Differential Equations. All Basics for Physicists.

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Күн бұрын

• Differential Equations...
00:00 Why do I need differential equations?
00:30 What is a differential equation?
03:24 Different notations of a differential equation
05:03 What should I do with a differential equation?
06:15 How to identify a differential equation
07:11 What are coupled differential equations?
08:36 Classification: Which DEQ types are there?
15:48 What are DEQ constraints?
18:08 Difference between boundary and initial conditions
20:39 Solving method #1: Separation of variables
23:03 Example: Radioactive Decay law
24:49 Solving method #2: Variation of constants
28:02 Example: RL Circuit
31:33 Solving method #3: Exponential ansatz
37:17 Example: Oscillating Spring
43:21 Solving method #4: Product / Separation ansatz
More: en.fufaev.org/differential-eq...
Books by Alexander Fufaev:
1) Equations of Physics: Solve EVERY Physics Problem
en.fufaev.org/physics-equatio...
2) Alexander Fufaev and His Never Ending Story:
en.fufaev.org/lifestory

Пікірлер: 130

@fufaev-alexander 3 жыл бұрын

Support me if you want me to create more maths videos: kzfaq.infojoin Do you want to solve every physics problem? Try my eBook! ✅ Contains many useful physics formulas. ✅ Understandable for everyone, because it contains no vectors and integrals. ✅ Formulas are colored and visualized. ✅ Perfect for high school and undergraduate physics students. Click on the following link to get the book: en.universaldenker.org/physics-equations-book

@WildGamez 2 жыл бұрын

Yeah amazing 👏

@jonathanv.hoffmann3089 7 ай бұрын

🙏

@sakkariyaibrahim2650 Жыл бұрын

This is the best introduction on differential equation I could find in KZfaq. It deserve millions of likes

@fufaev-alexander Жыл бұрын

Oh wow, thank you very much sakkariya Ibrahim!

@josecarlosserralwigge519 5 ай бұрын

I agree totally

@peterverbeke1383 2 жыл бұрын

You are, quite honestly, the best, clearest instructor on youtube. I hope you persevere and continue making videos. Looking forward to your videos on electromagnetic waves. This is the highest quality teaching I have ever had the pleasure of watching. Thank you! I watch your maxwells equations videos about once a day because it is so good.

@douglasstrother6584 Жыл бұрын

Maxwell's Equations are coupled, first-order partial differential equations. Otherwise, a very good presentation.

@fufaev-alexander Жыл бұрын

yep, you're right. Thanks!

@Thomas-cat 3 жыл бұрын

youre so gifted at explanations ... thanks for your hard SIR

@fufaev-alexander 3 жыл бұрын

Thanks for the positive feedback!

@Thomas-cat 3 жыл бұрын

@@fufaev-alexander hey your video on maxwell equations is one of the best lecture on this planet thanks for putting that masterpiece I hope youre having a nice day

@andreranulfo-dev8607 9 ай бұрын

I just loved the minimalistic design!!

@surkewrasoul4711 10 ай бұрын

Cool channel, I think I will keep watching your videos to keep refreshing my knowledge of most of the topics here as I barely watch anything maths or physics related. Can't wait to start again though. Thank you for the awesome videos. 🤟

@fufaev-alexander 10 ай бұрын

Good decision! Better than wasting time with entertainment videos. ^^

@bhagatrishi5454 9 ай бұрын

Superb after 20 years of my college a good explanation with logic.

@AdorjanVas 9 ай бұрын

A very cool introduction, thank you!

@jack.d7873 Ай бұрын

Among the clearest communication of differential equations online. Very well done

@spaceman4286 10 ай бұрын

Really clear and thorough introductory explanations thank you very much.

@AkarshSundareswar 2 жыл бұрын

I just sat through and watched your entire Maxwell equations video. Awesome content

@revothuang Жыл бұрын

Explained all these very clearly. Thank you!

@fufaev-alexander Жыл бұрын

Thank you for the positive feedback! #### Become a channel member 🏆 #### As a channel member you have many cool benefits: * Badge next to your name * Unique channel emojis * Your vote counts 10x! * and much more kzfaq.infojoin ############### Of course, I would also appreciate a small donation: tinyurl.com/denker-donate -------- Top supporters appear here: universaldenker.org/hall-of-fame

@arj123sub 7 ай бұрын

Thanks for making this excellent video

@lowerbound4803 6 ай бұрын

It's so well-done!! So clear So good😻😻😻😻

@arkadevkundu3210 3 жыл бұрын

Thanks for your great explanations....please make a video on waveguide wave equations and different types of mode of operation in waveguide.

