@@abdielsalamabdirahman2681 in my state, the doctor is the one with phd but professor is the higher "rank" than teacher. Basically every professor is doctor but not every doctor is professor
This guy is a fantastic teacher. A lot of teachers make things as complicated as possible, possibly to keep an air of superiority over those they are teaching. He keeps it as simple as possible, in order that if people can learn it, they will.
In the first 4 minutes you've already taught me more about deriving functions than my math teacher did in a whole year of school. So many people would be interested in computer science and mathematics if they would have had great professors earlier in their lives.
Yes I think the presentation of mathematics is all wrong in schools. I understand there has to be basic levels to get most people up to a functional level, but I really think the creativity and artistry of mathematics is criminally underplayed. Instead of attracting people who are good at and attracted to rigid structure, you could also be bringing in the artists and creatively minded people. As is I think most of these people get completely turned off by the 'follow these steps over and over' approach. More theory / proof / fundamental topics early on would also hook the philosophers, english and even lawyerly types.
This totally. Teaching is only half knowing the content. The other half is being able to actually teach what you know and that requires, an engaging charismatic teacher. There is a reason someone like Brian Cox was successful on BBC
This is fantastic! After nearing the end of my semester of calculus 2, I was a bit nervous about multivariable calculus next fall, but this introduction to partial differentiation was very logical and much more approachable than I would have expected! Thank you for the wonderful content Tom!
i'm a freshman doing an engineering degree and i just spent the last ten minutes struggling with other channels telling me about graphs and i was sooo close to giving up before i found this video, so thank you so much, your straight forward teaching method helped me a lot
As someone who struggled to get the old Oxford GCE at grade 4 some 50 years ago (ie before you were born), but needs to be able to manipulate Karl Friston's Free Energy Principle, I am utterly grateful for your enthusiasm and clarity.
Tom, I'll tell you that I'm a pre-college student who so far has only seen algebra up to the topic of limits (I'm not in college yet and haven't seen calculus), but I understood this video 100%. you really make it very easy
@@ahmedgadeIhaq currently taking fp1 and fp2, i'd say it's worth it if you really love pure over applied and it's not as impossible as some people say but there are definitely tricky parts. Gets easier with practice though
Wow This is the clearest explanation I have come across, I understand every word you said, I grabbed the concept within 18 mins and it's one of the most meaningful 18 mins in my life, jusy by listening to how you talk is already very healing for me, not to mention the precise content, Thank you very much !
Superb! Hadn't thought about partial differentials in almost 30 years (learnt about them in 1st year Econometrics), but your crystal clear explanations and thorough worked examples made everything come flooding back to me! Had to grab a pencil and paper half way through to work out the answers myself. Inspiring!
I did my Maths A Levels in 1983, but this was a fun way to revise. You remind me of my Pure Maths teacher Mr Hobson (a Cambridge graduate, not Oxford), and wished at the time that everyone could be taught by someone with his enthusiasm for playing with numbers so they could overcome that silly 'maths is hard and boring' attitude that kids hear from other kids and adults too. And now, thanks to the internet, and your RUclips channel in particular, everyone can have that sort of learning experience. Keep doing what you do.
This is so true I’m in 12th grade (United states so we don’t get exposure to most of these while we’re young) I hated math for the longest but After having an IB geometry teacher it’s easily my favorite subject and I enjoy learning it. Hopefully I can head off to college and study EE
Thank you professor. You did a phenomenal job explaining this. It’s easy to understand and taught me how to do the δ^2f thing which is was struggling with
Well, it just so happens that the Tom Rocks Maths merchandise range launches TODAY. So now you can get the shirt for yoursefl here: beautifulequations.co.uk/pages/tomrocksmaths :) Use the code TRM25 to get 25% off before Monday!!
