Finite-Dimensional Vector Spaces
Vector spaces and subspaces
Basis of a vector space
Inner products, norms, and metrics
Contravariant and covariant components
Coordinate systems
Change of coordinate systems
Exercises
Vector and Tensor Algebras
Vector Algebra
Tensor Algebra
Exercises
Tensor Calculus
Tensor fields
Integral theorems for scalar and vector fields
Exercises
Physical and Anholonomic Components of Tensors
Physical and anholonomic components of vectors
Physical and anholomic components of tensors
Coordinate transformations of physical components of tensors
Examples of transformation of coordinates for physical components
Anholonomic connections
Strain tensor
Dimensional analysis for tensors
Exercises
Deformation of Continuous Media
Stress tensor and equations of motion
Strain-displacement relations for elastic bodies
Characterization of thin shells
Strain-displacement relations for shells
Kinematic relations for shells
Equations of motion for shells
Constitutive equations for thermoelastic shells
Bibliography
Index
Biography
Wolf Altman obtained his Ph.D. from Stanford University in 1966. His dissertation was published in the Journal of IABSE and became a classic. Professor Altman is an engineering educator and researcher with experience as a consultant in structural mechanics in general and in the City Hall of Sao Caetano do Sul. His research endeavors, which include over 60 articles in international journals, have been mainly on weak variational formulations, including the effects of conservative and nonconservative loads on beams, plates and shells, and on physical and nonholonomic components of tensors with application to the theory of elasticity and shells.
Antonio Marmo De Oliveira
earned his doctorate at the Instituto Tecnologico de Aeronautica in 1977. He was full professor at Instituto Tecnologico de Aeronautica and University of Taubate until his retirement. He performed research in the broad fields of mechanics, applied mathematics, and engineering science, and he has published nine books and over 50 articles in journals and magazines and 300 chronicles in Taubate's newspapers. He was awarded the 1966 Esso Prize of Sciences and some commendations in Taubate city, where he was the head of the university during 2000-2002. He currently works as a consultant for reinforced industrial plastics."This book provides a clear explanation of the mathematical properties of tensors, from a physical perspective. The book is rigorous and concise, yet easy to read and very accessible. The reader will enjoy the wide variety of examples and exercises with solution, which make the book very pedagogical. I believe this can be a very useful book for anyone interested in learning about the mathematics of tensors, no matter the field of study or research. I would definitely like to have this book on my shelf, and use it as a reference in my own lectures."
—Román Orús, Institut für Physik, Johannes Gutenberg-Universität
