5 comments about Introductory Real Analysis.

1. I speak Russian and read it so-so - this is not the original work of Kolmogorov and Fomin but is a "freely" translated version. Unfortunately, "free" is not always "correct".



2. The advantages of this text have been pointed out by other readers, so I will attempt to exhibit the problems of this book.
   
   There are a lot of mistakes. And by 'a lot', I mean that the careful reader should be able to find at least 5 mathematical mistakes in each chapter. I used this text mainly as a supplement to a fairly advanced analysis course, and we'd often have problems from it used in our problem sets. At first, it appeared as if this were a very well-written text, but once we started with our problem sets, there were at least 2 e-mails sent out per week addressing a concern a student had pointed out. After a while, students stopped e-mailing the professor with their concerns, instead just assuming that they were correct whenever they spotted something weird.
   
   Let's take an example:
   
   Problem 1, pg. 137: Let M be the set of all points x = (x1, x2, ..., xn, ...) in l2 satisfying the condition \sum^{\infty}_{n=1} (n^2) (x_n)^2 \le 1. Prove that M is a convex set, but not a convex body.
   
   The problem with this is that M IS easily a convex body, precisely because x = (0,0,...) is in M.
   
   There are many more big mistakes and little mistakes throughout the exercises, oftentimes destroying the entire POINT of the problem. Take, for example, Problem 1 of pg. 76: Let A be a mapping of a metric space R into itself. Prove that the condition p(Ax,Ay) < p(x,y) (x\ne y) is insufficient for the existence of a fixed point of A.
   
   Now, a counterexample here can be easily produced, even by the most elementary reader. But the exercise quickly becomes worthwhile if we make R complete. It's the little things that count in mathematics, and the small errors like these are clearly detrimental to the student.
   
   But the errors in the text aren't limited to exercises. I was reading independently at the front of the book to get some info on Zorn's Lemma and ordinal numbers, and as I read, I found the following definition:
   
   Let M1 and M2 be two ordered sets of type 01 and 02, respectively. Then we can introduce an ordering in the union M1 U M2 of the two sets by assuming that
   
   1) a and b have the same ordering as in M1 if a,b are in M1
   2) a and b have the same ordering as in M2 if a,b are in M2
   3) a < b if a in M1, b in M2
   
   The set M1 U M2 ordered in this way is called the ordered sum of M1 and M2, denoted by M1 + M2.
   
   There is a clear problem with this definition pointed out here: http://www.physicsforums.com/showthread.php?t=200985. How is the student expected to learn such important material when even the definitions have loopholes? By the end of our experience with this book, our professor was giving out exercises to correct Kolmogorov/Fomin's incorrect definitions.
   
   Note also that Silverman uses very weird words. For example, 'countably compact' is used instead of 'sequentially compact'.



3. I didn't like this book at first because it wasn't what I expected. I think the word "introductory" should be removed from the title. It's actually not an introductory book. I would recommend this book for graduate studies. Most real analysis courses at the graduate level focus on the measure theory and integration. However, I appreciate this book more now.



4. This is not the original work. Just like Emily Dickinson's poems, sometimes you get an "edited" version of a beautiful mathematical work. I am SO sorry that I bought this book. Besides the problem with messing with a finished work, there are serious errors in proofs all over the book.
   
   Get Elements of the Theory of Functions and Functional Analysis instead (also by Dover).



5. This is a very good intermediate math book. I used it to write my undergraduate monograph and it actually helped a lot (I'm an economics student). However, it is difficult to understand without the help of other books. In fact, if you want to use this book I recommend to get also: "Topology" by Munkres and "The Way of Analysis" by Robert Strichatz. They all make a very useful math kit and if you are thinking in a Ph.D. in economics they can help you a lot if you read them (not all, buy selected chapters) before you start the math review at the begining of the Ph.D. program.

5 comments about Elementary Analysis: The Theory of Calculus.