He has the brain, the skills and the material for a strict online course. This man can math to the extreme details like the work of Joseph Edwards, Treatise on Integral Calculus. It's time to get dirty with the theorems, proofs, the details on each of these courses. Anything this man explains, becomes transparent. I would like to see math courses where the professor develops the whole theory in every painstaking detail without omitting the difficulties of the theories. Yes math is fun and of course he is an outstanding profession but I think it's time people understand how complex it is throughout the details. Tensor Calculus, Differential Geometry, Measure Theory, Statistics deriving all distributions and proving all the theorems, Relativity Theory, Mechanics and so on. People are hungry for knowledge. These things are not magical or mysterious. They require a ton of work, hours with pencil and paper in hand and writing the proofs of those theorems. Books are available. It's inspiring finding people like him in the net.
I kind of regret not discovering this channel a long time ago. Just by watching this specific short vid I already learned a lot. The way the lesson was presented and explained from the smallest and most crucial details was multiple times better than the way our professer teach in our university. Super informative. I mean it. Thank you ^^
Just stumbled by accident. I wish you were around twenty years ago, you give a great explanation and help visualise the equations. Great teacher never judge a book by its cover 😂 Now its my review refresher channel 🎉🎉🎉 subs and liked
Very well explained. The concepts are lucid and easily understood. Best video on explaining the concept of limit and partial differentiation. Thank you!!!
A fantastic math teacher ! The student's are so lucky to have you. I just finished high school and to be honest I'm not good at math's at all. I can't blame the teacher's, but it would've been more fun and more easier to learn math's with teacher like you.
The most important information in all of multivariate calculus is as follows: the symbol ∂ for the partial derivative is called "cursive d", but it's OK to spell it in LaTeXese as "\partial"! :D Great video! I simply love this part of Calculus, it is incredibly beautiful.
A good teacher, like a good entertainer first must hold his audience's attention, then he can teach his lesson. You are a good teacher as you can grab the attention of all students watching you.
It's amazing. Watching you solving problems, really makes these calculous so much fun. Please makes some videos on Fourier series, wave equation, heat equation problems. Many of us don’t understand the topics well.
Man, if I had access to this video when I was taking high school Physics, my life would have been so much easier! Sadly, the Internet wouldn't be prevalent in homes for another 5-10 years (I'm 50 now, and when I needed it would have been around age 18, or a nice clean 2^5 years ago), so I wouldn't have had a proper grasp on Schrödinger's equation for a while yet. ... No, we weren't learning about Schrödinger's equation yet, but an essay that I did for Physics involved it and I didn't quite understand what was going on. This would have helped a lot!
OMG! For the first time it is so clear to me. That graph, that writing I suddenly understand it all. I implied there were some kind of rules for the example, I suppose you can lookup for, so that was not a problem neither. And then, just like that: WTF is second derivative?! How can I picture this in my mind? And could not continue past 10 minute mark. But subscribed to have a chance of more of those 10 minute revelations.
Thank u so much!! After a devasting morning in which I didnt understand a thing of my calculus class, I come across your video and feel theres hope again!
Love the way you explain things. It's been a while since I had to do these problems (in college) - I love that these vids inspire me to crank out a few practice problems, just for the fun of it. Thanks Tom :)
Wow this video is great! I just got through DE and I was curios what came after. You are really awesome about the way you break it down and explain it.
Thanks! When I first encountered the partial derivative concept, an analogy based question arose in my mind. In single variable case, we could plot the curve on a 2D paper and then fix a point on that curve and draw a tangent at that point and then take the slope of that tangent (trigonometric tangent of the angle made by that tangent with respect to horizontal, namely the X axis), which we call the ordinary derivative of that function at that point. Now taking this analogy to two variables, we have a surface in 3D(instead of a curve like we did in 2D). We fix a point on the surface which is of interest. Just like we could roll a tangent over the 2D curve until it touched the curve at that point, could we roll a plane over the surface so that it touches the surface at the point of interest. If so, then the plane would make an angle with the horizontal namely the XY plane. Now does the trigonometric tangent of this angle mean anything at all? may be not and I'm just visualising too much! I'm not sure about this though as I haven't seen any textbook mentioning this, so i'm assuming this value may not be an interesting quantity, even though we could somehow derive it as a function of the the two partial derivatives.
