Oxford Calculus: Integrating Factors Explained

[@TomRocksMaths]

Practice the 'Integrating Factor' technique with this free interactive worksheet from Maple Learn: learn.maplesoft.com/index.html#/?d=MOLTEIOLPLCLMKAPJUFFHIANENLGMLLOGSLLKGDSPTGNJSLGHLLOERETKFDRDMDQGPARIRIMJNJMBLBIHSKONTJQGSDMCNPHNKJQ

[@keyoorabhyankar5863]

Sir, How does one come up with these integrating factors? Surely, the one mentioned in the vedio cannot be the only one.

[@TomRocksMaths]

The video explains where the general formula comes from no matter what differential equation you have.

[@keyoorabhyankar5863]

@@TomRocksMaths I'm sorry i didn't understand. Are you saying that's the only IF everybody uses?

[@adamlasry1691]

I’m a middle aged man and granddad who loves to learn maths. Your beautiful style and explanations are really great! Thank you so much for your efforts. Very appreciated. Thank you.

[@TomRocksMaths]

Awesome thanks Adam!

[@SC-RGX7]

Lol, imagine entering uni for the first day, expecting to see an old dude as your match teacher and see that this dude is gonna take your class. You'll definitely be confused for some classes until you get used to it.

[@Gonduska]

That explanation, and showing how non-homogeneous and homogeneous equations can be connected via the integration factor was beautiful. It makes math so much more fun when I understand how it works, not just learning how to solve stuff and calling it a day. And also, as a non-native English speaker, I really appreciate the way you speak. So articulate. Thanks a lot

[@eastonpeter1242]

Wonderful!!!! I'm an 81 year old Calculus hobbyist, and this lesson is wonderful.

[@monstermauz8158]

This was absolutely amazing. I took diff equations with a professor that would just read his PowerPoint’s so I didn’t get time to truly appreciate what was going on. But after viewing this video (specially when you got to the solution of the non homogeneous solution) my jaw dropped. Brilliant, simply brilliant

[@TomRocksMaths]

[@BrainsAndBeats_]

Hey Tom, thanks for helping a lot with forming my intuition for advanced maths. The U.S. education system really didn’t teach me a lot of the “why” more so “just solve it for the exam.” Used to have lots of trouble with this subject, but now thanks to your videos and others, I’m a lot less apprehensive toward calculus and physics

[@TomRocksMaths]

Great to hear - thanks!

[@Jajareto]

Never have had a crush on a professor until today.

[@מיכאלקונטרוביץ]

Actually, the idea of integrating factor is much more general than this particular case of the linear equation. In much more general way, it's intended to solve equations that get to be exact after multipling by the integrating factor. Exact first order ODE is very strongly related to something that well known in physics by a conservative force, or a field with potential, like the gravitational field or the electric field. These are vector fields which have a potential, or an antiderivative. It's a generalization of the main theorem of calculus. Thank you Dear Tom for awesome explanation!

[@kummer45]

This man must be a fan of Prodigy. But this guy is a prodigy at math. I'm glad that such spirit is carried throughout the ages. A fresh look at math never hurts. On the contrary we go throughout those proofs on such theorems understanding the strategies behind them. There should be more teachers like this.

[@bint-abdullah]

Thank you for the simple explanation Tom. I've been struggling to wrap my head around this concept for long time

[@TomRocksMaths]

You're very welcome!

[@lordnookes]

This is the best explanation of integrating factor I have come across. Thanks Tom!

[@dalisabe62]

This is how you present a material after you have thought it through very well and allow your brain to be fueled by inquisition and entertaining logic without forcing your audience to believe or wonder about your conclusions.

[@SalehGoodarzian]

Thank you for your video and explanation. You made it easy to recall everything from 22 years ago. Best regards...

[@xyzxyz9107]

Thanks for explaining it all in such fine detail. I quit maths after GCSE but recently went back to uni for an engineering degree, there is so much assumed knowledge in maths and it can be really hard to find things explained as a whole. You taught me this in 20 minutes what 2 hours of melting my brain on my lecture couldn't! Really lovely video

[@TomRocksMaths]

amazing - you're very welcome :)

[@Georgexb]

This is a lovely explanation, Tom

[@TomRocksMaths]

Thanks George!

[@cameronbrown7231]

You are such an inspiration to me man. Love the new hair btw!!

[@TomRocksMaths]

Awesome! Thank you!

[@likithstochastic]

Great! I think it is always good to do the derivative steps (Those 3 steps) than remembering the final result.

[@TomRocksMaths]

Agreed.

[@wetteddog333]

Hi Tom, Great video, thanks a lot :D. If you plan on making another one similar, a video on second-order homogenous differential equations would be excellent. Sadly I've just left school so I can't speak to my teachers, but your videos are amazing. Solving them is a part of the edexcel a level further maths course.

[@TomRocksMaths]

I talk about ODEs in my video here: kzbin.info/www/bejne/fGaXqpuId56keqs

[@socialdgirl011]

Not really sure how I ended up here, why I watched the whole thing, or plan on watching more yet here we are.

