Vector Calculus in the Context of Space (Published)
The aim of this paper is to align with the Russian school of mathematics to derive new mathematics concepts by emphasizing the physical insight of the concepts. The concept of directional derivative is derived by first building a scalar field in Euclid space, followed by defining a small change of position vector,ds and a unit vector, u; the directional derivative then can be derived by using a parametric variable t. The concept of gradient can be derived from equation of directional derivative as it is simply a specific condition of directional derivative. The concept of divergence and curl is derived by first defining a new mathematics concept from the interaction of vector field with other geometric concepts lay within the space, followed by logical reasoning. Reader shall find the symbol ∇ denoted ∂/∂x i+ ( ∂)/∂y j+∂/∂z k is naturally evolved when deriving the concepts of gradient, divergence, and curl.
Keywords: Divergence, Gradient, curl, directional derivative