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Oxford Mathematics Open Day 2021: Differential Equations

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Tom Rocks Maths

Tom Rocks Maths

Күн бұрын

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@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
If you want to see more of the Maths taught at Oxford check out the 'Oxford Calculus' playlist here: kzbin.info/aero/PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S
@8rboy
@8rboy 3 жыл бұрын
Two years ago, I was 22. Working a dead end job and felt sick and tired of it, didn’t know what to do in life. Back when I was in school, I wasn’t a very bright student nor very interested in any of the subjects. Therefore, I failed every math class and couldn’t apply for university because of that. I decided to fix it so I started from scratch in math (I don’t lie when I say that I didn’t understand math) and actually enjoyed it very, very much. Now, I am 24 and this fall I will study mechanical engineering at a university in Sweden. I just want to thank every youtuber out there who makes videos about math and showing us how wonderful and interesting it can be, if done right.
@lolhaha1921
@lolhaha1921 3 жыл бұрын
Good luck! I have my mock gcse in a couple of months rip
@ivanbeales3196
@ivanbeales3196 3 жыл бұрын
@@lolhaha1921 I’m sure you’ll do great 👍
@Saujas
@Saujas 28 күн бұрын
you will be graduating soon, how has the experience been so far? i bet terrible cause the folks at uni just dont have the dive and motivation to explain things,,,
@8rboy
@8rboy 17 күн бұрын
@@Saujas I graduate in 18 months, so not much more left. It's been really a great ride. I have not only been able to study interesting topics, but I have also met so many new people I can call friends for life.
@Saujas
@Saujas 17 күн бұрын
@@8rboy I know the topics are interesting, I am just the teachers aren't great at explaining things. They might hold doctorate and papers nonetheless
@thomasking684
@thomasking684 3 жыл бұрын
We completed the differential equations topic recently in further mathematics and this gave me a greater understanding of how it all works, thanks Tom :)
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
You're very welcome Thomas :)
@Stoic_Persistence
@Stoic_Persistence 3 жыл бұрын
You're just the best teacher ( professor) i've ever regarded. When i'm studying your videos it's not just the obligation to learn for school, it's the joy i have to learn new stuff. When you have some trouble in your life just think of your aid you served for all the students, including me. 😊
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
@RC32Smiths01
@RC32Smiths01 3 жыл бұрын
I'm a simple man, I see Differential Equations, I click.
@usernameofnik
@usernameofnik 3 жыл бұрын
I had been scrolling the youtube for 10 mins, finding something genuine and interesting to explaining this theorem, I couldn't believe that I got so much from a single video. Can't put enough thanks into words 🔥❤️👍
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
glad you found it helpful :)
@augustus7765
@augustus7765 3 жыл бұрын
Hi Tom Thank you for the great video. I am a second semester physics major with I minor in mathematics. Tomorrow I will write my calculus 2 exam. Always astonished who easy you can explain this topics. I think it is very important to have people like you explaining mathematical concepts to a wider audience, in school math stops at the point where it gets creative and becomes more like art. You do a great job (not just in this video) in showing people what math really is about. You are a great inspiration to me. Thank you for all the work you do :)
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
hope it went well!
@gddanielk8491
@gddanielk8491 2 жыл бұрын
This helped me look just a little deeper into the topic after teaching the further maths chapters to myself recently. So interesting how even though they strip it back for exam purposes, there’s so much more to explore!
@markhilliam2932
@markhilliam2932 3 жыл бұрын
Im just a highschool student,but the nerdness inside cant stop me from watching this.I hope i can go oxford one day
@polka678
@polka678 3 жыл бұрын
Not with that grammar.
@markhilliam2932
@markhilliam2932 3 жыл бұрын
@@polka678 hahaha
@markhilliam2932
@markhilliam2932 3 жыл бұрын
@@polka678 i have envisioned people like you to comment.
@xd-qi6ry
@xd-qi6ry 3 жыл бұрын
@@polka678 so your the guy that copy and pastes comments very nice.
@markhilliam2932
@markhilliam2932 3 жыл бұрын
@@bigpushing7167 thanks
@chilledvibes99
@chilledvibes99 3 жыл бұрын
Incredible how clearly and concisely you can put across some quite complex ideas. I'm currently towards the end of my first year of a mathematics degree and I wish I could have you as a professer. It is helpful seeing the "why" behind things not just the "how".