Cool Im on my 2nd year of studying electrical engineering and i haven't heard of the partial differentiation before, only partial integration. But this wasn't tricky at all nice teaching!
Thanks so much. In my view, the lecture is very easy for this subject and difficult examples must be solved to understand the partial derivative, such as, how to find out d^3y/dx^3 of f(x,y)=0.
I’m doing my maths gcse this year I thought I was good at maths but watching this I realise there’s so much more to do in maths (I would like to do it at uni) Whilst I don’t understand fully I didn’t lose myself in this and actually followed so you really must be a great teacher!
I'm fine with the concept of a partial derivative, but what do we gain by introducing additional notation in the form of the "swirly-d" or "del" symbol? For example, looking at the first function f(x) = xy² + yx³, and rewriting as z = xy² + yx³, what problem is created by writing; dz/dx = y² + 3x²y ? The notation dz/dx means that we are differentiating z with respect to x, so treating y as a constant is implicit. What issue exists with the standard dz/dx notation such that we need to use the "del" instead? Is this merely a custom to "remind" us that we're dealing with multivariable function? Or does it resolve some ambiguity or other difficulty in using the same notation as for single variable derivative? I'm still not sure, and I'm genuinely curious.
Brilliant In my first year of maths at university our course text was more like the philosophy of maths. I think Bertrand Russell could probably follow it but it was Greek to me.
I just love to see people who are passionate about what they teach, especially you Dr. Crawford. The way you teach will definitely incorporate the students'/viewers' curiosity, like myself, which changed my view on calculus from being hard to somewhat fun. Thank you!
I really feel like you get downvoted because you have tattoos and piercings. I am also a doctor (of Physics, but that also makes me a Mathematician), I’m Black and my hair is braided. It’s really inspiring to see another intellectual who does not fit the tired mould of “nerdy awkward guy with glasses”
Care to share your backstory? I am currently pursing a degree in Physics. I'm also bi racial (more African Am.), and also have a similar hair style lol. Would be interesting to hear your steps in how you got to where you are today.
@@damien7151 sorry but not on a video like this. This is pure, objective education. There is no falsehood stated. So you have to think "who disliked and why?"
@@Tommybotham on non-controversial videos I watch there is normally about a 100:1 like to dislike ratio - be it bots or weird, hateful people, and that’s pretty much what this has. 35 dislikes on a video with 100,000 views doesn’t seem like an issue to me, or that he’s getting hated on. Just seems like you’re making an issue out of nothing, because in the comments all I see is people appreciating Tom’s teaching.
Wow, I am preparing for my FE chemical engineering exam. I have stopped at partial differentiation lesson and this poped to my recommendations! Thank you now I dont need to review that xD
You are not only a Oxford professor but most importantly, you are a fantastic math teacher! I love your videos. :)
Thank you
Doctor, not professor. :)
@@Lolwutdesu9000 what's the diffrence?
@@abdielsalamabdirahman2681 big difference
@@abdielsalamabdirahman2681 in my state, the doctor is the one with phd but professor is the higher "rank" than teacher. Basically every professor is doctor but not every doctor is professor
This guy is a fantastic teacher. A lot of teachers make things as complicated as possible, possibly to keep an air of superiority over those they are teaching. He keeps it as simple as possible, in order that if people can learn it, they will.
After watching this, partial differentiation doesn't seems as intimidating as before! Thanks Tom!
You're very welcome :)
In the first 4 minutes you've already taught me more about deriving functions than my math teacher did in a whole year of school. So many people would be interested in computer science and mathematics if they would have had great professors earlier in their lives.
Happy to help :)
Yes I think the presentation of mathematics is all wrong in schools. I understand there has to be basic levels to get most people up to a functional level, but I really think the creativity and artistry of mathematics is criminally underplayed. Instead of attracting people who are good at and attracted to rigid structure, you could also be bringing in the artists and creatively minded people. As is I think most of these people get completely turned off by the 'follow these steps over and over' approach. More theory / proof / fundamental topics early on would also hook the philosophers, english and even lawyerly types.
