Because they obey the superposition principle, linear circuits are governed by linear differential equations, and can be analyzed with powerful mathematical frequency domain techniques, including Fourier analysis and the Laplace transform. These also give an intuitive understanding of the qualitative behavior of the circuit, characterizing it using terms such as gain, phase shift, resonant frequency, bandwidth, Q factor, poles, and zeros. The analysis of a linear circuit can often be done by hand using a scientific calculator.