Vector Calculus

Customer Reviews:

Inadequate for all purposes.......2007-10-08

This book's target audience is a little unclear. Ostensibly, this is a somewhat more rigorous treatment of multivariable calculus than a typical second-year sequence, but in fact this book is absolutely deficient as an analytical text. There are very few proofs in the book--the proofs of most theorems are relegated to an "internet supplement"--and the ones that are included are at far too low a level and fail to do what the theorems of a good text ought to do: gradually and methodically develop the topic. In some cases, such as the implicit function theorem, the statement of the theorem is just plain convoluted, apparently because the authors attempted to strike some kind of balance between being mathematically correct and working within the comfort zone of students coming out of low-level math courses.

Furthermore, nothing in the book is taught at an appropriate level of generality. For example, many "proofs" involve low-level calculations of dot products when it would be far more elegant, not to mention mathematically preferable, to use the general properties of inner product spaces instead. Many theorems and formulas are stated only for cases in which the domain is in two or three dimensions rather than working in n-dimensional vector spaces, and the complex field is essentially absent from the entire work.

So, since the book is not an analytical treatment, is it useful as a "standard" multivariable text? No. It's extremely difficult to learn the material for the first time from this book because there are numerous unexplained leaps, and examples are scarce. The exercises are useless for developing one's understanding; as other reviewers correctly noted, they frequently involve only a brief calculus setup followed by needlessly contorted algebraic operations, and students are likely to second-guess themselves when they arrive at (correct) answers that are so complicated they look wrong.

Part of the problem is that Marsden and Tromba's text is far shorter than the bulky book makes it appear. The margins, type, and spacing are outrageously generous; many pages are devoted to cute but unnecessary and often irrelevant history essays; and the pictures and figures (whose colors are badly aligned) take up huge amounts of space on the page. There is a vast amount of wasted space that could have been occupied by proofs, examples, motivation for the development of the subject, etc. It's just not worth the price of a textbook to have something with so little useful material.

Rejoice if your university made you use it!.......2005-10-24

First of all, what is this book about? It's just your regular multivariable calculus stuff, what some would have as calculus 2 (others as calculus 3).
That being said, from the standpoint of someone forced to live the horrors of another calculus 2 book, where the explanations are simplified to the point of not making any real sense, this is a *much better* book, because at least it attempts to give more detailed explanations, instead of shoving definitions. However, they don't appear to be exceptional and, in fact, some stuff is, well, condensed. I liked the rigor in the notation - very important to get used to healthy habits.
I do think it falls a little short of the Essence-Which-a-Calculus-Text-Must-Have, which is to relate the stuff to Physics and applications in a strong way. To reach that goal without dumbing down the explanations and theorems, or making the mathematics so detached from the applications that you loose the connections between the abstractions is a balance that falls upon an author to achieve. After all, Calculus was invented because of Physics (on that note, I liked McCallum's et al. Multivariable Calculus, which was taylored precisely with that aspect as one of its goals - but it's less mathematically advanced).
My guess is that there has to be a great calculus book for undergraduates out there, somewhere. I'm not sure this is it (Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, by Hubbard & Hubbard seems to be getting raving reviews).
It's also very nicely illustrated. As I looked more carefully, I came to realize great care was invested in crafting the illustrations - they are a notch higher in quality and really convey imporant information - you know, just the little details, or complexity, that really make a difference (but let's not get all hyped up about it - today, any modern book is - but this is book is very nice).
So, in a nutshell, although I can't vouch for the outstanding quality of the book, my message to those that complained about this being the textbook chosen at their alma mater is: rejoice! You've got a better book than I did!

Note: this review is about the 3rd edition; have only consulted the text (i.e., did not work through the whole book in a class).

Agree with K.Green.......2005-10-18

This is not a math nerd who learned calculus in middle school, nor a professor. This is just a lowly student that learned single variable calculus in 11/12th grade of High School. I found this book to be lacking in explanation and the examples in the text were not very helpful either.

Decent.......2005-09-26

After a couple of weeks of using this textbook, I am mostly happy with it. It does a good job of explaining the material, however, it is not very concise and takes a long discussion to make a point. It is longer than necessary and contains unnecessary features. Other than that, for the money it is a good deal, and thus the four stars.