This totally. Teaching is only half knowing the content. The other half is being able to actually teach what you know and that requires, an engaging charismatic teacher. There is a reason someone like Brian Cox was successful on BBC
This is fantastic! After nearing the end of my semester of calculus 2, I was a bit nervous about multivariable calculus next fall, but this introduction to partial differentiation was very logical and much more approachable than I would have expected! Thank you for the wonderful content Tom!
Awesome - thanks Sean :)
ruclips.net/video/wAnKokczAHM/видео.html CHECHOUT THESE AS WELL TO POLISH YOUR KNOWLEDGE
Being an engineering freshman with weak basics of derivatives (online classes lul) I understood everything. Thank you Dr Tom. God bless
i'm a freshman doing an engineering degree and i just spent the last ten minutes struggling with other channels telling me about graphs and i was sooo close to giving up before i found this video, so thank you so much, your straight forward teaching method helped me a lot
glad I could help :)
First time I clearly understood the implications of partials and not just the steps. Thank you!
Glad it was helpful!
As someone who struggled to get the old Oxford GCE at grade 4 some 50 years ago (ie before you were born), but needs to be able to manipulate Karl Friston's Free Energy Principle, I am utterly grateful for your enthusiasm and clarity.
Thanks David!
I'm a teacher of Mathematics and I can say that that lesson was exceptionally well explained !
Thanks John!
Tom, I'll tell you that I'm a pre-college student who so far has only seen algebra up to the topic of limits (I'm not in college yet and haven't seen calculus), but I understood this video 100%. you really make it very easy
Exactlyyy sameee
You just described this topic more clearly than an entire semester at university, and did it in 18 minutes. Damn. Good show man :)
Desperately need more maths teachers like Tom.
Youre such a good teacher, i am only mid way through a further maths a-level and i completely understand it
Amazing - thanks :)
uh i have a question ben, ur taking further so its safe to assume u finished pure, how difficult is further pure in comparison to pure?
@@ahmedgadeIhaq currently taking fp1 and fp2, i'd say it's worth it if you really love pure over applied and it's not as impossible as some people say but there are definitely tricky parts. Gets easier with practice though
Wow This is the clearest explanation I have come across, I understand every word you said, I grabbed the concept within 18 mins and it's one of the most meaningful 18 mins in my life, jusy by listening to how you talk is already very healing for me, not to mention the precise content, Thank you very much !
This is such a good intro to partial differentiation, your presentation is very easy to follow
Awesome - thanks :)
Superb! Hadn't thought about partial differentials in almost 30 years (learnt about them in 1st year Econometrics), but your crystal clear explanations and thorough worked examples made everything come flooding back to me! Had to grab a pencil and paper half way through to work out the answers myself. Inspiring!
The Core objective of Teaching is making people understand = Hence Proved
Thank you Dr.Tom
I did my Maths A Levels in 1983, but this was a fun way to revise. You remind me of my Pure Maths teacher Mr Hobson (a Cambridge graduate, not Oxford), and wished at the time that everyone could be taught by someone with his enthusiasm for playing with numbers so they could overcome that silly 'maths is hard and boring' attitude that kids hear from other kids and adults too. And now, thanks to the internet, and your RUclips channel in particular, everyone can have that sort of learning experience.
Keep doing what you do.
This has made my day
This is so true I’m in 12th grade (United states so we don’t get exposure to most of these while we’re young) I hated math for the longest but After having an IB geometry teacher it’s easily my favorite subject and I enjoy learning it. Hopefully I can head off to college and study EE
Tom is as skilled in the art of teaching as he is in maths. 10/10👍
Thank you. This didn’t just explain partial differentiations, but also clarified things regarding clarification in general.
Glad it was helpful!
I realise that you are born to be a teacher. I wish and appreciate if you lecture on more topics of higher mathematics . Thank you and god bless you.
You have an extraordinary gift for making the complex seem simple.
never knew that such an app like maple calculator existed on phones.... thank you
Please keep making videos like these, you’re so good at explaining complicated ideas!
will do!
