ABSTRACT
This chapter describes vector functions in three dimensions and the applications of differential calculus to them. Vectors simplify many calculations considerably and help to visualize physical and geometrical quantities and relations between them. Consequently, vector methods are used extensively in applied mathematics and engineering. The impact of these methods on the study of physical phenomena such as fluid flow, elasticity, heat flow, electrostatics, electromagnetism, and waves in solids and fluids, which the engineer must understand as the foundation for the design and construction of systems such as aircraft, laser generators, robots, and thermo-dynamical systems, is critical to the engineer. The goal of the chapter is to acquaint readers with vector calculus, a branch of differential calculus that applies the basic notions of ordinary differential calculus to vector functions. The gradient, divergence, and curl are three physically and geometrically essential concepts connected to scalar and vector fields.
