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.

Optimization by Vector Space Methods (Series in Decision and Control)

Average customer rating:

Elegant and astonishing
A Good Book but Seriously Overpriced
This is a true classic
Simply the perfect math book
Thank You Dr. Luenberger

Optimization by Vector Space Methods (Series in Decision and Control)
David G. Luenberger
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 047118117X

Book Description

Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

Customer Reviews:

Elegant and astonishing.......2006-03-17

Professor Luenberger unites many areas of optimization using a few principles from functional analysis. The explanations are clear and the proofs are compact and elegant. This book is your tool for understanding the deep connection between linear programming, convex optimization, game theory, optimal control and series approximation (e.g. Fourier series).

Luenberger's book has over 1300 citations as of March 2006. In my opinion, the material in this book is essential for any graduate student or professional who intends to contribute to the literature in optimization or optimal control.

A Good Book but Seriously Overpriced.......2005-01-15

The exposition is pretty clear and the book has a good number of worked non-trivial examples. At $40 this would be a great book, but $100 for a PAPERBACK book written 30 years ago is a bit ridiculous. The first 1/4 of the book is also a (very) basic introduction to functional analysis which, if you have had any contact with this subject before, you will probably skip making the book quite short.

This is a true classic.......2004-12-18

This book is a timeless classic, filled with extraordinarily powerful mathematics and applicable to just about every serious subject area. Luenberger did a masterful job of writing a book that will "unravel the spaghetti" seen in most other books. The visual perspectives he provides to seemingly abstract ideas are the key.

Simply the perfect math book.......2003-07-04

Optimization by Vector Space Methods, by David Luenberger, is one of the finest math texts I have ever read, and I've read hundreds. Many years ago this book sparked my interest in optimization and convinced me that the abstract mathematics I had been immersed in actually would be applicable to real problems. Since then, Luenberger's book has inspired several of my graduate students. I merely lent them my copy, and Luenberger did the rest; he drew them in by carefully laying the foundation for an elegant theory, with just the right mix of formalism and intuition, and opened their eyes to the beauty and practicality of abstract mathematics. Anyone with an interest in higher-level mathematics (beyond multi-variable calculus, say) would benefit from exposure to this finely-crafted book. I daresay, the rampant math anxiety that is so prevalent in the West would be substantially reduced if more authors would take such meticulous care in presenting their material.

The format of Luenberger's book is also extremely appealing in a way that I cannot quite put my finger on. The typography and illustrations are inherently crisp and inviting; they draw you in. There is nothing at all superfluous or gratuitous in this book. It is utterly to-the-point, methodical, and above all, clear. The techniques are developed starting from an elementary treatment of vector spaces, then proceeding on to Banach spaces and Hilbert spaces. Along the way, Luenberger introduces convexity, cones, basic topology, random variables, minimum-variance estimators, and least squares, among many other things. There is a recurring theme of duality, which can be used in a way analogous to the inner product of a Hilbert space. In particular, the familiar projection theorems of Hilbert spaces can be echoed in simpler normed linear spaces using duality, which Luenberger motivates and covers beautifully.

The book also covers some of the standard fare of functional analysis, such as the Han-Banach theorem, strong and weak convergence, and the Banach inverse theorem. However, Luenberger never wanders too far off into abstract nonsense; around every corner lay tantalizing application of these ideas to optimization. Luenberger first explores optimization of functionals then covers constrained optimization, which builds upon concepts such as positive cones and Lagrange multipliers. The optimization methods themselves have endless applications in fields such as computer vision, computer graphics, economics, and physics. Indeed, the list is effectively endless as optimization techniques pervade math and science.

I'm certain that the appeal of this book is helped immeasurably by the inherent beauty of the subject matter. Hilbert-space methods are lovely in themselves--they possess a structure that engages one's geometric intuition while at the same time admitting convenient algebraic properties. Once you are in the habit of phrasing problems in abstract settings such as Hilbert spaces, it forever changes how you look at things; you cannot help but look past the clutter to the essence of a problem (or, at least try very hard to do so). While this material is not nearly as abstract as, say, category theory, it nevertheless hits a high point in mathematics--a point more people ought to experience.

