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1 PART 1: INTRODUCTION TO TENSOR CALCULUS A scalar п¬Ѓeld describes a one-to-onecorrespondencebetween a single scalarnumber and a point. An n-dimensional vector п¬Ѓeld is described by a one-to-one correspondence between n-numbers and a point. Introduction Continuum mechanics is a mathematical framework for studying the transmis-sion of force through and deformation of materials of all types. The goal is to construct a framework that is free of special assumptions about the type of material, the size of вЂ¦

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AN INTRODUCTION TO CONTINUUM MECHANICS 2.5.4 Tensor Calculus 45 2.5.5 Eigenvalues and Eigenvectors of Tensors 48 2.6 Summary 55 7.7 Solution Methods 224 7.7.1 Types of Solution Methods 224 7.7.2 An Example: Rotating Thick-Walled Cylinder 225 7.7.3 Two-Dimensional Problems 227 Chapter 1 VECTOR AND TENSOR CALCULUS The physical quantities encountered in fluid mechanics can be classified into three classes: (a) scalars, such as pressure, density, viscosity, temperature, length, mass, volume and time; (b) vectors, such as velocity, acceleration, displacement, linear momentum and force, and (c) tensors, such as stress, rate of strain and vorticity tensors.

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problems associated with the stress tensor) are also discussed. Chapter 5 is dedicated to the derivation of the governing equations of mechanics using the conservation principles of continuum mechanics (or laws of physics). The principles of conservation of mass, linear momentum, angular momentum, and energy are presented using one-dimensional Chapter 1 VECTOR AND TENSOR CALCULUS The physical quantities encountered in fluid mechanics can be classified into three classes: (a) scalars, such as pressure, density, viscosity, temperature, length, mass, volume and time; (b) vectors, such as velocity, acceleration, displacement, linear momentum and force, and (c) tensors, such as stress, rate of strain and vorticity tensors.

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