that's not always the case, in some cases you will require the full version stated in the video, eg you must you the full version to calculate the particular integral to the equation: d^2y/dx^2 + y = 5xe^2x
@@BicenMaths Following up from @niven's response: (From what I've worked out) In general, any differential equation with two distinct roots from the auxiliary equation, and where f(x) = kxe^(px) assuming p != α and p != β, has a particular integral in the form of y = λxe^(px) + μe^(px). (where μ is non-zero, except for when p equals the average of the roots) So the differential equation: y'' - (α + β)y' + y = kxe^(px) where p != α and p != β Using the particular integral of y = λxe^(px) + μe^(px) and solving results in λ = k / ((p - α)(p - β)) and μ = k (α + β - 2p) / ((p - α)(p - β)) Since k is non-zero and p != α and p != β, μ cannot be zero (unless 2p = α + β). The working out gets a bit messy but it simplifies nicely. I will now check whether this holds for repeated roots and imaginary roots. -Ryan
@@BicenMaths From exploring further with repeated and complex roots (to the auxiliary equation), I found that for all the differential equations we cover, μ is only equal to zero when 2p = α + β, where f(x) = kxe^(px) and α & β are the roots. (This means that μ is non-zero for all repeated roots as p != α). Otherwise, y = λxe^(px) + μe^(px) is required. Whilst solving I also noticed that either particular integral does not work when p equals one of the roots, which makes sense as we have to multiply by x. (This isn't very important but it is cool that it is consistent with other rules).
Thank you so much for these resources. These are incredibly useful. I'd be very grateful if you couldone for Further statistics 1 as well ,please. Hoping to see that before the exams. thank you so much.
Hi, how different is the syllabus content of Edexcel compared to OCR? Currently doing OCR and most the topics are the same but just wondering. Thank you!
Although I don't teach OCR, I am familiar enough to know that the content is very similar, and any overlapping chapters will be the same 'maths', so this video will still help you. Further Maths has compulsory content across the exam boards, which is all in Core Pure. You could take a look at some Edexcel papers, and you'll recognise lots of the questions! Good luck!
Thank you for your support over these 2 years sir the vast improvements throughout have been from your fantastic videos! Cp1 went really well so hoping to replicate that for cp2 🤞! Good luck everyone!!
Thank you Mr. Bicen. With the help of your videos i believe i got almost 100 percent in the cp1 paper and hope ill do the same with todays cp2 paper. Thank you for bringing me all the way here. Much love ❤️
As a further maths student who has their first core pure exam today, I’d like to thank you for the help as it’s given that a little bit of extra confidence that I can do my best today and helped me properly understand the topics I found hard!!!
That’s great to hear! Good luck with your self-study. Also, check out my Google Drive (linked in the About section of the channel) for lots of useful things, from exam questions to lesson notes that match my video tutorials.
not sure if you recognise my name yet from comments but i cant recommend you enough , just keep coming back to these be it in y12 or y13, absolute lifesaver
Sure - you can find my email when on the About section of the channel, but only when viewed on a laptop/computer browser. It’s under business email. I’ll comment it under here separately, as sometimes UA-cam blocks email addresses being posted as comments.
Hi is there a video like this for Alevel Further Maths Statistics I've been looking through your page and I just can't see it if anyone does know could you please link that video
Yes - but this is because the document/video is designed for Edexcel Core Pure Year 2 which doesn’t feature those topics :) They are in a different module (FP1).
@@BicenMaths oooh yes i see. I apologise. I was taught cross product alongside with dot product so i assumed they were covered in cp 1 and 2. Speaking of which, thank you for these videos i am glad to come across ur channel. Just curiously asking, are u going to make a fp1 video too or is tat not in been considered yet?
