Vectors and Tensors in Engineering and Physics develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications. The book provides equations for predicting: the rotations of gyroscopes and other axisymmetric solids, derived from Euler's equations for the motion of rigid bodies; the temperature decays in quenched forgings, derived from the heat equation; the deformed shapes of twisted rods and bent beams, derived from the Navier equations of elasticity; the flow fields in cylindrical pipes, derived from the Navier-Stokes equations of fluid mechanics; the trajectories of celestial objects, derived from both Newton's and Einstein's theories of gravitation; the electromagnetic fields of stationary and moving charged particles, derived from Maxwell's equations; the stress in the skin when it is stretched, derived from the mechanics of curved membranes; the effects of motion and gravitation upon the times of clocks, derived from the special and general theories of relativity. The book also features over 100 illustrations, complete solutions to over 400 examples and problems, Cartesian components, general components, and components-free notations, lists of notations used by other authors, boxes to highlight key equations, historical notes, and an extensive bibliography.

The second edition develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications, to make this successful text an even more useful and user-friendly book than the first edition.

Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.

Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.