Against the other reviewers.......2005-06-03

I've never seen the other book people have been referencing in their reviews of this one, but I honestly can't comprehend why people find this book so confusing. I was interested in calculus since age 13 and, though I found this book amazingly intricate and confusing at first glance, I was able to solve many of the problems in the book due to the explanations in it. Of course, I was reading the older version with ISBN 0716718561, but I still got what they were trying to explain.

Vector calculus isn't an easy subject for anyone to grasp, and this book puts a good majority of it in clear focus, even for very young math-nerds. Check it out.

Average customer rating:

A Great Book to Study Multivariable Calculus!
Superlative
INCOMPREHENSIBLE!!!
Little confusing
Awesome

Vector Calculus (3rd Edition)
Susan J. Colley
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

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ASIN: 0131858742

Book Description

A traditional and accessible calculus book with a strong conceptual and geometric slant that assumes a background in single-variable calculus. It uses the language and notation of vectors and matrices to clarify issues in multivariable calculus, and combines a clear and expansive writing style with an interesting selection of material. Chapter topics cover vectors, differentiation in several variables, vector-valued functions, maxima and minima in several variables, multiple integration, line integrals, surface integrals and vector analysis, and vector analysis in higher dimensions. For individuals interested in math and calculus.

Customer Reviews:

A Great Book to Study Multivariable Calculus!.......2006-06-01

I'm a math major and it was my first course that I took to meet the math requirements. I had assignments almost daily but we didn't go over the assignments deeply in the class. Therefore, I had to self-studied a lot and I actually got more help from the Student Solution Manual of the book. This book is very concise to read as well. I always think that if I paid more attention in this text seriously, I would do better in the class. I suggest to buy the solution manual book together.

Superlative.......2006-02-18

This book covers all the standard vector calculus material. What sets it apart is the pedagogic skill of the author. It is very carefully written and motivated, with clear worked examples for each new concept. A student could work through this book independently.

The author has included a brief section on differential forms in the last chapter and she presents Stokes' theorem in the language of forms. This is a modern formulation and she is to be praised for doing this. It is possible to move from this book on to modern texts on manifolds and differential geometry (such as the books by John Lee and Barrett O'Neill, for example).

INCOMPREHENSIBLE!!!.......2006-02-03

Hope and pray that your professor is awesome, because the explanations in this book are absolutely incomprehensible. Also, some of the hints in the exercises are ridiculous, such as "Be careful when you do this" and "Think carefully"!!! Is the author implicitly saying that the rest of the problems can be done while being careless, or what?
P.S. I'm obviously not a kid ... just didn't want to login for writing this review.

Little confusing.......2004-11-05

I have been using this book for a course in Vector Cal. this
semester. I have to say that the large price tag was a big turn
off to start, but I can get past that if the book is worth it. So far I am not impressed with this book. The examples are poor and the methods taught are a little confusing at best. Some have
found this book to be great in the way that the material is explained but I had some serious issues with the way the material was presented. I ended up buying several other books on vector calculus and using internet sites from other universities to supplement this book. As a stand alone this book has some serious issues. Try to avoid it if you can.

Awesome.......2004-07-20

Professor Colley's book excels in all the areas one would look for including abundant examples, fine graphics, excellent graded problems, clear writing, good organization and so on. It stands out particularly for the author's sensitive presentation which not only presents the material in a clear, logical form but in such a way as to anticipate the questions of the reader. The use of geometric intuition is especially effective. Not being a great talent at mathematics, I found that this book clarified many ideas that I had not understood before. How the negative critics came up with their ideas is a mystery.

Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition

Average customer rating:

Great Book!
easy to read
Positives/Negatives of Div,Grad,Curl
Should be a required textbook for all freshman/sophomore physics and engineering students
Great way to learn your basics!

Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition
H. M Schey
Manufacturer: W. W. Norton
ProductGroup: Book
Binding: Paperback

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ASIN: 0393925161

Book Description

Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics. The Fourth Edition has been carefully revised and now includes updated notations and seven new example exercises.

