ABSTRACT
This chapter introduces the concept of a vector along with its basic algebraic properties. It discusses vector fields and their continuity and differentiation properties along with the notions of gradient, divergence and curl. The chapter presents three fundamental theorems of vector calculus, namely the Green-Ostrogradski theorem, the Gauss divergence theorem and the theorem of Stokes. The concept of a vector can be traced to the development of affine and analytic geometry in the Seventeenth century and, later, the invention of complex numbers and quaternions. Vector calculus serves as a basic mathematical tool in all areas of science and engineering where mechanical, electromagnetic and thermodynamics forces determine the behaviours of solids, fluids, electric conductors, semiconductors and magnetic materials. The chapter explores an introduction of matrices and their relationship with system of linear equations frequently occurring in diverse fields of study like physics, biology, chemistry, social science, medical science and different branches of engineering.
