/sci/ - Science & Math

[Anonymous No.5228295]

I need to learn ODE in some hours.

What resources would you recommend?
(evidently, I already have differential and integral calculus knowledge).

Thank you

[Anonymous No.5228322]

> What resources would you recommend?
I would use whatever resources recommended by the people who make you feel that you "need to learn ODE in some hours".

[Engineer No.5228333]

I solve my ODEs exclusively by the means of Laplace transform.

[Anonymous No.5228354]

http://bookfi.org/dl/492425/0149e5

[Anonymous No.5228355]

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

[Anonymous No.5228372]

>>5228333

And what do you do when you don't have initial conditions?

And what do you do if you have a function that is not easily Laplace'd?

And why would you waste time on tedious transforms when some solutions are quite easily solvable with other methods?

[Anonymous No.5228396]

Well, the introductory way to solve a homogenous ODE is making an algebraic equation to find certain numbers, usually called lambdas, that you can then throw in to an exponential function which will be the answer to your ODE.

For example, given

y'' + ay' + by = 0

(homogenous means the side with the "y" equals zero)

we try a solution in the form e^(lambda*t)

(t is the variable that y depends on)

so... the original ODE becomes...

lambda^2(e^lambda*t) + a*lambda(e^lambda*t) + b*e^lambda*t = 0

We can now divide by e^(lambda*t)

lambda^2 + a*lambda + b = 0

Which is a polynomial equation. We can then solve for the lambdas and we'll have a couple of functions (e^lambda*t) that satisfy the equation.

[Anonymous No.5228442]

>>5228354
>>5228355
>>5228396

I am really grateful!