Thank you professor. You did a phenomenal job explaining this. It’s easy to understand and taught me how to do the δ^2f thing which is was struggling with
It is always important to explain these things from first principles. You did a wonderful job at that. Thanks.
What a timely upload, this is exactly what i needed right now! Another great video as always (btw I love the shirt)
Well, it just so happens that the Tom Rocks Maths merchandise range launches TODAY. So now you can get the shirt for yoursefl here: beautifulequations.co.uk/pages/tomrocksmaths :) Use the code TRM25 to get 25% off before Monday!!
He has the brain, the skills and the material for a strict online course. This man can math to the extreme details like the work of Joseph Edwards, Treatise on Integral Calculus. It's time to get dirty with the theorems, proofs, the details on each of these courses. Anything this man explains, becomes transparent.
I would like to see math courses where the professor develops the whole theory in every painstaking detail without omitting the difficulties of the theories. Yes math is fun and of course he is an outstanding profession but I think it's time people understand how complex it is throughout the details.
Tensor Calculus, Differential Geometry, Measure Theory, Statistics deriving all distributions and proving all the theorems, Relativity Theory, Mechanics and so on. People are hungry for knowledge. These things are not magical or mysterious. They require a ton of work, hours with pencil and paper in hand and writing the proofs of those theorems. Books are available.
It's inspiring finding people like him in the net.
I kind of regret not discovering this channel a long time ago. Just by watching this specific short vid I already learned a lot. The way the lesson was presented and explained from the smallest and most crucial details was multiple times better than the way our professer teach in our university. Super informative. I mean it. Thank you ^^
Just stumbled by accident. I wish you were around twenty years ago, you give a great explanation and help visualise the equations. Great teacher never judge a book by its cover 😂 Now its my review refresher channel 🎉🎉🎉 subs and liked
Very well explained. The concepts are lucid and easily understood. Best video on explaining the concept of limit and partial differentiation. Thank you!!!
A fantastic math teacher !
The student's are so lucky to have you. I just finished high school and to be honest I'm not good at math's at all. I can't blame the teacher's, but it would've been more fun and more easier to learn math's with teacher like you.
The most important information in all of multivariate calculus is as follows: the symbol ∂ for the partial derivative is called "cursive d", but it's OK to spell it in LaTeXese as "\partial"! :D
Great video! I simply love this part of Calculus, it is incredibly beautiful.
Agreed.
Though i knew most of it already, its just amazing to see the enthusiasm !!
Thanks Prasoon - glad you enjoyed it!
Wonderful, nay, excellent maths teacher. He imbues clarity on a topic that befuddles many a student!
You explain this so clearly and with wonderful pace! I wish you were teaching when I was in school 40 years ago. Thanks for the videos.
I feel the same. Over the years I've gotten better at Maths through self-study. Teachers like Tom would have helped greatly.
awesome explanation, just came back from uni and wanted to understand this chapter
A good teacher, like a good entertainer first must hold his audience's attention, then he can teach his lesson. You are a good teacher as you can grab the attention of all students watching you.
Bro saved me the trouble of goin thru old notes. Much thanks.
I love your approach to teaching. Very clear and detailed explainations, taking us step by step. Excellent.
Glad it was helpful :)
This gentleman is an excellent teacher
Clear and concise, delivered at a pace which allows the viewer to grasp the concepts and pause the video if necessary. Well done! 👍
Not even close to being first ;_;
Better luck next time papa...
@@TomRocksMaths ;_;
Papa Flammy !!! :)
Ah yes, fappable maths
After I saw the tats, I came straight to the comments, Inspiring. Thanks
Finished my maths degree about 4 years ago and I absolutely love this explanation!
awesome - thanks :)
just doing this at year 1 undergrad at leicester and it makes more sense now, thanks
Happy to help :)
I'm glad I can find this stuff on your channel as I'm not in university yet, but I'm still interested in the maths involved with physics.
Simple and straight to the point. Thanks a million, prof !