If you've had some exposure to optimization methods, or need to apply them in the context of computer vision, graphics, or finance, to mention just a few areas, then I urge you to take a look at Luenberger's fine book. It too hits a high point in clarity of mathematical writing. Combine beautiful theory with endless applications and lucid writing, and you have a winner of a book.

Thank You Dr. Luenberger.......2002-10-15

I owe Dr Luenberger a million thanks for writing this book. As his student, I think he is the master of putting complex issues in simple words. Your faithful student..Jayanth Krishnan

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.

Schaum's Outline of Differential Geometry (Schaum's)

Average customer rating:

Differential Geometry review
Good as a basic textbook and a source of solve problems
Differential Geometry - A Schaum's Outline Series

Schaum's Outline of Differential Geometry (Schaum's)
Martin M. Lipschutz
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 0070379858

Book Description

Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study.

Customer Reviews:

Differential Geometry review.......2007-01-04

I have found this to be an excellent addition to my library.

Good as a basic textbook and a source of solve problems.......2006-06-05

This book is intended to assist upper level undergraduate and graduate students in their understanding of differential geometry, which is the study of geometry using calculus. Usually students study differential geometry in reference to its use in relativity. I personally have a rather oddball application for the subject - modeling of curved geometry for computer graphics applications. The fundamental concepts are presented for curves and surfaces in three-dimensional Euclidean space to add to the intuitive nature of the material.
The book presumes very little in the way of background and thus starts out with the basic theory of vectors and vector calculus of a single variable in the first two chapters. The following three chapters discuss the concept and theory of curves in three dimensions including selected topics in the theory of contact.
Great care is given to the definition of a surface so that the reader has a firm foundation in preparation for further study in modern differential geometry. Thus, there is some background material in analysis and in point set topology in Euclidean spaces presented in chapters 6 and 7. The definition of a surface is detailed in chapter eight. Chapters 9 and 10 are devoted to the theory of the non-intrinsic geometry of a surface. This includes an introduction to tensor methods and selected topics in the global geometry of surfaces. The last chapter of the outline presents the basic theory of the intrinsic geometry of surfaces in three-dimensional Euclidean space.
Exercises are primarily in the form of proofs, and there are plenty of worked examples. Since the examples are kept to no more than three dimensions, the outline contains plenty of good instructive diagrams that illustrate key concepts. This Schaum's outline has quite a bit of instruction in it past the bare required minimum, but you might still want a good primary textbook. My personal favorite is Pressley's "Elementary Differential Geometry". Overall I find this to be a very good outline and source of solved problems on the subject and I highly recommend it.

Differential Geometry - A Schaum's Outline Series.......2000-06-25

As with all of the Schaum's Outline Series, this book is particularly useful if the readers intent is to gain a working knowledge of the subject. The subject of Differential Geometry is no exception. Dr. Lipschultz has done an excellent job of communicating the essential aspects of differential geometry to the reader. The book assumes a fairly low level of mathematical ability having calculus as the primary prerequisite. From this humble beginning, Dr. Lipschultz takes the reader through the necessary discussions of vector functions, curvature, fundamental forms, and tensor analysis. Given the theoretical nature of the subject, Dr. Lipschultz has included most of the theorems and associated proofs necessary for a general understanding of the subject. However, this book is not a substitute for a serious study of differential geometry. In addition most of the problems are limited to two dimensional surfaces and this reader would have enjoyed a more adventurous investigation of higher dimensional spaces. Like all Schaum's series, the text is chock full of problems and their solution. I recommend this book for anyone interested in quickly gaining a working knowledge of the subject.

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.

Average customer rating:

Clear, Concise, and Useful
The older editions are better
Good for reference, not so good by itself
Great book for scientists!
This book is awful

Introduction to Vector Analysis
Harry F. Davis , and Arthur David Snider
Manufacturer: William C Brown Pub
ProductGroup: Book
Binding: Hardcover

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ASIN: 0697160998

Customer Reviews:

Clear, Concise, and Useful.......2004-10-10

This text presents each subject in a very clear manner. Every subject is developed in concise proofs that are easy to remember and satisfying to those who require mathematical proofs to understand the derivation of the subjects but are not interested in long-winded theory. After each section's quick and dirty derivation, the authors provide a small yet effective selection of challenging questions to be able to gain confidence in the subject. The style of the book is also refreshing in this age of heavy books with flashy photos and wasted space. This book includes 408 pages full of useful mathematics and vector diagrams but nothing else; the book is very light and small. This is a classic.