Customer Reviews:

Great Book!.......2007-08-25

This book really nailed out the nuts and bolts of vector calculus. A must have for anybody taking an electricity and magnetism class in physics at the same time as multivariable calculus.

easy to read.......2007-06-13

good reference book for people who want to study mechanical engineering

Positives/Negatives of Div,Grad,Curl.......2007-05-19

The book was easy to read and learn from. It draws parallels with electric field "stuff" which really adds to the understanding you gain from the math discussions, even if you are not already familiar with electric fields. The book provides concise discussions on the div, grad, and curl operators; however, it is not organized like a reference book or text book (e.g. it lacks tables of these operators expressed in cylindrical and spherical coordinates). I highly recommend reading through this book if you are at all confused about what div, grad, and curl are, the differences between them, or why you should be interested in them.

Should be a required textbook for all freshman/sophomore physics and engineering students.......2007-02-17

Simply put, this book provides the best explanation of the gradient, the divergence, and the curl in any book I've seen. It really should be a required reference/text for every physics and engineering program in the country. All the mathematics is here, but the author also lucidly explains in words and diagrams the physical meaning of these three operations. Many students learn how to manipulate these operations, but they often have trouble understanding exactly what they mean. This book is easy to read (how many textbooks can you say that about?) and there are lots of problems to illustrate key points after each chapter. The author uses the mathematical formalism to solve some basic problems in electrostatics to provide real-world examples. After working through this book, you'll not only be able to calculate the curl of a vector function, you'll know exactly what it means.

Great way to learn your basics!.......2007-01-03

I had three years of higher-level calculus between my BS and MS in mechanical engineering, and none of these classes have explained the concepts in this book with such clarity and accessibility. The sample problems at the end of each chapter cement the concepts just learned. For me, they were just challenging enough to test and hone my skills, but not so crazy that I felt like I was stroking some intellectual ego instead of learning practical concepts.

I highly recommend it to people of similar backgrounds as myself--people with already decent math backgrounds, but who need to hone their vector calculus skills to enter the world of physics, electrical engineering, fluid mechanics, continuum mechanics, or anything else along those lines (lines! Hah! Pun!). I feel like this book was written just for me! Are there really that many of us?

One tip on this book--get serious with it, and you will really cement your skills. Do the problems, for real--work them out with pencil and paper; don't just skim them while you watch TV. They are, as I've said, challenging enough to be rewarding, but none are the type that would send you sobbing to your prof in office hours. Suck it up, fix yourself a nice cup of tea, get your dog to sit with you, and go for it! It's well worth the effort.

Average customer rating:

You won't be disappointed
Superb! Easy to Understand
A didactical masterpiece
Excellent stand-alone introduction to vector analysis
Very Helpful Reference

Schaum's Outline of Vector Analysis
Murray R. Spiegel
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 007060228X

Book Description

This book introduces students to vector analysis, a concise way of presenting certain kinds of equations and a natural aid for forming mental pictures of physical and geometrical ideas. Students of the physical sciences and of physics, mechanics, electromagnetic theory, aerodynamics and a number of other fields will find this a rewarding and practical treatment of vector analysis. Key points are made memorable with the hundreds of problems with step-by-step solutions, and many review questions with answers.

Customer Reviews:

You won't be disappointed.......2007-07-20

This book is worth a whole lot more than the paltry sum they're charging. You really can't go wrong with any mathematics or physics material authored by Murray Spiegel but this text is in a class by itself. Even though it's a Schaum's "Outline", you'll find that it's actually a first rate textbook. I'd say it's an outstanding learning tool given the fact that I found myself actually enjoying working through it!

Superb! Easy to Understand.......2007-01-27

Hooray! Spiegel does a wonderful job of summarizing Vector Analysis simply and to the point. His definitions and explanations are concise and down-to-earth. Keep in mind this is an outline, and the format remains that way. But this is an extremely effective resource for this subject-- well done, IMO.

The examples are often proofs, but are also a comprehensive overview of applications and standard problems. One criticism: sometimes, Spiegel introduces 'new' concepts (e.g. Jacobians) in the problems without defining them in the outline text. So you have to go through the sample problems (with answers!) to get all the stuff that's in the text. Also, if this is your first exposure to Vector Analysis, the problems are just problems, without a lot of background explanation. Much is self-explanatory, but once in a while, especially without previous Vector Analysis exposure, I can see where it would be a bit overwhelming to just jump into it. There isn't a lot of context for some of the non-proof problems. I've read/studied other books on the subject, so I'm not completely new to the field (but I am certainly no expert, either!)

