crust said:Wow, that is a complex question. Electrical engineering really can emcompass several areas or just a few. The basic principles and concepts are often similar, so you need to master those. For example a 2nd order closed loop control system will have the same form of transfer function as an RLC circuit. What does this mean? The same circuit that you would likely study early in a university will have the same basic math that a motor/speed control system will have your last year.
Math is important for both circuit analysis and simulation. In fact, when you perform circuit analysis on even simple RC circuits, you have to solve a differential equation (though after some experience you get a feel for the form of the equation w/o going through the math). A good book might be a "fundamentals of AC and DC circuits" or something along those lines.
Of course, this is my opinion, others will have their own opinions.