Differential equations and calculus from scratch

[@Ragnarok540]

Please do not apologize for making long videos, feel free to make them as long as they need to be. Thanks for sharing your knowledge.

[@aditya_a]

What a gigachad

[@mrvzhao]

I know this may be intended as an intro to calculus, but it servers even better as a review that chains everything together in an intuitive way that makes so much sense!

[@debuggers_process]

I am excited to see a video on numerical methods (and especially - optimization techniques, dynamic time steps, that sorts of stuff) in the future. Currently, I myself am working on physics simulations in conjunction with machine learning, and in this particular setting, some surprising things emerge, which I find interesting. For instance, let's consider simulating a fast-moving Lennard-Jones particle approaching a group of "cold" particles (particles with low thermal motion velocity). To prevent the simulation from "exploding" I need to perform several substeps of integration. Fun aspect of it is that the more energy there is in the simulated collision, the more energy I have to spend in real world on computing more substeps, to maintain a stable simulation. However, it seems there might be a more efficient approach. I'm considering tracking time separately for each particle and adding substeps based on the particle's energy in relation to its surroundings. In my example, particles that are far from the fast-moving particle in empty space or the cold particles before or even during the collision (if they are sufficiently far form it) don't require as many substeps since their local interactions have low energy. This mechanism surprisingly resembles time slowing down in the presence of high energy density. What makes it even more intriguing is that I only use local interactions on a hash grid, which essentially incorporates a finite max speed, "speed of light" - one grid cell per integration step. Another aspect is when I use a neural network as a black box computing local particle interactions, using a small square picture of the particle's surroundings as input and obtaining position and velocity corrections as output. I aim to maximize the time step while minimizing deviation in the total energy from the initial value. If I'm correct, this loss function can be seen as the action (as in "the principle of stationary action", in joule-seconds). It appears that our Universe utilizes the second law of thermodynamics, time dilation and the principle of least action to optimize its computations, spreading energy as much as possible and allocating its computation power on really cool things like black holes and supernovas)

[@TenMinutePhysics]

I all, sorry for the long video. I will go back to 10 minute videos after this 🙂

[@Z_Z.t]

Just make sure to add time codes in description, so people can find where they were left off.

[@TenMinutePhysics]

@@Z_Z.t Good point, just did it

[@ImaginaryBlend]

You don't have to apologize for giving us more good content ;)

[@nolram]

No need to apologise - this kind of content is incredibly valuable.

[@MrLB101]

I would also say, please do not apologise, this content is really great, how it combines so many areas of math with physics. Many thanks for this :)

[@MarcoGiordanoTD]

oh wow! That is A LOT of work! Thanks for taking the time! Always instant click when your new videos pop up

[@gameofpj3286]

I always like to watch videos about fundamentals, even if I already know a lot about a topic. I always get new insights! Thank you for this very cool video!

[@leolaroca]

Wonderful video! As years go by, it's easy to forget some of those details and proofs. This video is an excellent review!

[@yanvarskii8054]

hi! thank you very much for this video! i'd like to ask you a question, if i may. i haven't quite understood the "Are the Solutions Equal" slide [36:55]: how do you derive the equality of these two functions from the facts given? for instance, at the second point [the part about functions split] you've proved that if these two functions have equal values, then their derivatives are equal too. but i thought that we wanted to prove the first part of this assumption, i. e. show that these functions' values are indeed equal

[@williamchurch8401]

Thank you so much for your tutorials! I’m a beginning programmer and your clear and concise tutorials are amazing! Please do more on physics simulations. I would love to see one about plastic deformation or object tearing.

[@EggCess]

This video is incredible. I deeply love good explanations that are self-contained, and I am always fascinated by emergent properties and their capacity to blow ones mind. You really kick it out of the park with your explanations. I cannot even begin to understand the level of intuition you must have about these topics for you to be able to explain them so clearly and succinctly. Thank you, from the bottom of my heart, for sharing your knowledge with the world and for all the time you take to create these beautiful lectures and tutorials.

[@chyldstudios]

awesome, i'm looking forward to watching!

[@molybd3num823]

me too

[@tarekulyuo2487]

Nice video . I have a small remark concerning i^i: you need to handle it in the same way as when we calculate the nth root of x^n = -1: i^i = [e^(i*PI/2+2k*i*PI)]^i = e^(-PI/2)*e^(-2k*PI) for k in Z(set of integer numbers).

[@johnadriandodge]

Shalom evening Mr. TMP Outstanding videos you have. Thank you for sharing and teaching. Night

[@motbus3]

Hey! Thank you. I believe this kind of content fills the gap in the education.

[@LowLifeGraphicsProgrammer]

Honored to learn some serious math from the realtime physics master himself

[@sergio3674]

This channel: 10 minutes physics. Also this channel: 1:10 h video. 😮 It's a joke, I'm going to enjoy it for sure. 😊

[@TenMinutePhysics]

Watch the intro, I apologize for it there :-)

[@rfpixel]

nice explanation! thank you for a great video! expecting a lot more!!!!!!!!!

[@laurentlyaudet]

Nice video, it is funny to see what fits in one hour video when the same content at "le lycée" took many days. There is an error. If you play the square game with 2, you will not obtain 2, 4, 8, 16, 32, 64 but 2, 4, 16, 256, etc.

[@TenMinutePhysics]

Correct. I realized it after uploading the video 🙂 Great that you made it all the way to this point!

[@dprophecyguy]

Thanks for this video

[@nononononobita]

Awesome!

[@naztar4323]

Giga Chad Energy

[@bankrupt3am932]

This guy....

[@galangal4803]

Sorry. I would love to have watched the whole video but the background music was too distracting. I appreciate all your efforts though.

[@nicholascureton933]

I watch longer video if it's explained clearly like you did. Video duration is not a problem for me since the topic is deep. If explained clearly, I can also watch 10 hours video. I would rather watch 10 hours of clearly explained video than 10 min video which I don't understand anything.

[@melodymonger]

I got about 2 mins into the video but couldn't continue because of the background music. I'd love it if you'd re-released it with no music at all. The subject matter is something I seriously want to learn. Thank you for sharing your knowledge 🙏😃✌️