Tensor Analysis and Continuum Mechanics

Book Description

This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics. Firstly, a detailed tensor analysis is developed in Cartesian and general coordinates. Definitions, propositions, and examples relative to operations on tensors, canonical isomorphism, Euclidean vector spaces, exterior algebra, point spaces, metric element, Christoffel symbols, covariant and absolute derivatives, adjoint, differential operators, and many other concepts are introduced in a rigorous and practical way. The topic is not merely viewed as an autonomous mathematical discipline, but as a preparation for theories of physics such as general relativity theory, fluid-dynamics, engineering, and differential geometry. Secondly, developed in symbiosis with tensor analysis, continuum mechanics thoroughly covers Lagrangian and Eulerian descriptions, deformations, kinematics of continua, fundamental laws, principle of virtual work, linear elasticity and more. This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.

Vectors and Tensors in Engineering and Physics

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Excellent introductory book on tensors
Vectors and tensors in engineering and physics

Vectors and Tensors in Engineering and Physics
D.A. Danielson
Manufacturer: Addison-Wesley Pub (Sd)
ProductGroup: Book
Binding: Hardcover

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ASIN: 0201524260

Book Description

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.

Customer Reviews:

Excellent introductory book on tensors.......2000-12-11

I've not come across another book that introduces tensors successfully to non-mathematics graduates. It would not be easy to appreciate and comprehend every part of the book as it covers a wide range of physics & engineering applications. (not many of us are experts in all fields) However, the book is an excellent platform to start learning about tensors, after which one can go on to read the classics on tensors. I'd recommend the book to any senior or graduate engineering student (physics and maths students might find the book "less challenging").

Vectors and tensors in engineering and physics.......2000-04-02

It's a good-level book in tensors' algebra and calculus. Besides, physical examples help you better understand the mathematical concepts. On the other hand, I think it does not have enough applications about vector calculus (Frenet formulas, scalar potentials, Maxwell equations...).I would have also preffered it to contain more about general tensor theory: pseudotensors, curvilineal coordinates, and also about Riemann spaces. Despite this, it's an excellent book where you can see mathematics aplied to science; this is the important thing for physicist and engineers

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Calculus with Early Vectors
Phillip Zenor , Edward E. Slaminka , and Donald Thaxton
Manufacturer: Prentice Hall
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Binding: Hardcover

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ASIN: 013791203X

Book Description

This book focuses on the requirements of a specific group of readers, structuring the book so that calculus is presented as a single subject rather than a collection of topics. With a user-friendly approach that keeps the reader in mind, the material is organized so that vector calculus is thoroughly covered. Approaches the theoretical aspects of calculus with the belief that, at the introductory level, it is important to understand the geometric basis for theorems and develop an intuitive understanding for the statements of the theorems and their implications. Emphasizes the power of calculus as a tool for modeling complex physical problems in order to present the methods of differentiation and integration as necessary skills needed to solve problems that arise from mathematical models. Excellent as a refresher for those in fields requiring a strong mathematical background.

Vector analysis for mathematicians, scientists, and engineers (The Commonwealth and international library of science, technology, engineering, and liberal studies. Physics division)

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Vector analysis for mathematicians, scientists, and engineers (The Commonwealth and international library of science, technology, engineering, and liberal studies. Physics division)
S Simons
Manufacturer: MacMillan
ProductGroup: Book
Binding: Unknown Binding

Mathematical Methods for Engineers and Scientists 2: Vector Analysis, Ordinary Differential Equations and Laplace Transforms

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Mathematical Methods for Engineers and Scientists 2: Vector Analysis, Ordinary Differential Equations and Laplace Transforms
K.T. Tang
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Mathematical Methods for Engineers and Scientists 1: Complex Analysis, Determinants and Matrices

ASIN: 3540302689

Feed-Forward Neural Networks: Vector Decomposition Analysis, Modelling and Analog Implementation (The International Series in Engineering and Computer Science)

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Feed-Forward Neural Networks: Vector Decomposition Analysis, Modelling and Analog Implementation (The International Series in Engineering and Computer Science)
Jouke Annema
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0792395670

Book Description

Feed-Forward Neural Networks: Vector Decomposition Analysis, Modelling and Analog Implementation presents a novel method for the mathematical analysis of neural networks that learn according to the back-propagation algorithm. The book also discusses some other recent alternative algorithms for hardware implemented perception-like neural networks. The method permits a simple analysis of the learning behaviour of neural networks, allowing specifications for their building blocks to be readily obtained. Starting with the derivation of a specification and ending with its hardware implementation, analog hard-wired, feed-forward neural networks with on-chip back-propagation learning are designed in their entirety. On-chip learning is necessary in circumstances where fixed weight configurations cannot be used. It is also useful for the elimination of most mis-matches and parameter tolerances that occur in hard-wired neural network chips. Fully analog neural networks have several advantages over other implementations: low chip area, low power consumption, and high speed operation. Feed-Forward Neural Networks is an excellent source of reference and may be used as a text for advanced courses.

Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory (Ieee-Oup Series on Electromagnetic Wave Theory)

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long awaited book

Generalized Vector and Dyadic Analysis: Applied Mathematics in Field Theory (Ieee-Oup Series on Electromagnetic Wave Theory)
Chen-To Tai
Manufacturer: Oxford University Press, USA
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Binding: Hardcover

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Waves and Fields in Inhomogenous Media (IEEE Press Series on Electromagnetic Wave Theory)

ASIN: 0198592140

Book Description

An indispensable reference tool for engineers, mathematicians, and physicists, this book offers details on previously unpublished methods of treating and presenting vector and dyadic analysis. Along with pointing out various fundamental misunderstandings in the presentation of concepts to
date, Tai presents original findings on a new symbolic method with the aid of a symbolic vector. Additional features include: detailed derivations of theorems identities; coverage of new topics such as surface vector analysis and dyadic analysis; and a concise but rigorous treatment of a symbolic
vector.

Customer Reviews:

long awaited book.......2001-12-29

If you ever came across the need of expressing vector operators in curvilinear coordinates, while writing numerical codes or solving PDEs in generalised coordinates, then you might have felt the need of a rigourous presentation of the subject.
Rigorous yet usable, I would say. This is not a book for pure mathematicians (the theorem you need is at pag. 435 consisting of one line saying the proof follows from the 2000 previous Lemma-theorem-corollary scattered all around...). The author has the physical problems well in his mind (he's Emeritus at Univ of Michigan, dept of Electrical Engineering) and makes frequent references to where in physics or geometry you will encounter such mathematical entities.
Chapter 8, devoted to the history of vector analysis, makes you clear why you haven't been able to find a neat rigorous presentation so far. This digression (I'm reluctant to use this expression for it's not a minor chapter in my opinion) gives you an even sharper feeling of what's the core of the matter by comparing critically different approaches.
The first introductory chapters on geometry, coordinate systems, dyadics provide a sound general background, presenting derivatives of vectors in generalised coordinate system from the beginning, resulting in a powerful and unifying exposition of the matter. All is extremely clear, a characteristic of the book in its whole.
The author always stress upon the transformation properties of the objects which have been defined, thus clarifying their meaning and mathematical character.
The appendix on vector analysis in the special theory of relativity is enjoyable and makes you clear how E and B can be treated as vectors even if they transform like the components of a tensor (OK, you already knew that, but you were using tensor analysis from the start, didn't you?).
There is much more in this book, which I would suggest to keep as a reference to any physicist, applied mathematician, biologist, engineer, numerical people and (even!) mathematician (developing communication skills...). First years students, which are always a bit confused on why one should use vectors at all and having accepted that think that everything is a vector, which is not, should definitely start with this book. Next time I will be asked to teach anything related to mechanics, I will adopt this book for the fundamental mathematics (but also check the excellent Biscari-Poggi-Virga Mechanics Notebook, 1999 Liguori ed. Napoli (IT) ).
It's also an excellent way to approach what you want next, which is likely to be tensor analysis which this book, unfortunately, cannot cover (can you hear me, Professor Tai?...).

High Performance Computing in Science and Engineering ' 06: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2006

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High Performance Computing in Science and Engineering ' 06: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2006

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540361650

Book Description

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2006. The reports cover all fields of computational science and engineering ranging from CFD via computational physics and chemistry to computer science with a special emphasis on industrially relevant applications. Presenting results for both vector-systems and micro-processor based systems the book allows to compare performance levels and usability of various architectures. As HLRS operates the largest NEC SX-8 vector system in the world this book gives an excellent insight into the potential of vector systems. The book covers the main methods in high performance computing. Its outstanding results in achieving highest performance for production codes are of particular interest for both the scientist and the engineer. The book comes with a wealth of coloured illustrations and tables of results.

High Performance Computing in Science and Engineering ' 07: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2007

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High Performance Computing in Science and Engineering ' 07: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2007

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540747389

Book Description

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the Stuttgart High Performance Computing Center (HLRS) for the year 2007. The reports cover all fields of computational science and engineering, ranging from CFD and computational physics and chemistry to computer science, with a special emphasis on industrially relevant applications. Presenting results for both vector-based and microprocessor-based systems, the book makes it possible to compare the performance levels and usability of various architectures. As the HLRS operates the largest NEC SX-8 vector system in the world, this book gives an excellent insight into the potential of such systems. The book further covers the main methods in high performance computing. Its outstanding results in achieving the highest performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of coloured illustrations and tables.

