What are physicists doing?
newt0311: So... Special relativity is called "special" because it specifically assumes no acceleration and therefore, no force. That formula you have is an approximation for "small" forces. General relativity is what actually explains space with acceleration (using Riemann Geometry, another fascination and extremely complex topic in of itself relying on tensor calculus, which is another  fascinating and extremely complex topic in of itself). Secondly, the Lorentz transformation is critical to special relativity, because that is what gave rise to the entire theory and also because the Lorentz transformation is exact (up to QM effects and 0 acceleration). Also, the Lorentz transform is sufficient to derive the result e = mc^2 among many other useful results on momentum and particle collisions (or at least the aftereffects thereof, since we can have no forces) which is why special relativity is even taught in isolation.As to the textbooks, all I can say is that you haven't come by the right textbooks yet. I would advise reading the Feynman's lectures on physics (all 3 volumes). Expensive but worth it and if you want, you could probably find free pdfs online. FLs does indeed go into the gory details of special relativity (v1 I think) and even shows how to derive most of the useful results including (I think) information on how to derive the Lorentz transformation from the Special Relativity's base assumption: the speed of light is constant in all time frames. ENM along with several applications is also discussed in FLs (v2 I think). FLs V3 covers QM is great detail (well... the parts that we humans can solve mostly). Another very good book on ENM would be Electricity and Magnetism by Purcell, Berkley Physics Course Vol. 2.Oh btw. the central assumption of General Relativity is that force and gravity are just 2 different manifestations of the  same phenomenon. Thus, for very weak gravitational fields, you could actually use the formula you have. Just that it would not be very useful because a) you would have to interpret it as constantly changing time frames over small time intervals, and b) because I don't think the Earth's gravitational field (or the moon's) is weak enough to justify the approximations inherent in your equation.A note on finding good textbooks: Pick a good university. Any good university (I would advise Caltech but thats because thats where I study) and chances are very good that said universities will publish the course textbooks for their classes. Some will even publish the homework assignments and solution sets along with lecture notes. Eg. http://www.pma.caltech.edu/GSR/physicscourses.html is the place where CIT has currently placed a convenient listing of all the physics courses offered with links to their web pages which contain among other things: the textbooks, syllabus, and in most cases, the homeworks for the class. Finding textbooks from there shouldn't be very difficult.