Help Please - Maths and Differential Equations

dmg24

Hi guys,

Can I ask for your help please?

I am doing an essay, and trying to trace the learning route that you need to go down to be able to understand Differential Equations at A2 level.

The problem I have is, I don't understand Differential Equations! I made some vague notes in observation about Integration, Partial Fractions, and Division of Polynomials, but don't understand how they relate?

Thanks in advance for any help x

tr3mor

Are you a maths student / Do you know how integration, etc work?

If you do then you're probably best looking for a book with some good examples of solving differential equations.

I'd recommend KA Stroud - Engineering Mathematics. Best 1st year maths book ever!

If you're from a non mathsy background I'm not sure how you could explain it. There are a huge variety of differential equations, and they confuse the hell out of me. I'm doing 3rd year maths, but I really hate calculus. ( number theory!)

Strangely, I don't remember differential equations being in A2 maths, just in further maths.

dmg24

Thanks tr3mor,

They weren't in the syllabus when I did them either, but that was ten years ago!

I am on the Maths Enhancement Course, pre PGCE, but I won't actually have to teach A Level at all (although I do want to teach Stats and Decision ... eventually!).

I might just show my tutor your post - if you don't get it, then why should I?!!

Thanks again ... x

tomstickland

Differential equations express a mathematical situation where the gradient of a variable is of interest. This has to be the gradient with respect to some other variable.
Say the rate of change of water leaving a bath is proportional to the height of the water.
You might end with an equation along the lines of
change in water height per second is proportional to water height.

Say you call water height h and t is time.
dh/dt = k * h

So rate of change of height with respect to time is equal to a konstant multiplied by the height.

In order to solve such an equation then there are numerous methods (which only normally work on easy examples). Generally they involve integrating the equation.

tr3mor

dmg24 wrote: »

Thanks tr3mor,

They weren't in the syllabus when I did them either, but that was ten years ago!

I am on the Maths Enhancement Course, pre PGCE, but I won't actually have to teach A Level at all (although I do want to teach Stats and Decision ... eventually!).

I might just show my tutor your post - if you don't get it, then why should I?!!

Thanks again ... x

Nooooo, don't use me as an example of a 3rd year maths student, I'm hopeless. I intend to become a maths teacher too, and I hopefully will be teaching A-level.

I'm not sure that the school will appreciate my "integration by magic" approach though, it has served me well in exams. It goes along the lines of "I have no idea how to integrate this, but I assume that it will be along the lines of [something or other] and procede as such."

You should easily be capable of taking in the Stroud book. It's definitely a good read, and very useful for swotting up on stuff that you *should* know!

I've just had a look at the syllabus. It seems that differential equations are still in P4 (or C4 for kids these days :rolleyes:). Why schools would choose to teach this module in A2 over the piece of cake M2 is beyond me!

tomstickland

A thing to realise is that maths books always present proofs as if it fell out of the sky perfectly formed. When it comes to attacking a new (real) problem you have to batter it with many different attempts and it's only after a lot of refinement and fiddling that it all comes together to looking "perfect".

tr3mor

tomstickland wrote: »

A thing to realise is that maths books always present proofs as if it fell out of the sky perfectly formed. When it comes to attacking a new (real) problem you have to batter it with many different attempts and it's only after a lot of refinement and fiddling that it all comes together to looking "perfect".

I'm with Gauss on this, "no self-respecting architect leaves the scaffolding in place after completing the building".

dmg24

Thanks guys,

So what prior knowledge would you say is needed before you can do Differential Equations?

Great explanation Tom, am going to copy and paste that for future use!

At the moment "Integration by Magic" does seem to be quite popular with me and the rest of my group, scarily enough it does seem to come out with the right answer far too often to be healthy!

dmg24

Don't even talk to me about proofs! Back at uni on Monday for a term of them ... think I may revert to hiding in the union! x

tr3mor

dmg24 wrote: »

So what prior knowledge would you say is needed before you can do Differential Equations?

For the kind of differential equations that I remember from further maths: Integration, partial fractions, solving quadratic equations, messing around with complex trig...

I think the essay would turn out better if you understood some examples. The logic behind solving them is fairly straightforward, the problems lie in the complexity of the calculus.

There are lots of resources with examples on Google, I'd definitely look through a few of them.

tr3mor

dmg24 wrote: »

Don't even talk to me about proofs! Back at uni on Monday for a term of them ... think I may revert to hiding in the union! x

What subject are you studying?

One of my maths modules (on the Riemann Zeta function) is virtually all proofs, it annoys the hell out of me.