[@TomRocksMaths]

we love maths

[@ЕвгенияЛысенко-у4н]

Thanks for a nice, clear explanation! That helped a looot! 🤩

[@yichengao1010]

Thanks for your clear explanation

[@alexwolffe7805]

Love your content, love how you teach and love how your new look!

[@TomRocksMaths]

[@rishikkalagara6814]

Great content, very eductational. Keep up the great work!

[@giosanchez2714]

I was just looking for this! Thanks ❤️

[@rossg9361]

Beautifully explained. Bravo. 😀🏴󠁧󠁢󠁳󠁣󠁴󠁿🇨🇦

[@TomRocksMaths]

Thanks Ross - glad it helped

[@HimanshuBhagwat24]

Beautiful explanation

[@thenungod]

i love doing maths in my spare time even though iv only just finished my first yeear of my 2 year maths+further maths a level, today i worked out a general formula for the trapezium method (an estimation for integration)

[@johnchessant3012]

Great video! When I was learning this I remember y' - tan(x) y = 1 was the example that made this click for me!

[@TomRocksMaths]

Yes - a nice example indeed.

[@marianaboscolo9283]

This video is completely perfect

[@TomRocksMaths]

[@europeancolony]

Looking at the thumbnail, I thought you were Boris Johnson lol

[@lukeultimatefrisplays]

i found this video really helpful, thanks, its really interesting and cool

[@TomRocksMaths]

[@ahsanhabibkhan6217]

Good one Tom! I never understood the theory in my Cal 2 class just knew how to do the process! PS: Love your shirt !

[@TomRocksMaths]

thanks!

[@ompancholi5777]

Is this first year uni stuff, bc we we're taught this in school at 16. Obviously it gets much more complex, but it's nice that I actually get what's happening. Great explanation have a test on in it in 2 days.

[@TomRocksMaths]

hope it went okay!

[@ompancholi5777]

@@TomRocksMaths Yeah man, met my offer for med at aberdeen. Cheers for the help.

[@antoniobennett3588]

While I'm not thinking of going to uni to study maths directly, I do want to study physics and I just hope that I have a professor like you. Also any advice for uni, I'm thinking of doing a master's degree afterwards but I'm not sure if I should bother with it and get a phd after the degree? If anyone has any advice it would be much appreciated.😃

[@TomRocksMaths]

don't worry about planning everything right away... pick your degree and keep studying as long as you enjoy it :)

[@antoniobennett3588]

@@TomRocksMaths thanks will do, also love the content keep it up :)

[@NikonKanava]

This looks interesting.

[@spazmoidectomorf6209]

If you ever get the chance, I would be awesome to see how you fell in live with math and journey to where you are now, maybe even a draw my life if you still deem trendy and hip with the kids

[@TomRocksMaths]

Find out more in my Numberphile interview here: kzbin.info/www/bejne/lXnafHqkmNh6pZI

[@LearnEnglishwithJames.]

My man rocking nail varnish! Nice

[@camerontrew214]

3:46 my teacher says with a natural log of a function to put + ln |c| to make it easier to express as C is just a constant

[@ghst5354]

so im not sure if you may even read this sir, but it would be nice if you could attempt to do JEE papers (mains and advanced), the papers consist of 3parts physics chemistry and math but you can do only the math parts if you like, and if possible give your opinion on these exams and let us know how tough they truly are. love the content!

[@wisemkasare3918]

Thank you very much Sir. most grateful

[@TomRocksMaths]

Most welcome

[@gabefoster1737]

Is this the pace you teach your college courses at? Or do you go a bit faster/slower?

[@TomRocksMaths]

Depends on the level of the students tbh. As I teach them in groups of 2 or 3 I modify the pace to suit the students.

[@mnbv24653]

Love the new hair colour!!!😳😳😳😍😍

[@TomRocksMaths]

[@edmardupreez8742]

Why can't the math Lecturers at my university not be this good. I'm an engineering student currently busy with the last math module. All of our teachers have PhD degrees but not any of them explain nearly as well as you do

[@TomRocksMaths]

[@itsreeah2663]

On another social media i set up a maths party, where you can do everything maths tomorrow Saturday 22 May. Also, someone asked me online for maths help at like 23:30 and I was struggling was basic addition lol, i hope i got the answer right :( :)

[@rsports7713]

Dr Tom you never looks like a professor or mathematician but you look like a rapper

[@TonyMetal]

Would be cool to also see where the integration factor comes from since it looks a lot like the homogeneous solution.

[@TomRocksMaths]

I mention this in the video, it is very similar to the homogeneous solution.

[@vivekmishra8462]

Sir Any short Trick In finding Square Root

[@ValeriaMedina001]

Yooo thank you so much! You are inspiring me to learn a lot of math 😂

[@zs8460]

Hi! Love your videos, but I wanted to ask where did you get the shirt from? Trying to maximise my drip levels 😤

[@TomRocksMaths]

This was from Topman.

