Abstract
This chapter presents a brief study of differential and integral calculus of vector and tensor functions. A vector or a tensor function means a vector or a tensor, respectively whose components are real-valued functions of one or more real variables. The chapter discusses the gradient of a scalar field and divergence and curl of a vector field. It also discusses the gradient, divergence, curl, and Laplacian operators frequently encountered in tensor calculus. The chapter discusses the divergence theorem and Stokes' theorem in vector integral calculus and summarizes some consequences of these theorems. A vector is said to be solenoidal in a region if its flux across every closed regular surface in the region is 0. A vector field whose divergence is exactly 0 is called a divergence-free vector. A vector field is solenoidal in a simply connected region if it is divergence free.
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