McQuistan R. Scalar and Vector Fields

John Wiley & Sons, 1965. — 329 p.From the Preface: "...In Chapter 1 scalar and vector quantities are introduced;the concept of a field is discussed and the more common methods of representing them graphically are treated. The meaning of certain fundamental field characteristics, for example single-valuedness and continuity, are discussed in physical terms. Addition, subtraction, multiplication, and division involving vector quantities are treated in Chapter 2. Chapter 3 is concerned with the process of differentiation and integration as they relate to vector fields. The role of the coordinate system in the representation of vector fields and the transformation of the representation of a vector field from one coordinate system to another are discussed in Chapter 4. Orthogonality, the right-handedness of coordinate systems, frames of reference, and vector and function spaces are also considered in this chapter. Chapters 5, 6, 7, and 8 are a discussion of the physical aspects of the differential properties of fields, as well as the operator notation associated with these field properties. The integral properties of fields, Stokes, Gauss's, and Green's theorems are the subjects of Chapter 9. The subject of Chapter 10 is the representation of field operators in orthogonal curvilinear coordinate systems. Field potentials and consideration of the Helmholtz theorem for vector fields are discussed in Chapter 11. Chapter 12 is concerned with time-dependent fields, motion relative to a field, and retarded potentials. The problems of notation are always difficult to solve. No attempt has been made to be elegant; rather, the philosophy has been adopted that the learning of the notation should not impede the understanding of the physical significance of a topic.