Help Please - Maths and Differential Equations

dmg24

I've googled everywhere, maybe I just need sleep?!

Bit of a strange set up on our course, we just study 'everything that you may come across whilst teaching', so no particular subjects. Bizarre, I know.

Am going to give up for tonight and go to bed.

Big thank you to both of you for your help ... you both deserve extra stars! x

Ted_Bloke

Like straight integration (Integral (f(x) dx) (which is just the special case of solving the differential equation dy/dx = f(x) ) there is one and only one way to solve a differential equation.
That is to know the answer.
Not joking.
At least the general form of the answer then you fiddle it to fit the given constants, initial conditions.
The training then is like integration, basically drill in recognizing the main types of problem/solution and fitting these details. Can get to be almost fun.
For science and engineering they are almost exclusively concerned with a particular type of d.e., the “linear” d.e.’s of form a*d2y/dt2 + b*dy/dt + c*y = f(t) where a,b,c, are constants. The solution always involves trying y= exp(A*t) where A is a constant to be determined, A may be a real or complex number. They are very interested in the nature or stability of solutions, whether they are oscillatory or not, these depend on whether A is +ve, –ve (real part) or complex etc. This analysis is still useful for non-linear d.e.’s you can’t solve analytically as these do become appr. linear near the 'stationary points' and still gives you the main features of behavior of systems modeled. Handling simultaneous lde’s is also involved in any moderately advanced physical sci course.
Because all the math you’ve learned till then, algebra, matrices and determinants, straight integration, trig., complex numbers, and the physics (SHM, resonance, chemical kinetics,...) all come together teachers and lecturers are quite keen on l.d.e.’s
I tend to think if faced with a d.e. in or any integration in a sci textbook, if the answer is given work back from that, it is always easy to check, rather than how they solved it in the first place, because as I said the point is knowing the answer. Understanding nature of solutions types and fitting constants or intitial conditions is the essential.
Books are many. ‘Differential equations’ by Piaggio is a trad classic, more than you need yet quite efficient. You only need a short one or a chapter or 2 in a general book.

kr15snw

Hmm I remember doing these at gsce level, no fun

I remember our teacher helped us alot with this as we had coursework in which we had to include a large section about differential equations. Do you have anyone you could ask for help on the subject?

Like someone else said about, a good book is also amazingly usefull.

Wish I could help more, but I dont remember much about them now