@TheBluePhoenix008 3 ай бұрын

Good to see I know nothing about differential equations.

@Flynn-hl7ug 3 ай бұрын

Thank you so so much for making this, it's incredibly helpful and easy to follow, thanks so much 🙏

@naveenmysore1123 Жыл бұрын

WOW!! The way you explained everything... beautiful

@fufaev-alexander Жыл бұрын

Thank you Naveen!!!

@Mouse-qm8wn 6 ай бұрын

Please post more videos because you are so good at explaining 😊Cheers from Denmark 🇩🇰

@journeytotheinfinity440 3 жыл бұрын

Great source for deep understanding

@fufaev-alexander 3 жыл бұрын

thank you very much!

@journeytotheinfinity440 3 жыл бұрын

@@fufaev-alexander I had seen your videos on Schrödinger's Equation and Maxwell's Electrodynamics and I am convinced that your ability to teach complex topics with simplicity will lead all the young minds of today's to their destination.. I want these kinds of videos more often.. and please translate all your videos from original German channel to English..

@Moises817 2 жыл бұрын

Oh god, I have never imagined I could understand this easy. Thank you sm

@fufaev-alexander 2 жыл бұрын

Thank you! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzfaq.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzfaq.infojoin

@atrandom1438 Жыл бұрын

wow! what a explanation is! thankyou very much.

@aleksisiltala10 Жыл бұрын

Would be ideal if subtitles existed. But thank you, I think this will help me much with final exam. It's nice to have these concepts thoroughly enough explained, but also without myriad of text.

@fufaev-alexander Жыл бұрын

Maybe I'll add subtitles! Thank you! #### Become a channel member 🏆 #### As a channel member you have many cool benefits: * Badge next to your name * Unique channel emojis * Your vote counts 10x! * and much more kzfaq.infojoin ############### Of course, I would also appreciate a small donation: tinyurl.com/denker-donate -------- Top supporters appear here: universaldenker.org/hall-of-fame

@asmatminhas8644 3 жыл бұрын

Well explained....

@willygreg3489 2 жыл бұрын

Excellent presentation, thanx!

@fufaev-alexander 2 жыл бұрын

@haywoodjohnson2865 4 ай бұрын

Thank you for your explanation it is a great relief of my frustration due to poor explanation of the topic.

@plekkchand 9 ай бұрын

Admirably lucid, many thanks. Might I suggest that "searched function" is not quite English and may cause a bit of confusion? We would say rather, "the function we seek/ are searching for". Even saying the "searched-for" function works fine.

@solaokusanya955 Жыл бұрын

Thank you

@Flynn-hl7ug 3 ай бұрын

This video should be shown to every first year physics student

@aritrabhattacharyya2374 Ай бұрын

Thanks Sir ❤ From India

@TheBananaman-sg4xd Жыл бұрын

For the RL circuit the method with y_h was a good example but you can also differentiate both sides and get a nice homogeneous boi

@omarberraqui8193 3 жыл бұрын

Great Explaining. Thank u so much can you please do a video about gradient, what his purpose 😁

@fatmazehra1998 2 жыл бұрын

Please more videos. We are waiting you professor ✅

@TeamHarrisonMachine Жыл бұрын

I LOVE THIS GUY

@CYTOTIMUS 11 ай бұрын

Thanks!

@fufaev-alexander 11 ай бұрын

Thank you for your support!

@sergiolucas38 2 жыл бұрын

Excellent video, so much quality :)

@fufaev-alexander 2 жыл бұрын

Thank you very much! I would appreciate it if you subscribe to my channel :) kzfaq.info/love/er4jsLnkNGr2KTLHQWP4rQ

@diegogarcia8623 2 жыл бұрын

Great videos! Can you make a video on fluid dynamics??

@fufaev-alexander 2 жыл бұрын

Thank you! I'll include the topic in the next poll maybe. Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzfaq.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzfaq.infojoin

@matthewharrison8531 Жыл бұрын

Wow you are a fantastic teacher. Wow

@fufaev-alexander Жыл бұрын

Thank you!

