense in 10 minutes than my 6 week of my D.E. lectures. Thanks for your commitment.
Best,

[pinkpopcorn]

This video is good, I saw ODE for the first time today, couldn't understand why we were using it or how useful could it be, but my math teacher was like "It would be good for you all to go home and do some research, examples and see how important this topic is for an engineer", in my country education is very hard to get and even the good ones (I am having now lol) isn't even close to extraordinary, it should be more like you did in the video, but we as students are not prepared enough (we don't have good exposure) and even having one or two good teachers isn't enough to have an amazing learning, a lot have to be done by ourselves and this isn't something cultural in my country (people do cheat a lot or a not real interested in studying at all), learning English makes possible to me to get this good stuff for free, I feel so lucky to cross your channel because I have internet and a clear background in English, so, thank you so much!!!

[forresthu]

I really like the way you are performing physical experiment while teaching on how to solve Newton Cooling formuar. It really make the math relevent to our day to day life, and it is fun to compare experiment result to model prediction.

[jlee]

How did you know I was taking Diff eq this sem. Impeccable timing. Bravo, sir, bravo.

[pradeepattri]

You're my favourite person to learn and most of UNDERSTAND differential equations.

[prabeshgautam]

Man, that was terrific teaching. I have known this for years and have watched tons of videos but this is the clearest anyone ever explained it.

[raymondlancaster]

This is really good instruction. This is the first video I have seen by this gentleman but my guess is he does quality work consistently.

[items]

That was great sir a cup of coffee made my sepereable differential solution

[j.o.]

Me like. So that's why we use e^ so much in ODE's. That's also where the extra constants comes from, e^-k, by using logarithms. I also like how you model the situation. Question to self: what is a situation that I could model this way? I got a coup of instant noodles, it takes 5 minutes to cook. I could probably estimate some function of how soft it becomes, using time t, temperature and a way to measure softness (like how much it'll stretch).

[georgesadler]

Professor Bazett, thank you for a solid analysis of the classical Newton's Law of Cooling in Differential Equations. This is a great experimental/analytical law by one of the founders of Calculus.

[prydt]

I just HAVE to comment and say that these videos and your channel in general is amazing!!! Keep up the awesome work!!!!

[simran]

I was looking for an ODE and PDE course and I am glad you have started ODE. If you don't mind could you please upload videos faster 😅? I love your teaching skills.

[pennyyang]

So much better than Prof I have in my uni today about ODE almost die for catching the blackboard and the small volume

[akif]

Using real life scenarios is much more understandable for us, thanks Dr. !

[Escarii]

Thanks for this video, I really understand maths better when I see it applied!

If you don't mind me asking, why don't we need the Constant on the left-hand side integration? Can we ignore it because constants on both sides are effectively a single (different) constant on one side?

[jonoliahjohn]

This video was so fun to watch. I've been trying to figure out how to do this ODE for more than a few hours now 😅. This explanation just made it plain as day for me

[gilernt]

great video! just a small correction - i think at the end when you used the model to predict the temperature of the tea after a certain time, you originally said the reading was taken at 5 minutes, but used 7 in the equation. T(5) = 143.8 here, which is only about %0.77 off the measured value of 142.7; maybe you just used 7 or maybe it's a total coincidence that after 7 minutes the measured temperature almost perfectly matches the 5-minute theoretical, but either way, i learned a lot from this video, so thank you!

[axbowf]

Thank u. Recently found ur channel through the logic class.
I am glad that I found your channel.
Ur videos will be helping me a lot.❤

[synapticmemoryseepage]

Great example of a DE in action! I love it.