I wished my math teachers where like you Dr.Tom , instead they would yell and scold us for not understanding. your student are so lucky to have a teacher like you!
We had a maths teacher who would just simply walk out and not return if the class was talking. As a teen you think that is great until you are sat in front of an exam with your future riding on it and you haven't a clue!
I often see especially in physics videos that trick of multiplying/dividing/... by dx or dy with a note saying that it is not mathematically precise but does work. I would like to learn more about it why it is actually possible to treat dx or dy as operands in various operations and also when it would fail. Just a suggestion for future video :) Thanks Tom
It doesn't fail. But you are right, it works for the wrong reason, because we can't treat y as an independent variable! y is a function of x. To see why it works try solving the diffrential equation: y'=x in two ways! First way using the fact that the antiderivative of y' is the function y and the antiderivative of x is x^2/2 and that two functions of x have the same derevitive if and only if they are different by a constant. And the second way by writing y' as dy/dx and using separation of variables. You can then solve other separation of variables problems by guessing the antiderevitive and you will quickly see the pattern and why this will always work.
When Leibniz used them they were called infinitesimals and lots of handwaiving got them to work and no-one knew actually why. Now they are called differentials and they are rigorously proved. Check the wikipedia article. You can also find from MIT multivariable calculus videos a video that goes trough the theory quite nicely although glossing over some corner cases which do not actually matter normaly eg. I mean in equations concerning physical nature.
The fact that a shaggy haired tattoo covered cartoony scientist looking dude (this is a compliment of the highest order) is a fellow at oxford is the most pleasant surprise ive had all year, love ur vibes
I didn’t think of adding and substructing in 7:42 that’s much easier than what I did I multiply both the numerator and denominator by e^(-x) and then multiplied by (-1) in the numerator and outside the integral then I had the integral of -e^(-x)/(1+e^(-x)) and the top is the derivative of the bottom so it’s equal -ln|1+e^(-x)| overall which is the same answer like you got in a different format its a great video thank you for making this videos
It doesn't make sense why you would add and substract an e to tjex at the top..it's not intuitive and you would need an e to the x mutliplying the log in the numerator not added anywah..
be careful - you can't add and subtract things from the top and bottom, what I'm doing here is rewriting it as 1 + something by adding and subtracting the same term from just the top.
your video is sooooooo fantastic!!!! Now I can easily understand a lot of things with the help of ur video😁🤗 and hope I can get a good mark in the final calculus exam
Can't wait until you solve non linear second order differential equations by the use of FEM or one of its many variants. The problem is that most natural processes of heat, mass and momentum transfers can only be solved this way ( and often simultaneously). It would be interesting to see you use and explain a CFD package.
@@TomRocksMaths Thanks for sharing. I hope you can respond to my comment about how to deal.wkth when studying maths becomes discouraging or boring when you can. Thanks very much .
Nope. Doctorate in music. Was always told I ought to be better at maths than I was. Keep coming back to this stuff,cannot understand it. But thanks anyway 😂.
Hi tom id like some advice for my 13-year-old he has already sat 3 GCSE higher maths papers and has scored a* in all, he's also doing much more advanced math as your doing here and getting it all correct he definitely doesn't get it from me he wants to attend Oxford or Cambridge but we are working-class so I'm worried about costs does he have a realistic shot and thanks. a concerned dad.
I wonder if this is Oxford Calculus or Universal Calculus and this topic figures in most of the 6th form Pure Maths of most of the English Examination Boards... I
I saw this video just now. I was amazed that a satisfactory answer was not received when solving the second differential solution. I didn't find any criticism in the comments, so I decided to find the answer explicitly: y=f(x). dy(x)/dx=sin(x+y(x)). Beginning as the author, u(x)=x+y(x) =>............∫du/(1+sinu)=x+C. And now, "universal trigonometric substitution": t=tan(u/2). Then sinu= 2*tan(u/2)/[1+tan(u/2)^2]=2t/(1+t^2), u=2*atan(t), du=2dt/(1+t^2). ∫1/[1+2t/(1+t^2)]*2dt/(1+t^2)=2∫dt/(t+1)^2=-2/(t+1) =x+C. t+1=-2/(x+C), tan(u/2)=-2/(x+C)-1, x+y(x)=-2 atan[2/(x+C)+1]. Answer: y(x)= -x-2 atan[2/(x+C)+1].
A cross between Marty out of Back to the future, a windswept Ed Shearon and a Coldplay roadie. I forgot to listen to the maths bit. Oh and a chalk board! How 1987.