@manishankaryadav7307 4 ай бұрын

Hi Alexander, Thank you for the videos. There is minor typo starting time stamp at 17:20 (2nd, 3rd and 4th order DE). Thank you. Great work!🙂

@yasinhosgor4403 3 жыл бұрын

Just perfect.

@user-pd4wz1oo3x 2 жыл бұрын

Thank you for really good explanation, you deserve more subscribers. btw I will join the polls you're doing in the community tab

@fufaev-alexander 2 жыл бұрын

Thank you for joining the polls I'm doing in the community tab 😄

@novakonstant 6 ай бұрын

Great video! Could you enable subtitles?

@MatthiasLehnen 2 жыл бұрын

Great videos!

@fufaev-alexander 2 жыл бұрын

@MindMatriX 2 жыл бұрын

Pls upload more....about ...complex analysis.......classical mechanics.....atomic and molecular physics....classical electromagnetics....i will share all videos to my whole class

@roland-friedrichstricker4027 Жыл бұрын

Danke!

@fufaev-alexander Жыл бұрын

Danke für die Spende!

@gamerpedia1535 6 ай бұрын

Some say di/dt = ï I say di/dt = 0 because i is a constant :p

@adritobiswas1982 4 ай бұрын

Fun fact= i is current and i=dq/dt :p

@jacobvandijk6525 2 жыл бұрын

The usual German quality we are used to know. Just very well done. Can't wait for Green's functions ;-)

@pixooo2808 2 жыл бұрын

You are Amazing👏

@fufaev-alexander 2 жыл бұрын

Thank you very much! I would be happy if you subscribe to my channel: kzfaq.info/love/er4jsLnkNGr2KTLHQWP4rQ Feel free to check out my new physics website as well: en.universaldenker.org/

@usdesk Жыл бұрын

Do you have a video why do we use eulers number ?

@fufaev-alexander Жыл бұрын

nope, not yet

@RBRB-hb4mu Ай бұрын

Pleas change to black background and light colors , it’s easier to learn

@averageclassicalmusicenjoyer 11 ай бұрын

for the exponential ansatz, is there a rigorous explanation for how you can just add the two lambda exponential terms together to make the homogenous solution at 35:15?

@armandoscognamiglio1649 11 ай бұрын

you add them just because you have 2 lambdas, if you would have like 3 lamdas, 3 terms are needed and so on

@douglasstrother6584 Жыл бұрын

Chaotic behavior is seen in non-linear, second-order differential equations; consider the Düffing Equation. It's surprising that such a simple tweak can have such profound consequences.

@bubububu8673 3 жыл бұрын

Jjoooo auf allleesss deine videos sind an sich sooo gguutt (also zumindest deine Deutschen). Bei den englischen bin ich noch nicht soweit. Aber auf jeden fall deine Betonung und allleess Andere brrooo deine Erklärungen. Mashaallaah einfach zu wild

@jan-willemreens9010 2 жыл бұрын

...ABRACADABRA becomes AHA for me, after watching this super crystal clear Universaldenker presentation on Differential Equations... Many thanks, Jan-W p.s. Grüsse an Sie von den Nachbarn aus den Niederlanden...

@fufaev-alexander 2 жыл бұрын

Wow, thank you for your feedback! Greeting from Germany! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzfaq.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzfaq.infojoin

@jan-willemreens9010 2 жыл бұрын

@@fufaev-alexander ...In addition to my first comment. I and my fellow friends finally found someone who can present a relatively difficult, but at the same time very interesting subject such as Differential Equations, in a way that is accessible and understandable to many struggling people, and we mean this very seriously. In our opinion you deserve many times more credit than the statistics on your channel indicate! Once again we are very grateful to you for your commitment to making education more attractive and last but not least accessible to more people. Only the best on behalf of us, Jan-W

@ko-prometheus 10 ай бұрын

Can you and I calculate the nuclear decay of particles? Let's calculate as accurately as possible the nuclear explosion of a uranium nuclear device.

@jks234 10 ай бұрын

Are you saying "surge function"? What exactly is this term? I tried looking it up. I will simply assume I can think of it as a "function" or the "dependent variable".

@fufaev-alexander 10 ай бұрын

searched function :D I mean, the unknown function that must be found out by solving the differential equation.

@UsefulMotivation365 10 ай бұрын

Are you calling "The search function" to the function that you are looking to find with the solution of the differential equation? Or is like its technical name?