My new favourite channel on RUclips.
Superb content.
Thanks Jack
It's amazing. Watching you solving problems, really makes these calculous so much fun. Please makes some videos on Fourier series, wave equation, heat equation problems. Many of us don’t understand the topics well.
calculus please
Professor Crawford thank you for an awesome lecture on Partial Differentiation with powerful examples.
glad it was helpful!
Your explanation of this topic is great ! I appreciate your efforts
Thanks Swarnil!
Man, if I had access to this video when I was taking high school Physics, my life would have been so much easier! Sadly, the Internet wouldn't be prevalent in homes for another 5-10 years (I'm 50 now, and when I needed it would have been around age 18, or a nice clean 2^5 years ago), so I wouldn't have had a proper grasp on Schrödinger's equation for a while yet.
... No, we weren't learning about Schrödinger's equation yet, but an essay that I did for Physics involved it and I didn't quite understand what was going on. This would have helped a lot!
OMG! For the first time it is so clear to me. That graph, that writing I suddenly understand it all. I implied there were some kind of rules for the example, I suppose you can lookup for, so that was not a problem neither. And then, just like that: WTF is second derivative?! How can I picture this in my mind?
And could not continue past 10 minute mark. But subscribed to have a chance of more of those 10 minute revelations.
Thank u so much!! After a devasting morning in which I didnt understand a thing of my calculus class, I come across your video and feel theres hope again!
glad it helped!
Best explanation thus far! Thank you Tom!
Really nice explanation. Subbed
Love the way you explain things. It's been a while since I had to do these problems (in college) - I love that these vids inspire me to crank out a few practice problems, just for the fun of it. Thanks Tom :)
You're very welcome Preeti :)
Are you Indian ?
Best Doctor of Mathematics
I was looking for that for weak. This edia is important for deep learning algorithms. Thank you friend
I do like your approach to explaining the subject. Easy to follow great video and thank you for sharing. Cheers!
thanks Larry!
Thanks for another video. I can't understand very well English. But your explanation is awesome.
Awesome, thanks Jorge!
Even foto learning math but english this Is Avery good video. Thanks Tom. Please continue doing great videos!!!
bro you're a KING- thanks for this
I just watched the first 6:50min and it cleared up a lot.
Hiiii Tom. Just wanted to thank you❤😍 I really liked that and it was useful a lot. A presentation with clarity😊
Glad it was helpful!
this was SO helpful for me to understand what PDEs were thank you
Coolest math teacher ever
Wow this video is great! I just got through DE and I was curios what came after. You are really awesome about the way you break it down and explain it.
Glad it was helpful!
Lots of love from Bangladesh. 🇧🇩🇧🇩🇧🇩
I hope I will join in your Department soon.
❤️❤️❤️
Thanks Muhin!
Thanks!
When I first encountered the partial derivative concept, an analogy based question arose in my mind. In single variable case, we could plot the curve on a 2D paper and then fix a point on that curve and draw a tangent at that point and then take the slope of that tangent (trigonometric tangent of the angle made by that tangent with respect to horizontal, namely the X axis), which we call the ordinary derivative of that function at that point. Now taking this analogy to two variables, we have a surface in 3D(instead of a curve like we did in 2D). We fix a point on the surface which is of interest. Just like we could roll a tangent over the 2D curve until it touched the curve at that point, could we roll a plane over the surface so that it touches the surface at the point of interest. If so, then the plane would make an angle with the horizontal namely the XY plane. Now does the trigonometric tangent of this angle mean anything at all? may be not and I'm just visualising too much! I'm not sure about this though as I haven't seen any textbook mentioning this, so i'm assuming this value may not be an interesting quantity, even though we could somehow derive it as a function of the the two partial derivatives.
The analogy should work! Though exactly what the tangent of the angle would be I'm not sure without working it out...
FAB TUTORIAL PROFESSOR TOM WILL LOOK FOWARD TO VIEWING MORE
You are a nice teacher. You explain math in such a way that I think everyone can understand and that is great : )
Thank you! 😃
Cool Im on my 2nd year of studying electrical engineering and i haven't heard of the partial differentiation before, only partial integration. But this wasn't tricky at all nice teaching!
