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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.

PART 1: INTRODUCTION TO TENSOR CALCULUS A scalar eld describes a one-to-one correspondence between a single scalar number and a point. An n- ... There is a range convention associated with the indices. This convention states that whenever there

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4025 AppA pp563-574

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TABLE A-3 tDistribution: Critical tValues

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4025_AppA_pp562-573 01/02/04 11:56 AM Page 568. Title: 4025_AppA_pp563-574.pdf Created Date: 4/22/2004 8:10:06 AM ...

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