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Awesome - thanks Adam :)
@jackpoore7866
@jackpoore7866 3 жыл бұрын
Love this! I’m currently in the 3rd year of my MMATH and ODEs still amaze me. We recently studied this class of ODE but using a series ansatz rather than exponential
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
I teach that method to my second years in what we call Differential Equations II.
@johnchessant3012
@johnchessant3012 3 жыл бұрын
Nice explanation! Even though I've taken some of these classes before, it really helps to hear you talk about it
@SmokeSolo1975
@SmokeSolo1975 3 жыл бұрын
The only things I remember about my degree ove 20 years ago was 2 things. Lotka Voltera modeling and using runge kutta approximations to solve differential equations using excel as a modeling tool. And I had a tutor who marked me down as I used orbital theory to show why a black hole is black due to when light particles get too close to a centre of gravity, it always ends up orbiting towards the gravitational centre. I supposedly wasn't meant to ask what if a planet was a light particle instead, and a star was a black hole. Thanks for reminding me how much I enjoyed maths all those years ago.
@mil9102
@mil9102 3 жыл бұрын
@Mohamed Ababou are you okay?
@MrRyanroberson1
@MrRyanroberson1 3 жыл бұрын
a bit more of a literal justification: because of that cancellation. it's a function that is never zero and is a(n algebraic) factor of its derivatives, which is exactly the requirement for it to cancel in that way. if you only have even-order derivatives, for example, you could just as easily use cos, sin, cosh, sinh, or any other d^2 f(x)/dx^2 = kf(x) function instead. So as a motivation, it's a guess that's basically trivial to check and work through, and for the likelihood that it gives a solution, it will save tons of time in the long run to just try it from the start regardless.
@kost4sk176
@kost4sk176 3 жыл бұрын
This is exactly what i wanted to watch !!!!!
@nates1202
@nates1202 3 жыл бұрын
Me being in HS trying to ask math questions none of the teachers don't understand and here you are asking them so clearly. Thank you
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
You're very welcome :)
@xd-qi6ry
@xd-qi6ry 3 жыл бұрын
I have 2 maths teacher in highscool that explain them very well, deffinitely something hard to find but i know university vs highschool the teachers are just so much better and the ways and techniques they give you make you think why did my hs teachers not do this, it’s hell.
@h4z4rd28
@h4z4rd28 3 жыл бұрын
Oh yes, i want to study at Oxford
@sparkleguy99
@sparkleguy99 3 жыл бұрын
One of the 1st things you do in physics is investigate what influences the time of oscillation T = 2pi * sqrt(l/g) the only thing that influences the time is the length of the pendulum not the angle or the height of the pendulum.
@_okedata
@_okedata 3 жыл бұрын
And what assumptions do you make about the angle of the pendulum?
@increasing_entropy5073
@increasing_entropy5073 3 жыл бұрын
Did i hear (Differential) equations stripped?
@Wolyzz-bk7qs
@Wolyzz-bk7qs 3 жыл бұрын
Would be cool to see you try a Singaporean A Level maths paper
@camerontrew214
@camerontrew214 3 жыл бұрын
Such a great video, makes me even more excited to start maths at uni (not Oxford but still)
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Good luck!
@gurkiratsingh7tha993
@gurkiratsingh7tha993 3 жыл бұрын
Dear sir Tom, I am researching on Riemann hypothesis for the last 3 years and successfully I have found a formula for 'a' in Zeta(a+ib) in terms of 'b' and some hard looking definite integrals which are in terms of 'a' and 'b'which I was not able to solve so I am challenging you to solve those integrals . I used Riemann xi function and Riemann functional equation for Zeta function to find the formula for 'a'. Please make a video on those integrals. Integrals are:- 1)integral from 1 to infinity of x^((a-2)/2)*f(x)*cos(ln(x)*b/2) + x^(-a-1)*f(x)*cos(ln(x)*b/2) 2)integral from 1 to infinity of x^((a-2)/2)*f(x)*sin(ln(x)*b/2) - x^(-a-1)*f(x)*sin(ln(x)*b/2) Where f(x) = summation from n=1 to infinity of e^(-(n^2)*π*x)
@MeMyselfForWho
@MeMyselfForWho 3 жыл бұрын
You use the word Ansatz in english as well?
