Vector Analysis

The electromagnetic field theory is a fundamental subject for the electrical engineering students. The student should be acquainted with a quite knowledge in differential and integral calculus, differential equations, vector analysis, matrix algebra, and complex numbers in order to understand the subject of electromagnetics and be able to analyze the behavior of electromagnetic fields in various media. The knowledge of the vector analysis is essential in the analysis of electromagnetic problems. This first chapter of the book is focusing on the important concepts and techniques in the vector analysis that are required to understand the topics of the electromagnetic fields in the later chapters of the book. The chapter covers the topics and concepts in the vector analysis including vector algebra, orthogonal coordinate systems, vector differentiation operators, and vector integration. The chapter also introduces the scalar and vector field concepts, in addition to the divergence and Stokes’ theorems. The chapter includes numerous illustrative examples covering each topic in the chapter, in addition to miscellaneous solved problems supported by illustrative figures to enhance the student problems solving skills. The chapter is ended by numerous homework problems covering the topics of the chapter.

Keywords: Curl, curvilinear orthogonal coordinate, divergence, divergence theorem, flux, gradient, Laplacian, position vector, right-hand rule, scalar, scalar field, scalar product, Stokes’ Theorem, vector, vector field, unit vector, vector product.