Leibni(t)z Integral rule

Hey, I mentioned that I did a project in summer on my PS and I was wondering if any one knew how to explain it to me (Im an A Level student) or any sites that could explain it ( I did use it on the project but I had someone to help me and I cant really remember) because Im afraid they may ask me about the project which I can talk about but the maths behind the solutions used is a bit tricky so I would like to try and understand the rule so that I have some understanding before interview.
Thanks

Reply 1

Dez

The Leibniz integral rule takes some pretty meaty calculus to understand properly, let alone use. Two-dimensional calculus isn't generally touched upon until university level anyway, I doubt any interviewers would seriously expect you to understand properly where the result comes from and all it's applications. If you understand how it's used in your project, I'd say that's pretty good going on it's own really.

Reply 2

twinsforever

Dez

Well, I know it is used to get from one formula to the next, and the latter was used in the codes (on Matlab) to find the solutions. Thank you for your help, Dez. I will try to look at as much as I can before the interview just incase. Anyway it will be good for me looking at some extra maths even if I dont understand most of it.

Reply 3

twinsforever

Dez

Sorry to bother you but do you know any websites or anything to teach ordinary and partial differential equations? Or are they very similar to first and second order differential equations?

Reply 4

around

Which one? There are two Leibniz integral rules: one is basically a generalisation of the product rule and the other is differentiating under the integral sign.

Reply 5

twinsforever

around

Which one? There are two Leibniz integral rules: one is basically a generalisation of the product rule and the other is differentiating under the integral sign.

Differentiating under an integral sign

Reply 6

Dez

twinsforever

Sorry to bother you but do you know any websites or anything to teach ordinary and partial differential equations? Or are they very similar to first and second order differential equations?

Blimey you're ambitious. I've got about half an inch's worth of notes on ODEs (to say nothing of partial ones) from second and third year and I can't say that I understand them properly (I'm more of a pure maths guy). Your best bet would be a library book I expect, I can't think of any online resource that'd teach you well enough, though Google may prove you wrong (Google books especially). Your best bet is to relax a bit though, studying differential equations before even attending uni is a bit extreme!

Reply 7

twinsforever

Dez

Thanks for the reply. It was something I came across on the project but Im learning first and second order differential equations at school atm. Obvisously these topics are a bit stretching, i may see what I can find out about them and see if I understand something. I didnt really know what level these techniques were so thanks for clearing that up.

Reply 8

Fungrus

twinsforever

Sorry to bother you but do you know any websites or anything to teach ordinary and partial differential equations? Or are they very similar to first and second order differential equations?

Unless I'm missing something, first order and second order are ODE's. PDE's, well, the only way I know how to solve them other than in a very general way is by hoping that they can be transformed into ODE's. So I think knowing ODE's is enough really.

Reply 9

twinsforever

Fungrus

You're not missing anything. I just didnt know what category they come under. Sorry. It seems Im being a bit ambitious in trying to look this up, I may just stick my A level syllabus.

Reply 10

Dez

The differential equations you learn at A-level are the deceptively easy ones, I'll say that much. You could do an entire degree studying differential equations, they come in all sorts of flavours and crop up in the most bizarre areas of mathematics and physics. To discuss ODEs properly needs quite a lot of study, and PDEs doubly so.