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Vector and Tensor Analysis with Applications
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
288 pages, Paperback
First published October 1, 1979
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Displaying 1 - 4 of 4 reviews
March 13, 2020
This is a well designed, pedagogically inspired and comprehensive introduction to a fundamental branch of applied mathematics: tensor and vector calculus.
Designed for the upper undergraduate or graduate student, this textbook is probably one of the most lucid, clear and eminently readable treatments of this subject.
Do not be misguided by the relative age of this book: it is still surprisingly modern in its approach, and it does deliver a brilliant example of a concise yet comprehensive and highly informative account, supported by a substantial collection of solved examples from the physical sciences, with a particular emphasis on fluid dynamics but with also good examples from electromagnetism and the physics of deformable solids (objects such as the stress tensor and the rate of deformation tensor are explained quite well, for example).
The pedagogical merits of this book are many: conciseness, its abundance of examples, its design as a self-contained book requiring only a solid background in calculus at undergraduate level, the very gentle conceptual progression with which new elements are presented, the reliance on intuitive aspects, all contribute to a very pleasant reading experience.
This does not mean that the concepts are over-simplified: on the contrary, the authors do not refrain from addressing more sophisticated and complex aspects, including the supporting examples from the physical sciences. Just to name a few examples, the reader can find in this book items that are not always treated satisfactorily in introductory textbooks to the subject: the full development of the complete Navier-Stokes equation, the demonstration of the Kutta-Joukowski theorem, the derivation of the Thomson's theorem, a detailed treatment of the covariant derivative (and the associated Christoffel symbols of the first and second type), a good treatment of the stress and deformation tensors etc, are all items that are treated with great clarity and at a good level of detail.
The definition of tensor is focused on its intuitive aspects and it is therefore based on the traditional approach of defining tensors as intrinsically “geometric” objects defined by their transformation properties, ensuring their basis-independence.
An equivalent, but more contemporary and general approach (not explicitly used in this book) would be to use a more intrinsic (but less intuitive) definition (as typically used in differential geometry), whereby tensors are defined as multilinear maps of a set of dual vectors and vectors onto a field (such as R) relative to a vector space V. For this reason, I would recommend that the reading of this textbook be later complemented by more contemporary books. However, as a comprehensive and meaningful introduction to the subject, this book is pedagogically difficult to improve on.
The only real issue with this text is that I found a number of errors. They are quite easy to identify, and most of them (but not all) appear to be genuine “typos” rather than authors' calculation mistakes. Still, they do sometimes slow down the reading flow, they are quite disappointing in a text of generally very high quality, and in a couple of cases they may have induced the unwary reader into misleading assumptions/results. This is why I have assigned a 4-star rating to this otherwise excellent book.
Designed for the upper undergraduate or graduate student, this textbook is probably one of the most lucid, clear and eminently readable treatments of this subject.
Do not be misguided by the relative age of this book: it is still surprisingly modern in its approach, and it does deliver a brilliant example of a concise yet comprehensive and highly informative account, supported by a substantial collection of solved examples from the physical sciences, with a particular emphasis on fluid dynamics but with also good examples from electromagnetism and the physics of deformable solids (objects such as the stress tensor and the rate of deformation tensor are explained quite well, for example).
The pedagogical merits of this book are many: conciseness, its abundance of examples, its design as a self-contained book requiring only a solid background in calculus at undergraduate level, the very gentle conceptual progression with which new elements are presented, the reliance on intuitive aspects, all contribute to a very pleasant reading experience.
This does not mean that the concepts are over-simplified: on the contrary, the authors do not refrain from addressing more sophisticated and complex aspects, including the supporting examples from the physical sciences. Just to name a few examples, the reader can find in this book items that are not always treated satisfactorily in introductory textbooks to the subject: the full development of the complete Navier-Stokes equation, the demonstration of the Kutta-Joukowski theorem, the derivation of the Thomson's theorem, a detailed treatment of the covariant derivative (and the associated Christoffel symbols of the first and second type), a good treatment of the stress and deformation tensors etc, are all items that are treated with great clarity and at a good level of detail.
The definition of tensor is focused on its intuitive aspects and it is therefore based on the traditional approach of defining tensors as intrinsically “geometric” objects defined by their transformation properties, ensuring their basis-independence.
An equivalent, but more contemporary and general approach (not explicitly used in this book) would be to use a more intrinsic (but less intuitive) definition (as typically used in differential geometry), whereby tensors are defined as multilinear maps of a set of dual vectors and vectors onto a field (such as R) relative to a vector space V. For this reason, I would recommend that the reading of this textbook be later complemented by more contemporary books. However, as a comprehensive and meaningful introduction to the subject, this book is pedagogically difficult to improve on.
The only real issue with this text is that I found a number of errors. They are quite easy to identify, and most of them (but not all) appear to be genuine “typos” rather than authors' calculation mistakes. Still, they do sometimes slow down the reading flow, they are quite disappointing in a text of generally very high quality, and in a couple of cases they may have induced the unwary reader into misleading assumptions/results. This is why I have assigned a 4-star rating to this otherwise excellent book.
October 21, 2020
It is only one book which explains covariance and contravariance of vectors for me.
It`s an amazing book, it contains a few discontinuous only, very clear and continuous presentation of material.
It`s an amazing book, it contains a few discontinuous only, very clear and continuous presentation of material.
May 1, 2020
How can i read it?
August 16, 2020
The best one
Displaying 1 - 4 of 4 reviews