Most basic electronic, and AC and DC circuit analysis can be done with standard arithmetic and a good understanding of algebra and complex numbers (complex numbers are need for AC analysis). Calculus, Laplace transforms, fast Fourier transforms, and matrix knowledge is needed for more advanced circuit analysis.
A great tool to use in understanding and designing electronic circuits is a Spice type circuit simulator. There are many versions available from different vendors. A good place to start is LTspice, which is free and fairly easy to use. It basically does the grunt work by solving the equations for the circuit currents and voltages many thousands of times to simulate the dynamic circuit operation over a period of time.