I know this has nothing to do with math, but I was wondering something about your tattoos. Do you ever get scolded by other professors at Oxford for your tattoos? I could have a false perception of Oxford, but I always thought it was a strict old fashioned school (I could be off, I'm from Boston).
the unmentioned elephant in the room is that 99.9% of interesting differential equations are not solvable by any "technique" save brute force computing - this is why engineers mock mathematicians
I wished my math teachers where like you Dr.Tom , instead they would yell and scold us for not understanding. your student are so lucky to have a teacher like you!
Damn. Bad teachers should not be a thing.
mmm going back a good few years , our maths teacher used to hit us with lumps of wood. obviously we learnt nothing.
We had a maths teacher who would just simply walk out and not return if the class was talking. As a teen you think that is great until you are sat in front of an exam with your future riding on it and you haven't a clue!
Yeah same here. My maths teacher was totally shit.
My teacher will just solve one question and then rest of the excersice will it on us thats it he will do
It must be great being a student nowadays, doesn’t matter if you have crappy lecturers, there’s legends on UA-cam who can explain everything.
Had a lecture yesterday that did this and I realised I needed to learn more.. and my man has me covered, great timing
Glad it was helpful!
Fantastic explanation !!! It helped a lot. Please keep posting this kind of work.
Best wishes from Brazil 🇧🇷
Glad it helped!
Brilliant Tom. Going to have to play it a few times before I truly get it.
I often see especially in physics videos that trick of multiplying/dividing/... by dx or dy with a note saying that it is not mathematically precise but does work. I would like to learn more about it why it is actually possible to treat dx or dy as operands in various operations and also when it would fail. Just a suggestion for future video :) Thanks Tom
It doesn't fail. But you are right, it works for the wrong reason, because we can't treat y as an independent variable! y is a function of x. To see why it works try solving the diffrential equation: y'=x in two ways! First way using the fact that the antiderivative of y' is the function y and the antiderivative of x is x^2/2 and that two functions of x have the same derevitive if and only if they are different by a constant. And the second way by writing y' as dy/dx and using separation of variables. You can then solve other separation of variables problems by guessing the antiderevitive and you will quickly see the pattern and why this will always work.
See: ua-cam.com/video/JAV_nUBDaf8/v-deo.html
When Leibniz used them they were called infinitesimals and lots of handwaiving got them to work and no-one knew actually why. Now they are called differentials and they are rigorously proved. Check the wikipedia article. You can also find from MIT multivariable calculus videos a video that goes trough the theory quite nicely although glossing over some corner cases which do not actually matter normaly eg. I mean in equations concerning physical nature.
The fact that a shaggy haired tattoo covered cartoony scientist looking dude (this is a compliment of the highest order) is a fellow at oxford is the most pleasant surprise ive had all year, love ur vibes
I didn’t think of adding and substructing in 7:42 that’s much easier than what I did I multiply both the numerator and denominator by e^(-x) and then multiplied by (-1) in the numerator and outside the integral then I had the integral of -e^(-x)/(1+e^(-x)) and the top is the derivative of the bottom so it’s equal -ln|1+e^(-x)| overall which is the same answer like you got in a different format its a great video thank you for making this videos
nice!
Did my admission test today, I’ve gotta say this is just what I needed to calm down
hope it went well!
Learn more form the Oxford University calculus course on the playlist here: ua-cam.com/play/PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S.html
It doesn't make sense why you would add and substract an e to tjex at the top..it's not intuitive and you would need an e to the x mutliplying the log in the numerator not added anywah..
be careful - you can't add and subtract things from the top and bottom, what I'm doing here is rewriting it as 1 + something by adding and subtracting the same term from just the top.
@@TomRocksMaths I never mentioned the bottom so why would you say that sorry?
your video is sooooooo fantastic!!!! Now I can easily understand a lot of things with the help of ur video😁🤗 and hope I can get a good mark in the final calculus exam
I hope so too!
This is GOLD !
Can't wait until you solve non linear second order differential equations by the use of FEM or one of its many variants. The problem is that most natural processes of heat, mass and momentum transfers can only be solved this way ( and often simultaneously). It would be interesting to see you use and explain a CFD package.
Ooh that was a clever way to integrate 1/(1+e^x)! My first thought was to rewrite it as e^x/(e^x+e^(2x)) and set u = e^x
that would also work too!
Looking fit and well Tom!
hii, I sat the MAT recently, it would be so great if you could do a new video about the interviews pleasee
Thank you. This is always fun
thank you very much!!!