Glad you enjoyed it Albin :)
Thanks so much.
In my view, the lecture is very easy for this subject and difficult examples must be solved to understand the partial derivative, such as, how to find out d^3y/dx^3 of f(x,y)=0.
I explain how to solve simple PDEs like the one you mention here: ruclips.net/video/uztjxrGY6Jw/видео.html
Crystal clear explanation sir. I am from India.❤️ On 21.01.2021
glad it helped!
Best explanation I have ever seen ❤
I’m doing my maths gcse this year I thought I was good at maths but watching this I realise there’s so much more to do in maths (I would like to do it at uni)
Whilst I don’t understand fully I didn’t lose myself in this and actually followed so you really must be a great teacher!
Thank you
Thanks for the lecture! Super clear.
Glad it was helpful Anthony!
Wow, so glad to have stumbled on your channels it's Amazing thanks ,🙏
Welcome!
I'm fine with the concept of a partial derivative, but what do we gain by introducing additional notation in the form of the "swirly-d" or "del" symbol?
For example, looking at the first function f(x) = xy² + yx³, and rewriting as z = xy² + yx³, what problem is created by writing;
dz/dx = y² + 3x²y ?
The notation dz/dx means that we are differentiating z with respect to x, so treating y as a constant is implicit. What issue exists with the standard dz/dx notation such that we need to use the "del" instead?
Is this merely a custom to "remind" us that we're dealing with multivariable function? Or does it resolve some ambiguity or other difficulty in using the same notation as for single variable derivative?
I'm still not sure, and I'm genuinely curious.
Idk how I got here I don’t even do maths but he’s lowkey legendary anyways so I’m not complaining
Brilliant In my first year of maths at university our course text was more like the philosophy of maths. I think Bertrand Russell could probably follow it but it was Greek to me.
cleared up my misunderstandings in this topic, thx prof❤️
Hey! that was easy and i was so worried about it.
Thank you so much! This was very useful!
Very well done. Easy to follow.
Glad it was helpful!
I just love to see people who are passionate about what they teach, especially you Dr. Crawford. The way you teach will definitely incorporate the students'/viewers' curiosity, like myself, which changed my view on calculus from being hard to somewhat fun. Thank you!
Thanks Claurence!
I wish I had such teachers back at school or uni times!
Excellent, as always
This is so well explained!
glad it was helpful!
This was amazing. Thank you so much for this video!
happy to help!
I really feel like you get downvoted because you have tattoos and piercings. I am also a doctor (of Physics, but that also makes me a Mathematician), I’m Black and my hair is braided.
It’s really inspiring to see another intellectual who does not fit the tired mould of “nerdy awkward guy with glasses”
^^this
Care to share your backstory? I am currently pursing a degree in Physics. I'm also bi racial (more African Am.), and also have a similar hair style lol. Would be interesting to hear your steps in how you got to where you are today.
The like to dislike ratio is completely normal.
@@damien7151 sorry but not on a video like this. This is pure, objective education. There is no falsehood stated. So you have to think "who disliked and why?"
@@Tommybotham on non-controversial videos I watch there is normally about a 100:1 like to dislike ratio - be it bots or weird, hateful people, and that’s pretty much what this has. 35 dislikes on a video with 100,000 views doesn’t seem like an issue to me, or that he’s getting hated on. Just seems like you’re making an issue out of nothing, because in the comments all I see is people appreciating Tom’s teaching.
Oh my god you have made a brilliant app too!!
@tae's bae i am not preparing for any exam
Great explanation in only around 18 minutes!
Glad you liked it
awesome! You are an amazing maths teacher!
Thanks Nate :)
I'd like to understand that better, so I'm going to search for it.
made it so simple to understand!
Wow, I am preparing for my FE chemical engineering exam. I have stopped at partial differentiation lesson and this poped to my recommendations! Thank you now I dont need to review that xD
Good luck!!