When you're doing the Particular integral of f(x) =kxe^px i'm pretty sure it only needs to be λxe^px
You are correct! My bad!
that's not always the case, in some cases you will require the full version stated in the video, eg you must you the full version to calculate the particular integral to the equation: d^2y/dx^2 + y = 5xe^2x
@@BicenMaths Following up from @niven's response:
(From what I've worked out) In general, any differential equation with two distinct roots from the auxiliary equation, and where f(x) = kxe^(px) assuming p != α and p != β, has a particular integral in the form of y = λxe^(px) + μe^(px). (where μ is non-zero, except for when p equals the average of the roots)
So the differential equation: y'' - (α + β)y' + y = kxe^(px) where p != α and p != β
Using the particular integral of y = λxe^(px) + μe^(px) and solving results in λ = k / ((p - α)(p - β)) and μ = k (α + β - 2p) / ((p - α)(p - β))
Since k is non-zero and p != α and p != β, μ cannot be zero (unless 2p = α + β). The working out gets a bit messy but it simplifies nicely. I will now check whether this holds for repeated roots and imaginary roots.
-Ryan
@@BicenMaths From exploring further with repeated and complex roots (to the auxiliary equation), I found that for all the differential equations we cover, μ is only equal to zero when 2p = α + β, where f(x) = kxe^(px) and α & β are the roots. (This means that μ is non-zero for all repeated roots as p != α). Otherwise, y = λxe^(px) + μe^(px) is required. Whilst solving I also noticed that either particular integral does not work when p equals one of the roots, which makes sense as we have to multiply by x. (This isn't very important but it is cool that it is consistent with other rules).
absolute legend. The exams starting in about 3 hours and 20 mins good luck everyone
Who is watching this in the morning‼️‼️
when we get into that exam hall we are gonna COOK we’ve got this
😂 same
Guilty as charged
Good luck brothers
you got me
Got my exam today 😂
Really helpful video!
exam in 2 hours, videos helped a lot cheers.
@LinkNinja thanks bro you too.
Thank you so much for these resources. These are incredibly useful. I'd be very grateful if you couldone for Further statistics 1 as well ,please. Hoping to see that before the exams. thank you so much.
I'm hoping to do one for FS1 eventually, but I think before the exams might not be realistic. We'll see!
These vids are an absolute Godsend. Thank you.
You’re very welcome 👍🏼
6:40 dont forget to mention changing the limits!!
Good luck tomorrow guys : )
Very helpful even for different exam board
33:07 why do we need to treat this an exception? The CF is different than what we would try as a PI anyways i think..
Im confused how you divide the polynomial at 24:08 . Can you explain how you divide that polynomial?
Try this about 9:35 ua-cam.com/video/Uw6woc7U90c/v-deo.html
I thought the bike was outside at 8:33 💀
The beeeessst!
Hi, how different is the syllabus content of Edexcel compared to OCR? Currently doing OCR and most the topics are the same but just wondering. Thank you!
Although I don't teach OCR, I am familiar enough to know that the content is very similar, and any overlapping chapters will be the same 'maths', so this video will still help you. Further Maths has compulsory content across the exam boards, which is all in Core Pure. You could take a look at some Edexcel papers, and you'll recognise lots of the questions! Good luck!
Thank you for your support over these 2 years sir the vast improvements throughout have been from your fantastic videos! Cp1 went really well so hoping to replicate that for cp2 🤞! Good luck everyone!!
You're gonna smash it! Let me know how it goes!
Thank you Mr. Bicen. With the help of your videos i believe i got almost 100 percent in the cp1 paper and hope ill do the same with todays cp2 paper. Thank you for bringing me all the way here. Much love ❤️
Good luck! Pleased to hear things are going well!
morning of cp2 anyone?
Yup 😢
today's exam wasn't super challenging, so I'm sure they will have cooked up some devious matrix and calculus questions for paper 2...
As a further maths student who has their first core pure exam today, I’d like to thank you for the help as it’s given that a little bit of extra confidence that I can do my best today and helped me properly understand the topics I found hard!!!
Good luck! You’ll do great!
How did u find it? The ocr paper was absolutely awful
@@mika-tu6ld don't think it was that bad but honestly I still probably got like 40%
as a student who had my first core pure maths exam that day... wishing I'd seen this😂
@@mika-tu6ld I agree
Good luck to everyone watching this before the AQA further maths exam today ✨✌️😭
spent all day stressed about core paper coming up and this video cleared up loads of stuff and really helped me out, thanks a lot man 👍
Don’t stress! You’ve got this!
Thank you so much! I'm self-learning FM, and it's a lifesaver to see everything laid out like this
That’s great to hear! Good luck with your self-study. Also, check out my Google Drive (linked in the About section of the channel) for lots of useful things, from exam questions to lesson notes that match my video tutorials.