1. I found steven.R.Lay's book, analysis with an intro to proof to be a really good book. haven't felt like refering to this one at all



2. I love this book. I used it as an undergrad. In grad school I used it all the time to review simple proofs that I had forgot with too much topology. In addition, I used it to teach an advance high school student over the summer. However, there are a few proofs that I do not like. In addition, he makes some theorems that do not always hold with their proofs.
   
   However, this is the best book I found for an undergrad that wants to explore analysis without having to tear into topology right away



3. What an incredible math book and a great value. I picked this up to fill in some prerequisite knowledge and skill before starting a full on Real Analysis course in my new graduate program. I was stunned by how well the information is laid out and what care the author uses in guiding you through the process of proofs and other information. Simply said, the author is very cognizant of his own writing in addition to the material he is delivering. The examples are quite good and the explanations always make sense. There are FAR fewer places in this book that I have found myself not following the logic or stumbling on what the author is trying to point out or prove. Plus I am still shocked how inexpensive it is ...



4. This book cuts down the material to bare minimum. Skips lots of proof definitions, you may get confused when doing the HW. Three examples is not enough to help you understand a chapter.
   
   Examples in this book are theoretical. Symbols and Greek letters make the material more confusing.
   
   I find Steven Lay's book give definition of proof, and explains how to use it.
   
   Sellers online rate this book high so they can sell the book. Read the book for yourself before buying it, it may save you a lot of money.



5. Well written book. Tough construction is a real plus when you are dragging it around with you. The 12th edition has had the type reset so that it is easier to read.

5 comments about Schaum's Outline of Vector Analysis.

1. 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.



2. 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.



3. 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!



4. The book offers a good introduction to vector analysis for the undergraduate student. Quite simple, lot of practical examples. It is a good supplement to a more theoretical textbook. Also the price is fine.



5. Different schools of thought have different checks and balanaces. These checks and balances take the forms of rules and norms with their own judgements of right and wrong. Probably the human mind can only take so many rules and norms at any one time; each school of thought somehow subconsciously understands this.
   
   Still, time and the wisdom that comes with it should make what I am saying obvious to all. And perhaps my point is indeed obvious to Prof. Spiegel. If so, he should note in his book somehow. Either in the discussion or in the problems.
   
   My main point and problem with this presentation on Vector Analysis is that the definition of vector is graphically inadequate. Pictorally speaking, position, separation, and displacement vectors have features that many other vectors don't. Such vectors must be treated somewhat differently than velocity, acceleration, and force vectors. Now velocity and acceleration vectors may have different features and need to be treated differently, but my point has already been made in identifying the existence of unique features of location vectors.
   
   Murray R. Spiegel has proven himself again and again in book after book as a great master of many topics as mathematical subjects. From Complex Variables to Vector Analysis.
   
   Still, he makes no mention that mathematicians take great liberties when they define concepts. And vector as "a quantity with magnitude and direction" or, worse, as "a vertical column or horizontal row of numbers"
   are exact examples of such liberties and their problematic consequences.
   
   Bottom Line: Great presentation of the symbols and the symbolic logic of vectors. Conceptually, Graphically, and Physically, speaking the analysis (presentation) is quite weak and quite misleading.

5 comments about Elementary Real and Complex Analysis (Dover Books on Mathematics).

1. I purchased this book as a reference book for my first analysis course. It is very well written, and easy to follow. Dr. Shilov has a very nice way of organizing this text: He puts all the definitions at the beginning of the chapter and the subsequent sections are results of those definitions. It makes for a very quick reference. His presentation of the included proofs is also very nice. There were several occasions I found myself thumbing through it for a second perspecitve.

   As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology. He does keep in mind this is intended for undergrads and first year grads though.

   Oh, another nice feature is the price! I'd recommend this book to any math enthusiast as a reference, or to someone going through an early analysis course.




2. As Shilov write in the introduction "I have tried to accomodate the interests of larger population of those concerned with mathematics" and at that he seems to do. However, the book does require some mathematical background as he appears to omit defining a few things. I believe the book would be ideal for those who want a handy reference, or an easier book when struggling with an analysis course.

