Electronics Simulation

Paul Falstad is a software engineer, and he writes a lot of great tools for maths, physics and electronics. The one I use most is his circuit simulator. Its a great java applet that runs in the browser, so you dont need to download anything, although downloading is possible. When you first open it up, youre presented with a simulation of a simple RLC circuit, which shows the voltages, current flows, and important waveforms in the circuit. 

The software offers a plethora of components with which to build your own circuits, and a large library of existing circuits, from ADC converters to filters and flip flops. Its a great resource for circuit building, and while I wouldn't use it for anything complicated or important, its really good if you want to see how a circuit might work, or play around with an existing circuit. Its not as rigorous as more professional simulations, like LTspice, but its real time and very beginner friendly.