The last chapter on Tensor Analysis covers a ton of material in one lengthy chapter. A separate source on this complex subject would be a better way of approaching this area. Still, the definitions remains quite straight-forward and to the point, and the sample problems provide a nice overview. Call it a good quick-reference.

A didactical masterpiece.......2006-03-25

I bought this book many years ago and soon I felt it extraordinary. My idea has not changed along years. Clear, comprehensive, readable, even pleasant. You can really learn vector analysis step by step without a teacher. And you learn to use what you learn. All topics about vectors are explored, included differential operators and some differential geometry. It covers also tensor analysis (the last two chapter are on curvilinear coodinates and tensor). In my opinion there is a little more than a mere introduction to this subject. When I began to study tensors, I did't find a book that is completely satisfaying for a beginner. I turned out to my old Spiegel and the light was. Read first the last two chapters of Spiegel when you begin with tensors: you will understand basics concepts and you will avoid troubles. I feel to owe a debt of gratitude to this book and its Author. A true didactical masterpiece.

Excellent stand-alone introduction to vector analysis.......2006-03-08

I own many Schaum's outlines, and several by Mr. Spiegel, the author of this book. Mr. Spiegel's outlines have always been among the most excellent of the Schaum's outline series and this one is no exception.
This book is so clear and complete it can stand alone as a textbook in vector analysis, and it is much cheaper than all of the alternatives. Besides being of help to students in pure mathematics, it should also prove helpful to students of physics, mechanics, and especially electromagnetic theory, where visualization of problems and conversion of that visualization into equations that can be solved are the hardest parts of the course. This book will help with all of that.
Topics include the algebra and differential and integral calculus of vectors, Stokes' Theorem, the divergence theorem, plus other integral theorems together with applications drawn from many fields. There is also additional material on curvilinear coordinates and tensor analysis that will be very helpful to students of advanced engineering, physics, and mathematics. Highly recommended for anyone who has already had two semesters of calculus.

Very Helpful Reference.......2005-10-07

I have been using this book in conjunction with Stewart's Multivariable Calculus (a book that fails in many aspects) for my Multivariable Calculus class. This explains vector operators much better than Stewart does, and for a little over $12, that is less than 1/10 of the price of Stewart.

The quality of print in this edition is excellent. The reviewer below must have found a very old edition of this book in the library somewhere. Spiegel is good at explaining things, and helpful references like vector differentiation/integration tables are summarized and included.

Overall, well worth the money.

Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences)

Average customer rating:

A complete book by very erudite authors
A Unique Reference
mixed bag: many virtues but many weaknesses
Poorly writen, filled with errors, very long, poorly indexed

Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences)
Ralph Abraham , Jerrold E. Marsden , and Tudor Ratiu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387967907

Book Description

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.

Customer Reviews:

A complete book by very erudite authors.......2002-04-07

I actually read this entire book--it is quite long and dense. Actually I took the course from the author Jerry Marsden at Caltech and Tutor (Jerry's friend and co-author) gave a guest lecture while visiting. We flew through the entire thing and ch 9 on lie groups of his mechanics and symmetry text in a short 10 weeks! My background in math was relatively weak when taking the course so it was a little hard to keep up; i.e. I came from an engineering background. Anyway, it is probably the most complete/diverse text I've come across on the subject. Of course, it's actually more of a monograph than a text. Since I've read the whole thing, I have to admit there are "several" typos. But as it is that most people can't even write a damn email without a typo or two, the book really does a good job considering it is 800 pages of mostly dense mathematical rigor. I imagine that if I wrote 800 pages of mathematical symbols in latex, that I might forget a tilde or put something as subscript that should have been superscript here or there! None of these errors really matter too much-they should not hinder one's understanding. All and all I think that this book is a great ref, although I've never seen the index, if one exists. For the beginner, also check out Boothby's book, which covers a lot of the same material but tones it down a bit.

