The books I'm using though do not progress at the same pace as the schaum's outlines, so when I get to the section on Inductance and Capacitance I'm a little lost since I haven't encountered these concepts in the main books I'm reading yet. That said, I decided to give the problems a shot anyway. Here is one:

An inductance of 2.0mH has a current i = 5.0(1 - e^(-5000t)). Find the corresponding voltage and maximum stored energy. So I read the quick summary of inductance, and it says V = L di/dt. Great, so I just plug the numbers in and V = 50.0 e^(-5000t). Seems I have that part correct.

For the next part, the "worked solution" says "Since the maximum current is 5A, the maximum stored energy is ½L I_max^2 = 25.0 mJ.

I don't follow this logic.

The way I did this is to say P = VI, so P = 50e^(-5000t) × 5(1 - e^(-5000t)). And since P(t) = dW/dt, it should be the case that W is maximized when P(t) = 0. Solving the aforementioned P for 0, I get t=0. Sure enough, at t=0 the current is 5A as the solution suggests, and the voltage is 50V.

What next? Do I have to integrate this? Ugh. If I do it and set t=0 in the result I do get 25.0mJ, but I feel like I'm missing something, because the solution jumped straight to ½L I_max^2. It sure seems like it's integrating L I with respect to I, but why?

(BTW, is there a way to format superscripts and subscripts on this forum?)