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The basic elements of circuit design are components (resistors, capacitors, and inductors), and sources (voltage and current). We describe these elements as both ideal elements and real-world objects. We also develop precise terminology for how to talk about circuits and label voltages and currents.

Series and parallel resistors, delta-wye networks, and the voltage divider

Determine the state of a DC circuit using Kirchhoff's Laws, node voltage method, mesh or loop current methods.

Circuits containing capacitors and inductors change with time. The natural and forced response of RC, RL, and RLC circuits.

If we limit ourselves to input signals shaped like sines or cosines, we can develop a whole AC analysis method to figure out what happens in circuits with changing signals. The methods are far simpler than solving a differential equation.