First of all, realize that those equations are almost all ratios. Absolutely nothing worse than a cooking recipe. When you have two cups frequency and a teaspoon of capacitance, you need so-and-so inductance...
When you see a big long equation, force yourself to read it -- don't let your eyes glaze over and skip it! The first thing you will probably notice is, it's some quantity divided by some other quantity. A ratio. Next, look for the units. We're using real quantities here, and the units have to work out right.
Dimensional analysis itself has a simple algebra, because you have to know the definitions of conventional units. I'll grant you that -- it's annoying, and you have to memorize them all if you want to check the equation yourself.
FWIW, using circuit quantities (volts, ohms, seconds..), 1F == 1 second/ohm, and 1H == 1 second*ohm. 1 ohm = 1 volt/amp.
Physically speaking, capacitors respond to charge. Charge is 1 coulomb == 1 amp*second. The equation of a capacitor is I = C * dV/dt, where dV/dt is the rate of change of voltage. Or if we switch things around:
I dt = C dV
Current, applied for some time dt, causes a change dV in capacitor voltage.
Physically speaking, inductors respond to flux. Flux is 1 weber == 1 volt*second. The equation of an inductor is V = L * dI/dt, where dI/dt is the rate of change of current. Or if we switch things around:
V dt = L dI
Voltage, applied for some time dt, causes a change dI in inductor current.
And because of these, you can see why capacitance has units of amp*sec/volt, and inductance has units of volt*sec/amp.
Nice thing about switching supplies: as the waveforms are all square, you don't need to use any calculus. dt is simply the time difference (on or off), V is the applied voltage on the inductor (and I is the current in the capacitor to figure out supply input/output ripple, but that's secondary), dI is the amount the inductor's current changes by, and so on.
Note that the inductor doesn't care what the absolute value of 'I' is, only how it changes over time. This is why current mode control is paramount: you need a controller monitoring inductor current, to see that it doesn't just keep ratcheting up forever or something. Many, many controller designs fail to provide this basic functionality, so beware!
As for waveforms and getting a feel for that, check this out:
http://schmidt-walter-schaltnetzteile.de/smps_e/smps_e.htmlPop into a basic (say buck or boost) design and poke some numbers. See that the voltage, inductance and pulse width are always simple ratios of each other. You'll usually end up with a "1+ratio", or a "(1+qty1)/qty2", or something like that, because of how things average out during a cycle, versus what happens during a single pulse. (The formulas are listed on the help page.)
With this background, you should be able to get a more intuitive feel for what numbers and units matter.
Tim