Recent content by cocopops12

I have a feeling it's healthy...

The definition of the dot product is given by A = <a1,b1> B = <a2,b2> A dot B = a1a2 + b1b2 Is this definition valid for orthogonal coordinates only?

I see, thank you sir!

z = h(x) + ig(x) True or False: By the definition of the complex plane, h(x) and ig(x) will always be orthogonal. If this was true, wouldn't that mean that we can find a 'very general' Fourier series representation of any function f(x) as an infinite series of An*h(x) + infinite series of...

Thanks my friend. I understand that the Fourier transform is equivalent to the double-sided Laplace transform, but that doesn't explain anything clearly to me regarding the poles that have to be located on the left hand side of the s-plane in order for the substitution s = jω to be valid.

Can someone please explain WHY the statement below is valid: s = σ + jω ; left hand side σ < 0 So it basically says if all the poles have negative real parts then we can directly substitute s = jω to get the Fourier transform. This doesn't make sense to me, does it make sense to you...

(y^2)'' + (y^2)' + y^2 = 0 1) Is this DE linear? What if we substitute y^2 = h and solve for h y = sqrt(h) 2) Would that be valid? 3) Would that be considered a somewhat trivial type of linearization?

Can someone please explain WHY is it when the poles of F(s) have negative real parts, the system is stable. Why is it when the poles of F(s) have positive real parts the system is unstable? Why is it when the real parts of the poles of F(s) equal to 0 the system becomes metastable...

I see, thank you sir.

suppose we have ab why must 'b' be dimensionless? Mathematicians have defined crazy things over the centuries so why haven't they defined this one?

Thanks , now i understand what was the problem. :)

Thank you sir! does the ESR have to be of a specific value? isn't the natural resistance of the wires is enough?

What would happen if this circuit was implemented practically with batteries? This circuit makes no logic to me because how can the same node be at two different electric potentials?. But i tried thinking about it and here's my 'naive' explanation: The 12V battery will start supplying a...

Thanks haruspex so what i understand is that we need to know the domain of each independent variable and also some initial conditions to determine the constants?

When taking the limit as x -> infinity, i was talking about applying it to the part with polynomial expansion, not the the cosx -jsinx ∞ - i∞ can someone explain why this isn't an indeterminate form? i know ∞ isn't a fixed number, it represents a very large quantity, and if you scale that...