@garidmandakh6621
@garidmandakh6621 3 жыл бұрын
I just really miss my old regular classroom lessons, and every time chalk is touched on board, it sounds satisfying.
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
chalk is the best.
@paulopaulos8424
@paulopaulos8424 3 жыл бұрын
Just found you on KZbin. I don’t know why… I mean, I don’t understand nothing about maths. For me 2+2=5. 😳 Keep up the good work. From Spain 👍
@johnhippisley9106
@johnhippisley9106 3 жыл бұрын
Why would we not have a different solution for each root of the auxiliary equation? Why is it that we must take the combination?
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
The fact that the differential equation is linear means that if a(x) is a solution and b(x) is a solution then so too is a(x) + b(x). Therefore we add them together to get the 'most general' solution.
@sachamoser8291
@sachamoser8291 3 жыл бұрын
thanks for the video Tom!
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Any time!
@Subhan_232
@Subhan_232 3 жыл бұрын
I wish I could go back 4 years and take further maths instead of Biology at A level and apply for Oxford to be a student of the coolest professor ever 😂
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
@davidrobins1021
@davidrobins1021 3 жыл бұрын
Same. Wish I could go back 26 years and do physics and further maths instead of geology and biology. The trouble is that when you're 16, you often don't know where your real interests lie.
@cya3mdirl158
@cya3mdirl158 3 жыл бұрын
@Tom Rocks Maths When you explain a Banach Spaces?
@baylordsett2739
@baylordsett2739 3 жыл бұрын
seriously, this will save my A level Further
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Best of luck!
@NateCrownwell
@NateCrownwell 3 жыл бұрын
Awesome video! Have you studied Lambda Calculus?
@adityachaudhary5674
@adityachaudhary5674 3 жыл бұрын
One more heart Tom!!!!😘
@edmondscott7444
@edmondscott7444 2 жыл бұрын
What if m1 = m2.
@mathsmadefun6484
@mathsmadefun6484 3 жыл бұрын
Do a gcse maths paper edexcel
@physicsa5441
@physicsa5441 3 жыл бұрын
Could you please, make a video on second order differential equations with variable coefficients
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
thanks for the suggestion - I've added it to my list :)
@haha-qj8pw
@haha-qj8pw 3 жыл бұрын
What sorts of maths modules do you teach to physics students, if any?
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Physics students will learn some maths modules but they are organised by the physics department rather than maths. I do teach my mathematicians lots of 'physics' though for example quantum theory, fluid mechanics, special relativity...
@haha-qj8pw
@haha-qj8pw 3 жыл бұрын
@@TomRocksMaths can you show some of the ways the differential equations, you have discussed, can be a suitable language to model oscillations?
@marcread3222
@marcread3222 3 жыл бұрын
if we study subjects that are not well-posed what is its importance?
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Some of the most fundamental systems are not well-posed, eg. Navier-Stokes, double pendulum etc. Theses things exist in the real-world so they are worth studying!
@marcread3222
@marcread3222 3 жыл бұрын
@@TomRocksMaths I suppose whether a system is well posed or not allows us to choose an appropriate method of studying the system?
@judedavis92
@judedavis92 3 жыл бұрын
I know it doesn’t rly matter but I get the shivers when he holds the chalk like a pen 😫
@farhanshaqib8746
@farhanshaqib8746 3 жыл бұрын
They are in normal a level maths
@SuperCaptain4
@SuperCaptain4 3 жыл бұрын
Mohamed Ababou is the aluminum foil hat version of a mathematician 😂
@ujjwalprasad3575
@ujjwalprasad3575 3 жыл бұрын
How can we apply ode in real world application
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
Anything involving a 'rate of change' will require a derivative of some sort.
@ujjwalprasad3575
@ujjwalprasad3575 3 жыл бұрын
@@TomRocksMaths can we pursue astronomy after msc maths
@maruf10155
@maruf10155 3 жыл бұрын
y=0 is a solution to the equation. my question is how do the equation has an unique solution?
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
this can be proven with something called 'Picard's Theorem'
@shinjiikari0290
@shinjiikari0290 3 жыл бұрын
nice. tnx prof.
@Hboojy
@Hboojy 3 жыл бұрын
When ur in yr 12 and thought the first principle of differentials was gonba be the hardest thing 😳
@peterpoli2839
@peterpoli2839 3 жыл бұрын
As a second year Physics student at cambridge, you got a hell of a lot more coming mate.