The older editions are better.......2003-05-01

I have the third edition and the latest edition of this book. In my opinion, the later editions have been dumbed down considerably. In addition to developing the basics of vector analysis, the older editions included splendid discussions of curvilinear coordinates, tensor analysis and touched on differential forms (the wedge product being introduced). While the latest edition features appendices covering specific applications such as Maxwells and Navier-Stokes equations, the explanations are far too brief to be of much use. I suggest that interested parties attempt to get used older editions whose content were presumably under the control of Davis (not Snider) being much better written and probably less expensive. The older edition had few typos with very useful and entertaining problem sets. A better alternative book might be "Vectors and Tensors in Engineering and Physics" by Donald A. Danielson in paperback.

Good for reference, not so good by itself.......2002-06-04

This book was used in my vector calculus class at UCSD. I think if I was in one of my upper division engineering classes it would be great to use as a reference to help me figure out problems. However, as a math book alone, this was not too helpful. Many of the explanations lack clarity and are from a mathmatician's point of view (in other words, very difficult for lower division students who are not math majors to understand). Also, a lot of the problems are practically impossible. The only reason I did alright in this class was because I had a great teacher. I would recommend this book for people who are in science or engineering classes and need a superficial introduction to vector calculus, but NOT for math classes that go into deep analysis of vectors.

Great book for scientists!.......2001-10-15

This book provides a great reference for people studying the physical sciences. I'm a Ph.D. student in Physical Chemistry and have been using it extensively to help out with some other courses. It might not be as good for someone with a more puritanical or abstract interest, e.g. a mathematician, but it's great for anyone that needs a handy reference that explains the rudiments of vector analysis.

This book is awful.......2001-06-09

This has to be one of the worst math books on the market. While it starts off OK (with the review of vector addition and algebra), the treatment of later material is terrible. The authors provide skimpy and disorganized explanations with insanely difficult problems. Get a good teacher for this class (or a better book) or you'll be in for a rough ride.

Average customer rating:

Effective AC Drive Control

Vector Control of AC Drives
Ion Boldea , and Syed A. Nasar
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849344085

Book Description

Alternating current (AC) induction and synchronous machines are frequently used in variable speed drives with applications ranging from computer peripherals, robotics, and machine tools to railway traction, ship propulsion, and rolling mills. The notable impact of vector control of AC drives on most traditional and new technologies, the multitude of practical configurations proposed, and the absence of books treating this subject as a whole with a unified approach were the driving forces behind the creation of this book. Vector Control of AC Drives examines the remarkable progress achieved worldwide in vector control from its introduction in 1969 to the current technology. The book unifies the treatment of vector control of induction and synchronous motor drives using the concepts of general flux orientation and the feed-forward (indirect) and feedback (direct) voltage and current vector control. The concept of torque vector control is also introduced and applied to all AC motors. AC models for drive applications developed in complex variables (space phasors), both for induction and synchronous motors, are used throughout the book. Numerous practical implementations of vector control are described in considerable detail, followed by representative digital simulations and test results taken from the recent literature. Vector Control of AC Drives will be a welcome addition to the reference collections of electrical and mechanical engineers involved with machine and system design.

Customer Reviews:

Effective AC Drive Control.......2001-01-23

During the last few years the field of controlled electrical drives has undergone rapid expansion due mainly to the advantages of semiconductors in both power and signal electronics and culminating in micro-electronic microprocessors and DSPs. These technological improvements have enabled the development of really effective AC drive control with ever lower power dissipation hardware and ever more accurate control structures. The electrical drive controls become more accurate in the sense that not only are the DC current and voltage controlled but also the three phase currents and voltages are managed by so-called VECTOR CONTOL. It is a great book and I would recommend it to anyone who want to be an expert in the field of AC Drives Control.

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.

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