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1. I How would one calculate the distance and bearing of a signal source?

That's the standard approach. But if you are able to determine the distance to multiple receive points based on power measurements, you can geolocate the source that way as well.

23. I Fourier series representation

I can see why you prefer the trigonometric form and are a little distrustful of the complex form. These are representations of real signals. As such, they only have positive frequencies, and their value better turn out to be real. The exponential form is much easier to deal with mathematically...
24. I What is the proof of the rules of significant figures?

Let's say for instance you have a measured value which you write as $x = 2.3$. What that is supposed to mean is that you're confident of the 2 and the 3, but not of any further figures. You don't mean that the real value is 2.3000. You mean it's approximately 2.3. You mean that it could be...
25. I Fourier series representation

That's incorrect. Having only one frequency at baseband doesn't mean you'll have only one frequency after mixing up. Let's analyze a simple amplitude modulated carrier wave. Let's say the carrier frequency is $\Omega$ (I'm going to use angular frequencies such as $\Omega = 2\pi F$ to avoid...
26. Is there anything wrong in this question statement?

As @DaveE says, it depends on what type of model you're studying and supposed to be applying. A more common model for growth is exponential, $P = P_0 e^{at}$ or $P/P_0 = e^{at}$ in which case you're expected to use the given value of $P/P_0$ first to solve for the rate constant $a$.
27. MATLAB Plotting standard deviation in Matlab

It sounds like you want the ERRORBAR function. https://www.mathworks.com/help/matlab/ref/errorbar.html
28. A The partial derivative of a function that includes step functions

S is a function which takes on discrete values, and jumps instantaneously between those values. The time derivative is either 0 (between jumps) or doesn't exist (at jumps). Yes, in physics we do that. It's not exactly rigorous but makes a certain kind of sense. The Heaviside function has a...
29. What avenue of physics can a scientist in the Star Wars galaxy study?

They could work on more accurate weapons for Stormtroopers. Also armor that can't be defeated by rock-wielding Ewoks.
30. I Ambiguous Results for two Fourier transform techniques

So let's check. You have $F(\alpha) = \frac {\alpha} {b + i\alpha}$. So that gives $F(-\alpha) + F(\alpha)$ = $\left ( \frac {-\alpha} {b - i\alpha} \right ) + \left ( \frac {\alpha} {b + i\alpha} \right )$ = $\frac {-\alpha(b + i\alpha) + \alpha(b - i\alpha)} {b^2 + \alpha^2}$ = ##\frac...