@fufaev-alexander 10 ай бұрын

By "searched function" I mean "unknown function" that has to be determined. Sorry, for the word-for-word translation from German... :D

@UsefulMotivation365 10 ай бұрын

@@fufaev-alexander Yeah, I guessed that the exchange German-English was giving you problems. Thanks man!

@egozMaster Ай бұрын

will you put subtitle?

@bernardoramirez1759 2 жыл бұрын

This is just beautiful, man. Can’t thank you enough Liked, subscribed and if I wasn’t broke woulda donated

@fufaev-alexander 2 жыл бұрын

Thank you very much for the positive feedback! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzfaq.infocommunity

@crogi7413 6 ай бұрын

Excuse me, at 30:37 why is L / R taken outside?

@crogi7413 6 ай бұрын

and at 35:40 how is the quadratic formula giving those soltuions?

@uyka32 6 ай бұрын

U_0/L multiplied by L/R is the same as U_0/R

@stimulantdaimamld2099 2 жыл бұрын

GREAT

@aris.konstantinidis 2 жыл бұрын

You make the "Ansatz" hahaha best :)

@fufaev-alexander 2 жыл бұрын

😁

@fufaev-alexander 2 жыл бұрын

Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzfaq.infocommunity

@amiasam3354 3 жыл бұрын

That intro😂🤣

@atrandom1438 Жыл бұрын

sir; reply please.... which state are you from? what is your name? what is your profession(job)?

@Jehannum2000 3 жыл бұрын

I have never heard the word 'ansatz' before. I thought it was a mishearing / mistranslation or something!

@fufaev-alexander 3 жыл бұрын

"approach" ^^

@morosanvalentin2524 2 жыл бұрын

great

@fufaev-alexander 2 жыл бұрын

@atrandom1438 Жыл бұрын

nice

@fufaev-alexander Жыл бұрын

thank you!

@lonelystudent Жыл бұрын

god-tier video🔥

@fufaev-alexander Жыл бұрын

Thank you!

@arthurbruno9193 5 ай бұрын

Who uses D for the stiffness of a spring?

@arthurbruno9193 5 ай бұрын

Very nice video tho

@roccraz 3 жыл бұрын

Someone came up with a new theory of gravity, the theory of everything at theoryofgravity org

@rubenlarochelle1881 Жыл бұрын

First part of the video: playing with a spring Last part of the video: speaking German with upside-down Greek letters

@gysghost5126 3 ай бұрын

27:58 why is it +A and not -A

@Kinpin42 3 ай бұрын

It's arbitrary

@IoT_ Ай бұрын

Can be any arbitrary form : ln(A) cos(A) , you name it. It's done for simplicity. Anyway , when you get the coefficient based on the initial conditions, it will get always the correct form.

@user-ds9wl2ke8d 5 ай бұрын

i assume you meant Newton's second law 1:05

@fufaev-alexander 5 ай бұрын

yep!

@user-ds9wl2ke8d 5 ай бұрын

@@fufaev-alexander okie dokie

@safrilhidayat9672 2 жыл бұрын

Come here for understanding navier stokes eq, now i understand that Navier Stoke is a final boss.. Great explanation btw.. 👌

@fufaev-alexander 2 жыл бұрын

Haha 😄 You watched the whole video? Wow, not bad! Thanks! Feel free to join the polls I'm doing in the community tab. There you can vote for the next video topic: kzfaq.infocommunity If you regularly visit my channel and like my videos, I would be happy about 1 x coffee ☕ per month: kzfaq.infojoin

@ishtopor 3 ай бұрын

Интересно, нафига делать название и описание на русском, если отказ от языка - принципиальная позиция и нету даже субтитров...

@Downlead 2 ай бұрын

Your videos are very good, but they don't have subtitles. Could you fix it?

@jameshopkins3541 Жыл бұрын

LA HACE LARGA THIS IS TOO SLOW!

@federicopagano6590 11 ай бұрын

8:20 those equations are wrong its without square root

@jeffreychen1191 9 ай бұрын

It would be valid for the field of gravitational potential (proportional to r), not force (proportional to r^2). He never specified it was a force field.

@federicopagano6590 9 ай бұрын

@@jeffreychen1191its an acceleration equation (left hand side)hence a=F/M it keeps the r^2