Wow! eBook
A Geometrical Introduction to Tensor Calculus
by: Jeroen Tromp (Author)
Publisher: Princeton University Press
Publication Date: 2025-03-04
Language: English
Print Length: 248 pages
ISBN-10: 0691267979
ISBN-13: 9780691267975
Book Description
An authoritative, self-contained introduction to geometrical tensor calculus for scientists and engineersTensors are widely used in physics and engineering to describe physical properties that have multiple dimensions and magnitudes. In recent years, they have become increasingly important for data analytics and machine learning, allowing for the representation and processing of data in neural networks and the modeling of complex relationships in multidimensional spaces. This incisive book provides a geometrical understanding of tensors and their calculus from the point of view of a physicist. With a wealth of examples presented in visually engaging boxes, it takes readers through all aspects of geometrical continuum mechanics and the field and dynamic equations of Einstein, Einstein-Cartan, and metric-affine theories of general relativity. A Geometrical Introduction to Tensor Calculus gives graduate students, advanced undergraduates, and researchers a powerful and mathematically elegant tool for comprehending the behavior and applications of tensors across an array of fields.Offers a physicist’s perspective on geometrical tensor calculusIncludes dozens of examples that illustrate the geometrical use of tensors in continuum mechanics and general relativityCan serve as the basis for a course in tensor calculus for physicists and engineersInvaluable as a supplementary guide for anyone studying areas of physics that rely on tensor calculus, such as electrodynamics, geophysics, fluid and continuum mechanics, and general relativity
Editorial Reviews
An authoritative, self-contained introduction to geometrical tensor calculus for scientists and engineersTensors are widely used in physics and engineering to describe physical properties that have multiple dimensions and magnitudes. In recent years, they have become increasingly important for data analytics and machine learning, allowing for the representation and processing of data in neural networks and the modeling of complex relationships in multidimensional spaces. This incisive book provides a geometrical understanding of tensors and their calculus from the point of view of a physicist. With a wealth of examples presented in visually engaging boxes, it takes readers through all aspects of geometrical continuum mechanics and the field and dynamic equations of Einstein, Einstein-Cartan, and metric-affine theories of general relativity. A Geometrical Introduction to Tensor Calculus gives graduate students, advanced undergraduates, and researchers a powerful and mathematically elegant tool for comprehending the behavior and applications of tensors across an array of fields.Offers a physicist’s perspective on geometrical tensor calculusIncludes dozens of examples that illustrate the geometrical use of tensors in continuum mechanics and general relativityCan serve as the basis for a course in tensor calculus for physicists and engineersInvaluable as a supplementary guide for anyone studying areas of physics that rely on tensor calculus, such as electrodynamics, geophysics, fluid and continuum mechanics, and general relativity
