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# Differential Equations:After A-level

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1. Hi guys!
I'm sure some of you have been studying Differential equations at A-level and are wondering how they can be used after A-level.

As part of my university maths course I have created this video, to explain what they are used for and what you can study with them. this includes some basic concepts from my 2nd year Mathematical Modelling unit and 3rd year Mathematical Biology unit. (To give you a taster!)

https://youtu.be/L7UW9pnKJP8

Hopefully it will help you understand their significance and maybe you'll consider studying them further in one the subjects mentioned.

If anyone has any feedback, please comment on here! Part of my assessment is evaluating my work, so comments from A-level students are very helpful, even if they are negative!

Thanks guys!
Good luck with the exams!

Feel free to ask me questions about University Maths! I'm a final year BSc Mathematical Sciences student at The University Of Bath.
2. I study 2nd order differential equations , is that part of it too?
3. (Original post by beth-jane)
Hi guys!
I'm sure some of you have been studying Differential equations at A-level and are wondering how they can be used after A-level.

As part of my university maths course I have created this video, to explain what they are used for and what you can study with them. this includes some basic concepts from my 2nd year Mathematical Modelling unit and 3rd year Mathematical Biology unit. (To give you a taster!)

https://youtu.be/L7UW9pnKJP8

Hopefully it will help you understand their significance and maybe you'll consider studying them further in one the subjects mentioned.

If anyone has any feedback, please comment on here! Part of my assessment is evaluating my work, so comments from A-level students are very helpful, even if they are negative!

Thanks guys!
Good luck with the exams!

Feel free to ask me questions about University Maths! I'm a final year BSc Mathematical Sciences student at The University Of Bath.
I'm not an A-level student but I am offended you did not include any physics or mechanics examples
4. (Original post by Ayaz789)
I study 2nd order differential equations , is that part of it too?
I haven't explicitly discussed them, but they are also an essential part of modelling certain things, for example the wave equation is used within physics to model sound waves and light waves etc.
5. (Original post by beth-jane)
I haven't explicitly discussed them, but they are also an essential part of modelling certain things, for example the wave equation is used within physics to model sound waves and light waves etc.
Ahh okay thats great!
6. (Original post by TheBBQ)
I'm not an A-level student but I am offended you did not include any physics or mechanics examples
Intentionally done! At A-level I felt that the focus was based on Mechanics and Physics too much, so students, like myself, who don't hold as much interest in these can be put off from studying maths further.
The aim was to highlight other examples, so i'm pleased you have had that response!
7. (Original post by beth-jane)
Intentionally done! At A-level I felt that the focus was based on Mechanics and Physics too much, so students, like myself, who don't hold as much interest in these can be put off from studying maths further.
The aim was to highlight other examples, so i'm pleased you have had that response!
Maybe some physics examples that aren't really seen at A-level? Like SHM, schrodinger equation, general relativity?

Black-Scholes is a nice one for economics, and you can explain that with a substitution it essentially becomes a diffusion equation!

Maybe even Stochastic differentials for unstable stock markets, which are also used to explain the random motion (normally distributed) of particles in a gas/liquid if you feel particularly daring..
8. (Original post by TheBBQ)
Maybe some physics examples that aren't really seen at A-level? Like SHM, schrodinger equation, general relativity?

Black-Scholes is a nice one for economics, and you can explain that with a substitution it essentially becomes a diffusion equation!

Maybe even Stochastic differentials for unstable stock markets, which are also used to explain the random motion (normally distributed) of particles in a gas/fluid if you feel particularly daring..
Haha some good ideas! Maybe good as an extension video... I feel like adding that but keeping it below 5 mins would be hard! I agree that it would be good to be able to talk about a wider range of examples in detail, rather than just mentioning that they are used within that area.
9. (Original post by beth-jane)
Hi guys!
I'm sure some of you have been studying Differential equations at A-level and are wondering how they can be used after A-level.

As part of my university maths course I have created this video, to explain what they are used for and what you can study with them. this includes some basic concepts from my 2nd year Mathematical Modelling unit and 3rd year Mathematical Biology unit. (To give you a taster!)

https://youtu.be/L7UW9pnKJP8

Hopefully it will help you understand their significance and maybe you'll consider studying them further in one the subjects mentioned.

If anyone has any feedback, please comment on here! Part of my assessment is evaluating my work, so comments from A-level students are very helpful, even if they are negative!

Thanks guys!
Good luck with the exams!

Feel free to ask me questions about University Maths! I'm a final year BSc Mathematical Sciences student at The University Of Bath.
Very good voice!
10. I'm a Maths student and I hate the second year Differential Equations module at my uni. Terrible teaching with terrible structure. Easily the hardest. It's labelled as an applied course but we start the module with the Contraction Mapping Theorem...
11. (Original post by yl95)
I'm a Maths student and I hate the second year Differential Equations module at my uni. Terrible teaching with terrible structure. Easily the hardest. It's labelled as an applied course but we start the module with the Contraction Mapping Theorem...
Thats such a shame! I'm not much of a fan of the pure maths side of my degree and I have loved looking into differential equations as an applied subject!
I don't think I have come across that theorem within any of my courses, so cannot comment on it I'm afraid!

