This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics. Firstly, a detailed tensor analysis is developed in Cartesian and general coordinates. Definitions, propositions, and examples relative to operations on tensors, canonical isomorphism, Euclidean vector spaces, exterior algebra, point spaces, metric element, Christoffel symbols, covariant and absolute derivatives, adjoint, differential operators, and many other concepts are introduced in a rigorous and practical way. The topic is not merely viewed as an autonomous mathematical discipline, but as a preparation for theories of physics such as general relativity theory, fluid-dynamics, engineering, and differential geometry. Secondly, developed in symbiosis with tensor analysis, continuum mechanics thoroughly covers Lagrangian and Eulerian descriptions, deformations, kinematics of continua, fundamental laws, principle of virtual work, linear elasticity and more. This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics.
The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.
