Line, surface and volume integrals
In Chapter 11 we encountered continuously varying scalar and vector fields and discussed the action of various differential operators on them. There is often a need to consider not only these differential operations, but also the integration of field quantities along lines, over surfaces and throughout volumes. In general the integrand may be scalar or vector in nature, but the evaluation of such integrals involves their reduction to one or more scalar integrals, which are then evaluated. In the case of surface and volume integrals this requires the evaluation of double and triple integrals (see Chapter 8).
12.1 Line integrals
In this section we discuss line or path integrals, in which some quantity related ...