[@pragyadhungana6984]

thankyou for the lesson. i also loved your hair, its pretty cool.

[@TomRocksMaths]

[@mikefranz1056]

Great job. But as an engineer, I'd like to know how oft a real problem is reduced to this type of equation.

[@TomRocksMaths]

Surprisingly often (at least for my work in fluid mechanics)

[@johnforster4856]

Great explanation Dr!

[@TomRocksMaths]

Thank you John!

[@jijijiykykykyk6442]

thank you so much．very helpful.

[@TomRocksMaths]

you're welcome :)

[@azielkhong6865]

can u do sg a levels

[@baylordsett2739]

My god, thank thee for this blessing as I feel screwed for Further Maths

[@mlam4221]

Hi, Tom I was wondering why it called “ 1st order LINEAR differential equation “ What is the difference between 1st order differential equation and 1st order linear differential equation?

[@TomRocksMaths]

linear means the terms are of the form x or 2x rather than any higher degree polynomials like x^2 etc.

[@NateCrownwell]

This is really cool, thank you :)

[@TomRocksMaths]

Glad you enjoyed it Nate!

[@bloodonyx]

damn your seem so nice that the first impression i got from you is a primary school math teacher

[@shannonmarie9441]

I really want to watch these videos because he seems so lovely but I’m a literature student and I have never had such a poor linguistic grasp on anything as I have on maths lingo

[@rob876]

I could never remember the steps to do this during exams. So I would always start by assuming an Integrating factor I(x) s.t. y’I + Ipy = (Iy)’ and then solving for it. Otherwise, if the IF was easy to guess, I would just state it. I think even if I’d remembered all the steps and formulæ, I’d still prefer to do it my way.

[@NP-zl7dz]

Your new hair is looking good

[@TomRocksMaths]

[@itsreeah2663]

I can’t wait for your birthday so that I can wish you happy birthday

[@TomRocksMaths]

December :)

[@itsreeah2663]

@@TomRocksMaths oh my birthday was the 1st of May, or wish you happy birthday in December

[@itsreeah2663]

@@TomRocksMaths also I hope your weekend is going okay

[@TomRocksMaths]

Happy belated birthday!

[@BlackPillHurts]

You = too good to be true

[@TomRocksMaths]

[@mathsandsciencechannel]

VERY NICE, LOVE INTEGRAL. Hello there! I am your misery and secret math tutor. Don't tell anyone. thanks

[@itsreeah2663]

I haven't even started my GCSE causes yet and I'm lying in bed at 6:14am cuz I couldn't sleep watching Oxford Calculus despite being blind. I'm using a screen reader BTW and yes blind people don't have to have grey eyes! What am I doing right now?

[@mishalchowdhury5610]

why teacher got much drip??!?!!

[@aboplus1010]

I love your tattoos😍😍😍

[@pr_some148]

What happened to your hair? Actually it’s pretty cool😎

[@TomRocksMaths]

Blame lockdown.

[@coc9993]

From india

[@mohamedababou8067]

It is imperative that you start first by teaching those interested in Mathematics that Numbers have an end.

[@indeedhid380]

if you guys are worried about the kinda multiplying by dx, then think of it this way: write dy/dx as y'(x) int [1/y(x)]y'(x)dx= -int p(x)dx set u = y(x) -> du = y'(x)dx int du/u = -int p(x)dx

[@bazwardo7191]

my goal in life is to become you

[@TomRocksMaths]

I appreciate the compliment, but just be yourself - you’re awesome :)

[@PopPhyzzle]

Your Pokeball tat is sick. Love the 3-D aspect of it. I can literally hear what it'd sound like to get konked in the head with it.

[@bubbaluv6487]

his hair integrates a flock of seagulls

[@TomRocksMaths]

lol - nice 80's reference

[@akshatjangra4167]

You looked like that imaginary friend in A Beautiful Mind

[@王子維-y3g]

now i don’t have to image machinegun kelly teaching me calculus

[@jos2294]

my man quit his Rockstar career to teach puny mortals integrals

[@TomRocksMaths]

if only this were true...

[@adityachaudhary5674]

I want a heart

[@monmoymaahdie3177]

yaooo look at dat DRIPPP haircut

[@TomRocksMaths]

[@leviackerman5870]

Idk why I'm here. I only take alevel maths.

[@TomRocksMaths]

Integrating factors come up on some courses/syllabi I think

[@MaadEngineer]

YOU Deserve reading the Quran

[@ramnathyadav3507]

Flag

[@NateCrownwell]

Do you have a boyfriend or girlfriend?

[@itsreeah2663]

5 questions no one can answer: 1. Who let the dogs out? 2. What does the fox say? 3. What do we do with a drunken soldier? 4. What's the meaning of life. 5. Why does x show up all over maths???

[@blazbohinc4964]

This guy must be really good at maths if they let him dress up as a clown. Good for him.