Tensors for Scientists
A Mathematical Introduction
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Beschreibung
This textbook provides a compact introduction to tensors, which are physical or geometric entities that generalize vectors. Tensors are fundamental in engineering and physics, as they form the framework for formulating and solving problems across various disciplines. These include mechanics (inertia tensor, stress tensor, elasticity tensor), electrodynamics (electrical conductivity and resistivity tensors, electromagnetic tensor, magnetic susceptibility tensor), and general relativity (stress-energy tensor, curvature tensor). As such, tensors are integral to most engineering and physics curricula.
The material is presented with a rigorous mathematical foundation while emphasizing practical applications. The numerous exercises, accompanied by detailed solutions, further enhance the book's pedagogical purpose and facilitate self-learning. The book can be used for undergraduate and graduate courses in material science, engineering, and physics, providing a versatile resource for both teaching and studying.
This textbook provides a compact introduction to tensors, which are physical or geometric entities that generalize vectors. Tensors are fundamental in engineering and physics, as they form the framework for formulating and solving problems across various disciplines. These include mechanics (inertia tensor, stress tensor, elasticity tensor), electrodynamics (electrical conductivity and resistivity tensors, electromagnetic tensor, magnetic susceptibility tensor), and general relativity (stress-energy tensor, curvature tensor). As such, tensors are integral to most engineering and physics curricula.
The material is presented with a rigorous mathematical foundation while emphasizing practical applications. The numerous exercises, accompanied by detailed solutions, further enhance the book's pedagogical purpose and facilitate self-learning. The book can be used for undergraduate and graduate courses in material science, engineering, and physics, providing a versatile resource for both teaching and studying.
Provides a concise guide to tensors for engineering and physics students Contains many examples of applications of tensors in physics Includes a great number of exercises
Autor*in
Ana Cannas da Silva
Themen in »Tensors for Scientists«
Tensors Multilinear algebra Inertia tensor Stress tensor Strain tensor Change of basis Reciprocal basis Einstein convention Tensor product Covariance Contravariance