Calculus ❤️🇲🇦
Also by multiplying e^(-x) in both Numinator and denominator
Nice spot!
Yo tom, it would be really awesome, if u take up some calculus problems, from some prestigious exams in the world!
Could you do a video on non-linear PDEs- specifically non linear waves? There’s nothing on UA-cam that explains it well mathematically :)
do u do private online tuitions?
I sure do! Send me an email using the contact form on my website and we can figure something out: www.tomrocksmaths.com/contact
I’m in year 10 and would love to attend Oxford for a degree of some sort in maths
keep working hard and hopefully we'll see you here in a few years!
I feel like I relearned this better than I originally learned this couple years ago lol
Do you prefer log as natural log ?
I normally just write ‘log’ tbh but here I made an effort to make it clear what I was doing
Prof, you gotta do a video tour of your delightfully mathy/nerdy/awesome tattoos!
I explain a few of them here: www.tomrocksmaths.com/tattoos
@@TomRocksMaths
Where are the explanations? All I can see is titles and pictures.
@@TomRocksMaths Thanks for sharing. I hope you can respond to my comment about how to deal.wkth when studying maths becomes discouraging or boring when you can. Thanks very much .
Nope.
Doctorate in music.
Was always told I ought to be better at maths than I was.
Keep coming back to this stuff,cannot understand it.
But thanks anyway 😂.
Are you the naked mathmatician? You're very charismatic sir
Sure am!
You should try solving iit advanced maths paper
Hi tom id like some advice for my 13-year-old he has already sat 3 GCSE higher maths papers and has scored a* in all,
he's also doing much more advanced math as your doing here and getting it all correct he definitely doesn't get it from me he wants to attend Oxford or Cambridge but we are working-class so I'm worried about costs does he have a realistic shot and thanks.
a concerned dad.
Finally learning math from XQC himself.
I wonder if this is Oxford Calculus or Universal Calculus and this topic figures in most of the 6th form Pure Maths of most of the English Examination Boards... I
it's based on the calculus course i teach at oxford
Please do HL IB AA maths exam
Please solve jee advance maths paper
Could you forward me that calculator (link) if I get it will support me
download links are all in the video description (it's free)
Respectfully yours with sincere gratitude.
I saw this video just now. I was amazed that a satisfactory answer was not received when solving the second differential solution.
I didn't find any criticism in the comments, so I decided to find the answer explicitly: y=f(x).
dy(x)/dx=sin(x+y(x)).
Beginning as the author, u(x)=x+y(x) =>............∫du/(1+sinu)=x+C.
And now, "universal trigonometric substitution": t=tan(u/2).
Then sinu= 2*tan(u/2)/[1+tan(u/2)^2]=2t/(1+t^2), u=2*atan(t), du=2dt/(1+t^2).
∫1/[1+2t/(1+t^2)]*2dt/(1+t^2)=2∫dt/(t+1)^2=-2/(t+1) =x+C.
t+1=-2/(x+C), tan(u/2)=-2/(x+C)-1, x+y(x)=-2 atan[2/(x+C)+1].
Answer: y(x)= -x-2 atan[2/(x+C)+1].
this is the same solution - arctan can be rewritten as a combination of logs
Grazie
You're welcome!
Menga matematikani o'rganish qiyin bo'layapti.Qanqay maslahat bera olasiz
24:14 - a hobbit is solving a differential equation.
A cross between Marty out of Back to the future, a windswept Ed Shearon and a Coldplay roadie. I forgot to listen to the maths bit. Oh and a chalk board! How 1987.
I'll take it
@@TomRocksMaths All compliments of course! Absolute adore your channel . And Back to the future. And chalk boards.
So easy
I know this has nothing to do with math, but I was wondering something about your tattoos. Do you ever get scolded by other professors at Oxford for your tattoos? I could have a false perception of Oxford, but I always thought it was a strict old fashioned school (I could be off, I'm from Boston).
I've never had any issues, but then again I'm not sure I would notice if they did tbh! I tend not to play attention to what others think of me
the unmentioned elephant in the room is that 99.9% of interesting differential equations are not solvable by any "technique" save brute force computing - this is why engineers mock mathematicians
A
Only twelve minutes to start the video
love the enthusiasm!
i wish you worked harder on your geometry
sooo did he purposely try and look like mgk in this video lmao
he saw my style and clearly decided to copy
why are my teachers old hags. and oxford has u young cool teacher with so many tattos.
Brilliant, boy with tattoos helps me with my grocery bill. Rubbish. God help anyone stuck in a gay bar with this boy.