Abstract
This chapter discusses the calculus on Euclidean space. The chapter reviews that part of elementary calculus that deals with differentiation of functions of three variables, and with curves in space. Three-dimensional space is often used in mathematics without being formally defined. It is said to be the space of ordinary experience. Euclidean 3-space E3 is the set of all ordered triples of real numbers. Such a triple p = (p1, p2, p3) is called a point of E3. In linear algebra, it is shown that E3 is, in a natural way, a vector space over the real numbers. Differential calculus deals with another aspect of E3 starting with the notion of differentiable real-valued functions on E3. The chapter discusses some fundamentals related to it. Intuitively, a vector in E3 is an oriented line segment, or “arrow.” Vectors are used widely in physics and engineering to describe forces, velocities, angular momenta, and many other concepts.
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