A Geometrical Introduction to Tensor Calculus

Overview

An authoritative, self-contained introduction to geometrical tensor calculus for scientists and engineers

Tensors 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 calculus
• Includes dozens of examples that illustrate the geometrical use of tensors in continuum mechanics and general relativity
• Can serve as the basis for a course in tensor calculus for physicists and engineers
• Invaluable 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

Product Details

ISBN-13:	9780691267975
Publication date:	07/06/2025
Pages:	248
Product dimensions:	8.00(w) x 10.00(h) x (d)

About the Author

Jeroen Tromp is the Blair Professor of Geology and Professor of Applied and Computational Mathematics at Princeton University. His books include Theoretical and Computational Seismology and (with F. A. Dahlen) Theoretical Global Seismology (both Princeton).

What People are Saying About This

From the Publisher

“In this book, readers will find a clear and concise introduction to differential geometry. The fundamentals are present, but the book’s real strength lies in its discussion of more advanced topics and in the choice of motivating examples. Through these examples, readers can gain a unique insight into Tromp’s diverse interests and his approach to mathematical physics.”—David Al-Attar, University of Cambridge

“Deformation, warping, and twisting are ubiquitous in nature. Jeroen Tromp masterfully blends geometrical and analytical descriptions of these processes. His systematic treatment of the topic makes his book accessible to theoretically minded professionals in applied fields. This book exemplifies the unique combination of deep theoretical insights with didactic skills that characterizes Tromp’s career.”—Roel Snieder, Colorado School of Mines

“A Geometrical Introduction to Tensor Calculus provides a rigorous but concise and crisply written exposition of tensors and differential geometry for scientists and engineers.”—Eric Dunham, Stanford University

“A concise, self-contained, and very well-presented introduction to differential geometry and tensor calculus, distinctively oriented towards physicists.”—Andreas Schmitt, University of Southampton

Editorial Reviews

"A refreshing exploration of both the theory and . . . application of tensor calculus."—-Kymani Tieral Keden Armstrong-Williams, Physics Book Reviews

From the Publisher