In this introductory chapter, we have reviewed some basic mathematical concepts and techniques that are quite useful in applied electromagnetism. We have introduced first- and second-order differential operators': the gradient, divergence, curl and laplacian, whose expressions in rectangular coordinates should be committed to memory. We have stated two fundamental vector integral theorems: the divergence (or Gauss') theorem and Stokes' theorem.
In many applications it is convenient to use coordinate systems other than the rectangular one. The two most important systems are the circular cylindrical coordinates and the spherical polar coordinates, that we examined in some detail. As a reference, the formulas pertaining to a general orthogonal coordinate system were also given. The definition and some of the most important properties of phasors were introduced. In particular, time differentiation and integration in phasor domain were discussed. We saw how phasors can be useful in calculating time averages of the product of two quantities that vary sinusoidally in time (time-harmonic quantities) with the same frequency. Finally, similarities and differences between phasor domain and frequency domain analysis were briefly discussed.