PART 1: INTRODUCTION TO TENSOR CALCULUS

1 PART 1: INTRODUCTION TO TENSOR CALCULUSA scalar field describes a one-to-one correspondence between a single scalar number and a point. An n-dimensional vector field is described by a one-to-one correspondence between n-numbers and a point. Let usgeneralize these concepts by assigningn-squared numbers to a single point orn-cubed numbers to a singlepoint. When these numbers obey certain transformation laws they become examples of TENSOR fields. Ingeneral, scalar fields are referred to as TENSOR fields of rank or order zero whereas vector fields are calledtensor fields of rank or order associated with TENSOR CALCULUS is the indicial or index notation. In section 1 the indicialnotation is defined and illustrated. We also define and investigate scalar, vector and TENSOR fields when theyare subjected to various coordinate transformations. It turns out that tensors have certain properties whichare independent of the coordinate system used to describe the TENSOR .

general, scalar elds are referred to as tensor elds of rank or order zero whereas vector elds are called tensor elds of rank or order one. Closely associated with tensor calculus is the indicial or index notation. In section 1 the indicial notation is de ned and illustrated. We also de ne and investigate scalar, vector and tensor elds when they

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  Vector, Tensor, Vector and tensor

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