High Performance Computing on Vector Systems 2006: Proceedings of the High Performance Computing Center Stuttgart, March 2006

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High Performance Computing on Vector Systems 2006: Proceedings of the High Performance Computing Center Stuttgart, March 2006

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 354047692X

Book Description

The book presents the state of the art in high performance computing and simulation on modern supercomputer architectures. It covers trends in high performance application software development in general and specifically for parallel vector architectures. The contributions cover among others the field of computational fluid dynamics, physics, chemistry, and meteorology. Innovative application fields like reactive flow simulations and nano technology are presented. Furthermore, the use of supercomputers in the growing field of medical simulations is shown. All papers were chosen from presentations given at the fourth Teraflop Workbench Project Workshop held at the Höchstleistungsrechenzentrum Stuttgart (HLRS) in March 2006.

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Beauty from Ashes

Amazing Primary Source History

A fascinating story

Good Book

This book is a gift from a great man who lived 200 years ago

The Interesting Narrative and Other Writings: Revised Edition (Penguin Classics)
Olaudah Equiano , and Vincent Carretta
Manufacturer: Penguin Classics
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Binding: Paperback

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Equiano, the African: Biography of a Self-Made Man

Phillis Wheatley, Complete Writings

Incidents in the Life of a Slave Girl (Dover Thrift Editions)

Letters from an American Farmer and Sketches of Eighteenth-Century America (Penguin Classics)

A Vindication of the Rights of Woman (Penguin Classics)

ASIN: 0142437166
Release Date: 2003-05-27

Book Description

An exciting and often terrifying adventure story, as well as an important precursor to such famous nineteenth-century slave narratives as Frederick Douglass's autobiographies, Olaudah Equiano's Narrative recounts his kidnapping in Africa at the age of ten, his service as the slave of an officer in the British Navy, his ten years of labor on slave ships until he was able to purchase his freedom in 1766, and his life afterward as a leading and respected figure in the antislavery movement in England. A spirited autobiography, a tale of spiritual quest and fulfillment, and a sophisticated treatise on religion, politics, and economics, The Interesting Narrative is a work of enduring literary and historical value.

Customer Reviews:

Beauty from Ashes.......2005-09-13

Of all the firsthand accounts known to us as "slave narratives," Vassa's description is unique in many ways. To begin with, he takes his readers all the way back to his African roots, shedding historically-confirmed light on almost lost ancient traditions. His discussion of the harrowing and epically sad capture and separation of he and his sister are among the most moving in this genre.

He then describes the despicable, inhumane conditions in the holds of the slave ships with a "you-are-there" writing style. Again, confirmed by other sources, these are some of the most often quoted accounts in historical texts. In this same chronological phase, Vassa also depicts the shared empathy among the enslave Africans, helping us to see how they collaborated to survive.

His ongoing narrative offers one of the more balanced looks at slavery. Vassa clearly tells the horrors of this evil system and the people responsible for it. At the same time, he often shares accounts of Europeans and White Americans who befriended him. In fact, his positive statements about non-Africans lend further credence to his critique of the many evils of slavery.

His narrative also contains unique elements in his descriptions of his path toward freedom and his life as a freeman. We learn that in his era, for a man of his race, it was barely more tolerable to be free, given the hatred that he still endured.

Though some reviewers tend to minimize or criticize it, his conversion narrative is classic. In fact, it may well have been the standard from which later testimonies were crafted about how "God struck me dead." Perhaps the evangelical nature of his conversion turns off some. However, if we are to engage Vassa in his other accounts, we must engage him here. Further, coming as it did later in his life, it is easy to see how his account of his entire life is entirely shaped by his conversion experience. Clearly, Vassa sees even the evils that he has suffered as part of a larger plan. In doing so he never suggests that God condones the evils of slavery. Rather, he indicates that God created beauty from ashes.

Reviewer: Bob Kellemen, Ph.D., is the author of "Beyond the Suffering: Embracing the Legacy of African American Soul Care and Spiritual Direction," and of "Soul Physicians" and "Spiritual Friends."

