I can describe the steps I've tried taking so far.
1. Substitute for both ##V## and ##I_e## as given on both sides of the equation.
2. L.H.S then becomes ##\alpha\tau_m\frac{dx}{dt}##, since ##\frac{dV_0}{dt}## term equals 0.
3. Now divide throughout by ##\alpha\tau_m## to get just...
I have tried this. Even if the ##x## term vanishes, how about constant terms like ##V_L##, ##V_C##? Also, no value I choose for ##\alpha## is helping me make the current term ##\frac{R_mI_0}{\alpha\tau_m}## vanish simultaneously.
I am working on an assignment for my neuroscience course, and I'm running into a problem with one question which requires me to rewrite an equation into its nondimensionalized form. The equation is given below.
and I need to convert it to the form
by rescaling and shifting the given...
Thank you for your welcome.
I apologize. I meant to write ##\mathbb{R}^{n}##, not ##\mathbb{R}##. Yes, the notation ##\overrightarrow{a_i a_0},## is just used to represent ##(a_i - a_0) \in \mathbb{R}^{n}##. We can keep it in the latter form if it makes more sense.
And ## \hat{a_j} ## is just...
This question mostly pertains to how looking at affine independence entirely in terms of linear independence between different families of vectors. I understand there are quite a few questions already online pertaining to the affine/linear independence relationship, but I'm not quite able to...