How did it go? I'm self-learning FM too, was wondering if u did the full A-Level or just AS and how did u find it? Any tips?
This video may have just saved my Further Maths grade, ill let you know after the exam tomorrow eeeekkkkk
Good luck! 🤞🏼
How did it go
@@tagidinihousia4816 perhaps we’ll never know
All in 35 minutes?!?! Smashed it 💪🏽
You guys are gonna love the calculus bits from CP2! We’ll be starting it next 🙌🏼
This is absolutely brilliant! Thank you so much for providing blank ones, I cannot express how useful this series is!!!
At 27:43, shouldn't it be x.. + kx. + omega^2 x = f(x)?
edit: f(t) instead of f(x)
You're such an amazing person
Thank you so much
Great video
Could u do one for further stats 1 and 2?
I’m afraid I don’t teach these modules so can’t do this. But I’m pleased you like the video!
Hi on top of standard intergration you’ve written f’(x) is this is mistake I’m confused? Brilliant for region thanks!
Yes, no one has spotted that yet! Should be integral of f(x). I’ll change it on the pdfs 👍🏼
Thank you very helpfullll!
not sure if you recognise my name yet from comments but i cant recommend you enough , just keep coming back to these be it in y12 or y13, absolute lifesaver
Hi Bicen,
I have couple of questions regarding A level maths. Is it possible to email you? Thanks.
Sure - you can find my email when on the About section of the channel, but only when viewed on a laptop/computer browser. It’s under business email. I’ll comment it under here separately, as sometimes UA-cam blocks email addresses being posted as comments.
sebbicen@gmail.com
@@BicenMaths thanks much! 👍
At 11:56 for the even further identities, where do these come up in the textbook. I haven't come across them before.
Core Pure Year 2, 1.4 (page 13)
:)
Yep, it's there - but they don't make a big deal of them at all. So annoying!
I hadn't come across them either, but they are just the z^n+1/z^n and z^n-1/z^n formulae in exponential form (rearranged)
I just recommended this video to my further maths class as we have a mock tomorrow!!
I hope you all did well in the mock!
@@BicenMaths Thanks!! I found it mostly fine!! I haven’t spoken to the rest of the people in my class yet but hopefully they did well!
Amazing resources .Thank you
Men
Hi is there a video like this for Alevel Further Maths Statistics I've been looking through your page and I just can't see it if anyone does know could you please link that video
I don’t have one for FS1… yet! But I’m sure it’ll be coming in the future, just not sure when.
@@BicenMaths ok cool thank you
Paper 1 Wednesday! love you Mr Bicen. Still no Further Stats though
I’m sorry 😭 It’s my summer/autumn term project 😢 Which is too late, I know!
thank you so much
Hi do u have estimate for when the fm1 version of this is coming out? Would be useful for mocks coming up. Thanks for making these anyway.
Probably during the Easter break!
little disclaimer: This video does not include further vectors 2 (cross/vector product) or Taylor series
Yes - but this is because the document/video is designed for Edexcel Core Pure Year 2 which doesn’t feature those topics :) They are in a different module (FP1).
@@BicenMaths oooh yes i see. I apologise. I was taught cross product alongside with dot product so i assumed they were covered in cp 1 and 2.
Speaking of which, thank you for these videos i am glad to come across ur channel. Just curiously asking, are u going to make a fp1 video too or is tat not in been considered yet?
I’ve only made a few playlists for FP1 so far (at the bottom of the channel homepage) but there’ll be more coming eventually!
@@BicenMaths thank u for ur time sir
Sir please I want to get in personal communication with you 🤲🤲
My email is in the About section!
Please sir I don't get it please
sebbicen@gmail.com
Finally, now I've got everything except D1. Thank you so much
My pleasure! What modules do you do for FM? Doing further mechanics 1 video on here soon too... this one took ages, so much to summarise!
@@BicenMaths I'm not exactly sure what you mean by that sorry, but I think the answer is I'm doing FM1, CP1, CP2, and D1
Oh no problem - I just meant that I’m doing a memorising video for further mechanics 1 soon. 👍🏼
@@BicenMaths that's great, thank you very much for all this help