Amazing Primary Source History.......2005-06-28

Hemingway said of Tillie Olsen's "Tell Me a Riddle" that, however many readers it may have, it will never have enough. He expressed my feelings about this book. Yes, the "Autobiography of Frederick Douglass" is critical to achieve an understanding of the obscenities of black slavery in the New World, but Equiano's remarkable account dramatizes it in ways even more diverse. He summarizes in his single life the whole span of slavery, from his kidnapping as a child from Africa to the fiendish brutality of Caribbean sugar plantations. But he is also a celebration of the indomitability of the human spirit at its most resilient: from his insistence, against all odds, on his own worth as a person, his acquisition of seafaring and business skills, his achievement not only of literacy but of an Englishman's 18th century eloquence.
I didn't think I could learn more about the particular brutalities of slavery, but I did. An example: in the Caribbean some slavemasters "rented out" their slaves by the day to other masters for excruciating toil. Their temporary masters sometimes "forgot" to feed them lunch, and moreover sometimes sent them back to their masters without payment. For retribution, their masters then beat the slaves! This was a new twist for me, and reminded me that the psychological torture--imagining the starved and exhausted slaves returning to their masters, knowing what was awaiting--often outstripped physical torture for cruelty.
But this is no litany of abuses, and Equiano is careful to spare us gratuitous outrages. He lived the equivalent of five or six lives within his timespan, and the book likewise breaks up into episodes: the African years--during which he chronicles a clime of abundant food and privileged childhood; his adventures at sea, serving several captains on mercantile ships that faced enemy fire and perils of every kind; his strivings to buy his freedom in the Caribbean and North America; his conversion to Christianity; and his settling as a freeman in England with marriage to a British wife.
As with most primary source documents, there are lulls in the narrative. The writing about the author as a Christian aware of his "sins" (he who has so overwhelmingly sinned against) is as familiar as it is ironic. Episodes in the seafaring accounts will be of more interest to afficionados of Melville or Conrad. But what is finally amazing is Equiano's moderation and modesty in describing a most remarkable life. One wonders how many hundreds of thousands of uprooted Africans succumbed to the brutalization and denial of their self-worth for every one who managed to salvage some shred of dignity, but one is nevertheless grateful to Equiano for putting his own example in writing.
It is writing for the ages. I wonder whether it should be required reading, for high school students, for example. Perhaps it's a bit too difficult or tedious for everyone in that age group. But at the very least it should be mentioned in the same breath as Douglass's books. I was 62 before I'd even heard Equiano's name. This remarkable account should be better known.

A fascinating story.......2004-08-06

Many people -- including myself -- read science fiction and fantasy novels to see new vistas of the imagination, alien cultures and circumstances in which we could never imagine ourselves. Sometimes we look to distant futures or galaxies without remembering just how alien the planet we live on can be!

Equiano's account -- generally a clear, crisply written and unsentimental account with detailed descriptions of the places he visits, with the occassional sermon or rare florid description (Dr. Charles Irving's device "renders fresh Neptune's briny element") -- shows a whirlwind series of adventures, from his time as an Igbo village prince, to his enslavement and trek to the African coast under a series of masters, to his horrendous voyage across the middle passage, his amazement at the terrifying new world he was brought into, his conversion to Christianity, his service in the Seven Years War, his attempts to buy his freedom, and his varying adventures as a sailor. The account goes on to include his disastrous expedition to the North Pole and subsequent spiritual crisis upon such a close touch with his mortality, his management as a commissar for an attempt to settle freed blacks in Sierra Leonne, and, finally, his marraige (something touched on very cursorily, perhaps because he didn't wish to add too much to new editions of the book, which was initially completed before his marraige, or possibly because he was very busy raising his daughters, lecturing, and testifying for the abolitionist cause).

Some parts of the account seem, perhaps, slightly too convenient. One might be tempted to wonder if Equiano's memories, as a ten year old, of the customs of his people are shaped by his desire to retrospectively turn them into Jews, or if his account of, upon hearing that a book contain words, holding it to his ear is borrowed from countless other accounts of the "primitive" who misunderstands the nature of the written word, or if his account of himself as a determined fighter for the integrity of the Sierra Leone colonization project, undermined by the other corrupt managers of the project, who stole from the Exchequer and undersupplied the intended black colonists isn't a biased portrayal in his favor. Overall, though, the records that have been recovered by historians have been favorable to Equiano's story, and inaccuracies are remarkably rare for a book so extensive and often written from memories thirty-years old.

Good Book.......2002-02-09

This book presents an interesting and unique view into the world of slavery. Buy it...now!

This book is a gift from a great man who lived 200 years ago.......2001-03-22

An amazing story of a young man kidnapped from his African village as a boy, transported to the Caribbean from island to island and his dealings with the people who were in power. How he gained his freedom, then lost it, then gained it again. His struggle to reconcile what the Bible taught about kindness with what he saw the "Christians" actually doing to slaves. This book is essential reading for anyone living in the Caribbean who wants to understand the mental slavery that still exists there to this day. Its THE guide to "self-help" that beats all others. Its the story of a wonderfully determined man.

The Interesting Narrative and Other Writings : Revised Edition (Penguin Classics)

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The Interesting Narrative and Other Writings : Revised Edition (Penguin Classics)
Vincent Carretta Olaudah Equiano
Manufacturer: Penguin Classics
ProductGroup: Book
Binding: Paperback
ASIN: B000OJ77LW

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