A Unique Reference.......2000-10-10

Students of mathematical physics in general, and general relativity in particular, face a formidable challenge in attempting to find coherent, readable references on manifold theory and tensor analysis. I think it fair to say that for every well-written work on the subject, there are ten that do more damage than good. Very few texts can claim to (1) be clear enough to assist the person who is studying alone, (2) offer valuable PHYSICAL insight into the subject, and (3) pass the standards of rigor that mathematicians would impose. Abraham, Marsden, and Ratiu manage to accomplish all three of these goals in this profoundly useful text. I studied from the first edition and I have taught from the second. The two chapters on differential forms, Hodge star duality, integration on manifolds, and the generalized Stokes' Theorem alone are worth the price of the entire book. I am unaware of any other reference which which treats differential forms with the same combination of clarity, physical motivation, and mathematical rigor. The concluding chapter on applications offers one of the clearest introductions to the relativistic form of Maxwell's equations to be found in any text. For students of physics who want to see the mathematics "done right," one would be hard pressed to do better than Abraham, Marsden, and Ratiu.

mixed bag: many virtues but many weaknesses.......2000-02-18

I took a course taught by the 3rd author (Tudor Ratiu) at UCSC using this book; I found both good and bad in it. Much of the bad for me was overcome by the inspiring and energetic presentation by one of the authors. One may view this book as basically a detailed elaboration of the "preliminary" chapters of the book "Foundations of Mechanics" by the 1st 2 authors. The strengths of this book are (a) the treatment which is general enough to include infinite-dimensional manifolds and not just the finite-dimensional case (most books just talk about the finite-dim'l case) and (b) the attempt to cover all theorems "full strength" (in the greatest generality obtaining the strongest conclusions from the weakest hypotheses). Neither of these (not counting the many typos) recommends this as a first or even second text for students, but it's hard to find any other books that treat the material at the same level of generality and precision, which is a must if attempting "hard" global analysis in areas such as fluid mechanics (from a geometric point of view). Correction of the many typos could make this an indispensable reference book for those requiring the techniques discussed. More discussion of finite-dimensional examples before jumping to infinite-dimensional ones (e.g. discussing finite-dimensional Grassmannians before jumping to the infinite-dimensional Banach manifold version) could make this into a tolerable text.

As it is, it's problematic, aggravating, and not for the faint of heart, but not without its virtues.

Possible alternatives for the infinite-dimensional point of view are Lang's manifolds book or some volume of the expensive multi-volume treatise on analysis by Dieudonne.

Poorly writen, filled with errors, very long, poorly indexed.......1999-09-21

We used this book in a graduate course at UCLA. The professor had to hand out a list of all the errors we encountered, and it was about ten pages typewritten. The professor, Geoff Mess, wrote at the top of this list that many of the students had complained about this book, and that it was a disappointment to him as well. I often found myself scanning hundreds of pages in search of what should have been contained in their sparse index. The book is unnecessarily long and wordy for the matter covered. In the introduction, the authors mention that they invite comments from the readers. It seems that they depend on their readers to correct their copious errors and their poor writing.

Schaum's Outline of Tensor Calculus (Schaum's)

Average customer rating:

Tensor Calculus
Easy reading for a complex subject
An evergreen book
Helpful in Learning Relativity
Agreed, a must have...

Schaum's Outline of Tensor Calculus (Schaum's)
David C. Kay
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 0070334846

Book Description

This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too.

Customer Reviews:

Tensor Calculus.......2007-01-04

I have found it to be an excellent refernce for an otherwise difficult subject.

Easy reading for a complex subject.......2006-06-26

I've many books about tensors and this one is the best one to start learning such a difficult subject. It does not omit the things that are assumed you must know. It explains everything, even the simplest things in a easy way. However, you should know vector analysis and multidimensional calculus in order to understand the complex things in the last chapters.

An evergreen book.......2005-10-25

It's a pity Amazon doesn't declare the age of books that sells (date of edition).
This book - in spite of its oldness - is very useful to everyone that needs to know something about tensors.
Lionello Cantoni

Helpful in Learning Relativity.......2005-09-24

I have been studying a textbook in general relativity. A lot of the material that they gloss over is detailed in an understandable way in this volume.

Agreed, a must have..........2005-06-22

...for students, educators and practicing scientists and engineers. Great reference and learning/teaching tool.

