It's actually kind of hard to go from square wave -> sine wave. What you really want isn't a low pass filter but a band pass filter about 50Hz. This is basically what you're building with the inductor, resistor in parallel with a cap.
You're impedance is going to go down just because it's...
The final velocity is in an opposite direction (towards the spaceship) compared to the initial velocity (away from the spaceship). If you take the difference of the two you need to consider the signs (direction) of the velocities.
The way you're currently taking the difference you are assuming...
Because he wanted to motivate the decision to use a power series. In my copy Griffith's even makes a footnote stating that this is, as you reasoned, the idea behind solving diff. eq's using power series.
So to solve this problem you'll need to think about the directions of the astronaut and the tool both before and afterwards. In your answer you assume that the astronaut is traveling in the same direction both before and afterward he throws the tool. How would you correct this?
I'm not entirely sure about the polarity on the batteries (I just guessed in my schematic).
If my schematic is correct then you have the correct current for your circuit given my Ohm's law as you calculated: 19V / 12Ohm = 1.6A -- So what can we say about the current through each resistor?
Also...
I don't know what system you're trying to solve but if you just look at the Laplace transform for a single capacitor
You have i(t) = C \frac{dv}{dt} <==> i(s) = C(s*V(s) - V(0)) ==> V(s) = \frac{i(s)}{sC} + \frac{V(0)}{s}
Notice that i(s) and V(s) both have an s dependence. s is defined as...
Are you having trouble because you think Log(z) is undefined along the negative real axis? We can extend logarithms into the complex plane quite easily actually: http://en.wikipedia.org/wiki/Complex_logarithm
Two reasons:
1.) Anything useful is numerical simulations (most of which have been written for you)
2.) Non math majors are not in the best position to learn a lot of the mathematics involved.
You're just arguing semantics at that point.
Technically you are correct assuming you think space is a continuum but based on how the question is phrased I believe you knew what your teacher really wanted and it would have been very easy to write it down.
From my experience taking graduate level EE courses I've needed to know some abstract algebra (probably the most useful thing to know), and secondly PDE's and probability. However my class experience is limited to random signals course and an advanced fields course.
I'm just speaking of my experience as a physics/EE double major and so I can't comment for everyone.
Physics advantages:
Mathematically more rigorous which lends itself to quite a lot of areas of electrical engineering. Communications, nano/micro fabrication, fields, just to name a few. In...