@paultan5419
@paultan5419 3 жыл бұрын
@@peterpoli2839 Im curiuos, what kind of physics are you doing right now. Im also second year at a different uni. Doing a lot of (basic) quantum mechanics, and stat mech
@peterpoli2839
@peterpoli2839 3 жыл бұрын
@@paultan5419 I do thermodynamics, quantum, condensed matter physics right now for this term.
@Hboojy
@Hboojy 3 жыл бұрын
@@peterpoli2839 yh im doing physics and maths and im about to finish the AS half and its already hard.
@paultan5419
@paultan5419 3 жыл бұрын
@@peterpoli2839 nice! Do you prefer thermo or quantum. I find the maths of the latter more interesting, hoenstly thermo feels much harder imo. Gotta be really good at real lie applications and stuff aye.
@matthewdearsley123
@matthewdearsley123 3 жыл бұрын
I do not understand Long Division, it's like it's out there with it's own language for one purpose.... . Why is it so unique? Strangely I understand it for polynomials, even then it's still an odd form of algebra
@vijaysingbundhoo7393
@vijaysingbundhoo7393 3 жыл бұрын
Grateful if you could kindly clarify the motivation behind the initial assumption that y eqals e to the power of mx where m is a constant.
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
It's basically an educated guess! That's what i'm explaining in the video.
@CAT12480
@CAT12480 3 жыл бұрын
whagt only 22?
@itsreeah2663
@itsreeah2663 3 жыл бұрын
Maths hug???
@alibasaradja5255
@alibasaradja5255 3 жыл бұрын
I'm mathematics student I would like to study.. In competitive universities with free tuition can... You help me sir
@blaze7345
@blaze7345 3 жыл бұрын
what a lad
@arthurthompson7877
@arthurthompson7877 3 жыл бұрын
I’ll never understand why y= the sun of the 2 roots
@TomRocksMaths
@TomRocksMaths 3 жыл бұрын
because it's a 'linear' equation it means that if we have several solutions we can add them together and still get a valid solution. This isn't true for 'non-linear' equations.
@arthurthompson7877
@arthurthompson7877 3 жыл бұрын
@@TomRocksMaths idk still seems a bit Alien, like I understand the proof of why It works, I think it’s more the fact I had to learn this myself as of corona virus lockdown
@aniketeuler6443
@aniketeuler6443 3 жыл бұрын
Differential equations are the language in Which the whole of the universe is written as they study change 😀😀
@mugen2369
@mugen2369 3 жыл бұрын
Why do I see Mohamed ababou everywhere😂😂😂😂😂
@LeRainbow
@LeRainbow 3 жыл бұрын
I’m currently studying the analytical solutions of the heat transfer equation which at the base of it all is just a partial differential equation. (c*p/lambda) dT/dt = nabla^2 * T + Eta 👀 to be able to better regulate heat issues in LiIon battery backs, lol. (:
@sagacioussigma527
@sagacioussigma527 3 жыл бұрын
just a quick question: why are you a genius?
@sharoonaftab8894
@sharoonaftab8894 3 жыл бұрын
Maybe cause he studied maths seriously instead of just hoping to pass.
@aeulia4359
@aeulia4359 3 жыл бұрын
Mohamed ababou is like half the comments
@science_dar3022
@science_dar3022 3 жыл бұрын
I have no idea what's going on here. I just clicked because of the title "Oxford mathematics." 😅
@Iwanchek
@Iwanchek 3 жыл бұрын
I lost you completely after the letter; a…(first line) and I got the alpha….male….ok….quadratic…..ok….I go off it’s to much tho! Mohave a good day/night/month/year!! (Keep up Profesor!)
@Logicallymath
@Logicallymath 3 жыл бұрын
me: I like your funny words magic man
@jplikesmaths
@jplikesmaths 3 жыл бұрын
Too bad most ODEs in real life aren’t linear and so this magical method isn’t used that much
@someaverageguy2704
@someaverageguy2704 3 жыл бұрын
I want to be accepted into Oxford just so I can be the guy to reject the top university in the world
@77tigers26
@77tigers26 3 жыл бұрын
lol
@aeulia4359
@aeulia4359 3 жыл бұрын
🤣🤣
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