Vector Calculus Study Guide & Solutions Manual

Average customer rating:

As worthless as the book
Only useful becuase the textbook is bad.
Decent
useful adjunct to the textbook

Vector Calculus Study Guide & Solutions Manual
Karen Pao , and Frederick Soon
Manufacturer: W. H. Freeman
ProductGroup: Book
Binding: Paperback

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ASIN: 0716705281

Customer Reviews:

As worthless as the book.......2007-09-30

This manual only solves the problems listed in orange in the book and it solves them very briefly, to the extent that it is still difficult to follow. I did not care for the book and had trouble using it to solve any of the exercises in the back of each section. As a result, I bought the solutions manual hoping to shed some light on how to solve these exercises. However, the manual did no such thing to alleviate this problem; certainly not $30 worth of help. Not a recommended buy, you're better solving the problems using other math texts.

Only useful becuase the textbook is bad........2007-08-12

My title says it all. The text book that goes along with this is absolutely horrible. This book is also really bad, however becuase you will need all the help you can get I have to recommend this book. Why is this book bad? Well like the textbook this book is very confusing. The book constantly skips steps and assumes you actually know the material (which you wont). Like I said, if you are taking a class that requires the text book then you really need to buy this since it will be the only source of help you are going to get.

Decent.......2007-03-09

This book has helped me a pretty good amount with my math homework, and is probably worth the $30, but it can still be a tad confusing at times.

useful adjunct to the textbook.......2006-11-10

It is a great supplement to the textbook. It is almost required. First you need to check your work. Second, sometimes you can't do the problems without it. Cons: Some of the solutions are a bit cryptic. The typography is not as clear as TeX. The solutions are a little cramped and like the text, the presentation could benefit from better layout on the page. This whole class could benefit from more computerization.

Nonlinearity & Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis (Pure and Applied Mathematics, a Series of Monographs and Tex)

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Nonlinearity & Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis (Pure and Applied Mathematics, a Series of Monographs and Tex)
Melvyn S. Berger
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0120903504

Tensor Calculus and Analytical Dynamics (Engineering Mathematics)

Average customer rating:

comprehensive but biased view of tensor analysis...
The definitive book on tensors in analytical mechanics

Tensor Calculus and Analytical Dynamics (Engineering Mathematics)
John G. Papastavridis
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849385148

Book Description

Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: o tensor calculus in nonholonomic variables o Pfaffian nonholonomic constraints o related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Customer Reviews:

comprehensive but biased view of tensor analysis..........2006-01-26

Papastavridis is an author with a unique attitude towards mathematics. He avoids the coordinate free formulation of tensors on manifolds. In his view, the exterior differential calculus is an esoteric abstraction which is hard to grasp by many and thus has the danger of turning down able people from embarking on doing research in analytical mechanics. This is basically a recapitulation of his views which have been explicitly stated within the book in a broader context.

With that said, don`t expect to find anything pertaining to modern differential geometric view of mechanics. However, this book presents one of the most extensive survey of tensor analysis with indices. The bibliography is indeed comprehensive, and a welcome feature in such a monograph.

Personally, I benefitted alot from this book both in terms of physical aspects of mechanics and in terms of classical tensor analysis. However, I still believe in the power of mathematical abstractions in grasping of the holistic image of a physical and/or mathematical entity. In this respect, the language of differential forms is rather important and allows further useful topological generalizations like cohomology. It is true that the current engineering/science curricula does not leave much space for the modern view, but this is ultimately where it will be heading to. Despite his dislike of exterior calculus, Papastavridis inevitably builds a strong basis for delving into tensor analysis on manifolds. For the latter Bishop and Goldberg is still the best choice with an unbeatable price.

The definitive book on tensors in analytical mechanics.......2000-08-28

This book is not a text book. It is, in some sense, the final word on tensor formalism in finite degree of freedom (analytical) mechanics. It is one of the most scholarly books I have come across. The list of references is very exhaustive and the author is well read in the literature on the subject, not just in english, but also in russian, french, and german. The style is clear and concise, the notation is carefully chosen and summarized in a useful section where conventions, notation, and basic formulae are listed.

Calculus of Variations (Cambridge Studies in Advanced Mathematics)

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Calculus of Variations (Cambridge Studies in Advanced Mathematics)
Jürgen Jost , and Xianqing Li-Jost
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521642035

Book Description

This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues such as Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. The prerequisites are knowledge of the basic results from calculus of one and several variables. After having studied this book, the reader will be well equipped to read research papers in the calculus of variations.

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