If you aren't completely put off the topic yet, if your uni offers mathematical biology I would strongly recommend it as a interesting applied course! There are also some really clear textbooks available for it, which I have found rarely to be the case in other topics!
12. (Original post by beth-jane)
Thats such a shame! I'm not much of a fan of the pure maths side of my degree and I have loved looking into differential equations as an applied subject!
I don't think I have come across that theorem within any of my courses, so cannot comment on it I'm afraid!

If you aren't completely put off the topic yet, if your uni offers mathematical biology I would strongly recommend it as a interesting applied course! There are also some really clear textbooks available for it, which I have found rarely to be the case in other topics!
You never had to do the Contraction Mapping Theorem throughout the entirety of your degree? o_o
Yeah, there are optional courses in Mathematical Biology for third year. I enjoyed Biology at school. We did do an applied course in first year involving ODEs and PDEs in second year but I feel as though we could have done even more.
13. (Original post by yl95)
You never had to do the Contraction Mapping Theorem throughout the entirety of your degree? o_o
Yeah, there are optional courses in Mathematical Biology for third year. I enjoyed Biology at school. We did do an applied course in first year involving ODEs and PDEs in second year but I feel as though we could have done even more.
No, it's in a metric spaces module which I didn't chose as an option...
14. (Original post by beth-jane)
No, it's in a metric spaces module which I didn't chose as an option...
Ah, I envy you. We have a Metric Spaces option in second year as well.
15. (Original post by beth-jane)
Hi guys!
I'm sure some of you have been studying Differential equations at A-level and are wondering how they can be used after A-level.

As part of my university maths course I have created this video, to explain what they are used for and what you can study with them. this includes some basic concepts from my 2nd year Mathematical Modelling unit and 3rd year Mathematical Biology unit. (To give you a taster!)

https://youtu.be/L7UW9pnKJP8

Hopefully it will help you understand their significance and maybe you'll consider studying them further in one the subjects mentioned.

If anyone has any feedback, please comment on here! Part of my assessment is evaluating my work, so comments from A-level students are very helpful, even if they are negative!

Thanks guys!
Good luck with the exams!

Feel free to ask me questions about University Maths! I'm a final year BSc Mathematical Sciences student at The University Of Bath.
I really enjoyed the video!

Quick question, I do theoretical physics (first year) and have the choice of taking 'non linear differential equations' in my second year and I am just wondering how hard it is relative to first year maths? as I am doing well in my maths modules but just concerned it might be too hard

Might be a bit difficult for you to give a accurate view as I am at a different uni but I have linked the module description below and any advice you can give would be great!

http://webprod3.leeds.ac.uk/catalogu...=P&M=MATH-2391

Thanks and keep up with making videos that one was great!
16. Not sure whether this might be useful to the IMA or LMS, I know the IMA have got a big careers website, maybe they'd be interested in it for outreach to A level students (not sure how you'd go about asking them). Your uni probably has some kind of local outreach activities, speak to your lecturers and see if it's useful to them in any way.
17. (Original post by madmadmax321)
I really enjoyed the video!

Quick question, I do theoretical physics (first year) and have the choice of taking 'non linear differential equations' in my second year and I am just wondering how hard it is relative to first year maths? as I am doing well in my maths modules but just concerned it might be too hard

Might be a bit difficult for you to give a accurate view as I am at a different uni but I have linked the module description below and any advice you can give would be great!

http://webprod3.leeds.ac.uk/catalogu...=P&M=MATH-2391

Thanks and keep up with making videos that one was great!
Thanks! I'm considering making another one after I finish my exams, so I need to get thinking on what to talk about next!

That unit sounds incredibly similar to one of my second year modules! I found the content really interesting, and as a physics student I'm guessing you can visualise things pretty well, so you should have no problems with the two graphical elements(Phase planes and bifurcation diagrams), which is the section i found most people struggled with. I would not say that the unit is hard as such as its very interesting and can be applied to many things. It should also give you a really good basis if you want to look into modelling systems further.Its very process heavy, so if you can memorise step by step algorithms, then you should be able to follow it easily Overall I would say it was my favourite module last year and one of the most approachable (If well taught). There are plenty of good textbooks about it if you don't understand the lecturer.
18. (Original post by Associativity)
Not sure whether this might be useful to the IMA or LMS, I know the IMA have got a big careers website, maybe they'd be interested in it for outreach to A level students (not sure how you'd go about asking them). Your uni probably has some kind of local outreach activities, speak to your lecturers and see if it's useful to them in any way.
I made the video as part of my communicating maths module, which is run by one of the Bath Taps Into Science founders, so once its marked I'm going to have a chat with him about sharing it with some outreach programs Thanks for the suggestion!
19. (Original post by beth-jane)
I made the video as part of my communicating maths module, which is run by one of the Bath Taps Into Science founders, so once its marked I'm going to have a chat with him about sharing it with some outreach programs Thanks for the suggestion!
That sounds like an interesting module, is that part of a maths education type module? Excellent, that's quite a nice video and it would be nice to see it put to good use.
20. (Original post by Associativity)
That sounds like an interesting module, is that part of a maths education type module? Excellent, that's quite a nice video and it would be nice to see it put to good use.
Yeah, its teamed with Bath Taps Into Science, so the idea is you take part in 3 events the communicate an aspect of maths, with the bath taps science festival and a Royal institution masterclass being 2 of them. Then you reflect on your experiences and develop an individual piece to communicate an idea, so I chose this
It's a nice practical unit, usually aimed towards potential teachers

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