   However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin.




3. This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
   Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
   Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
   There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.



4. I purchased this book to study some complex analysis. Being a physicist I would like to brush up on this. The book was completely different to what I expected.
   
   Some applications would have been nice, but this text is pure maths. The book is well written, easy to follow and concise. I ended up reading it and gained and appreciation for the thorough consideration of elementary real and complex numbers.
   
   Shilov is thorough and avoids making leaps and assertions. This would make the book readable to lower undergraduates. However the significance of some things is not explained, or explained in a very dry manner so people might miss this.
   
   I highly recommend this book if you are interested in real and complex analysis from a pure mathematics perspective.



5. To me, the best chapters of this book are that about series and integrals. The text is plenty of interesting notions, like that of direction that is related with the notion of limit. I appreciated very much the study that Shilov does about parameter-dependent proper and improper integrals. The topological notions are placed in one intuitive manner. Without doubt, this is one very good and clear exposition about the subject. However, I think that the problems are not easy. Also sometimes Shilov states the theorems with additional conditions that are not useful. For example, this happens usually in the chapter about derivatives because the definition of derivative given by Shilov imposes that any function with derivative in the interval of the domain has continuous derivative in the interior points of its domain. However, Shilov charges some theorems with the extra condition of continuous derivative.
   When the Taylor's formula is presented in page 252 - Theorem 8.22, it is stated that the error of the approximation is computed in some interior point of the interval, what is not completely correct. For example, take the second degree Taylor's approximation around x = 0 of the function x raised to the third power, and you will see that in this case the error is computed on one extreme point of the interval.
   Also the proof of the theorem 10.49b (page 415) has logical problems of the kind that may arise during the translation.
   However, these remarks are small questions without consequences for the course of the exposition.

5 comments about Calculus: Early Transcendental Functions.

1. I love this calculus book. I transfered colleges once and ended up using Larson's at one and Stewart's at the other. In addition, I had to TA a course with Stewart's. I have to say that I think Larson's is more for geared to the Engineers and Science than Stewart's. However, I still think Larson's book works so much better on all majors at introducing Calculus to students that are new to college and have little background in theory. This is not a theory book. However, if the student is in the math field he will have plenty of time in his analysis series to learn all the theory.
   The one part that this book and Stewart's book lack is where theory is needed more, Vector Calculus. For this part, I always recommend (and am trying to get the department to make standard) is Vector Calculus by Marsden.



2. This book tries so hard to teach the material that it fails. It is not helpful and does not explain concepts very well.



3. it was a great decision to buy from this seller...it came within a few days and it was in GREAT shape...just as they descibed. i would definitely buy from this seller again.



4. This book was in like new cond. Seller was quick to e-mail confirmation of shipment.It arrived within a week of purchasing.



5. I have not received this textbook. It's been over a month now and the owner of the book doesn't respond. I didn't think I would have to submit a claim about this but I guess it happens and some people do it. I am unhappy with this serivice and hope it all resolves in the end.

4 comments about Advanced Calculus Demystified.

1. It's been a long time since I'd learned Calculus in H.S. and a bit in College -- when I needed a quick review, to do a couple of problems that cropped up at work, I stumbled across this book, and boy am I glad of that. Everything is explained clearly -- really clearly -- and sometimes with a touch of humor thrown in that makes the book so much more enjoyable to read.
   
   It was organized so well that I could immediately zoom in on just what I needed, and once I got to the right chapter, the info was well organized, well written, enabling me to review, get my answers, and apply it to the things I needed.
   
   Skimming other Calculus books in the bookstore, they were either too didactic, doing endless proofs (which I didn't really need...) or they were written so poorly that they didn't really help much. (Best way to compare books -- choose one topic, read about it in several books, see which book explains it best... this one did!) It stays true to the title "Demystified".
   
   If you're a bit beyond the intro level, such as in college, taking a math course or a few, this would be a great way to review before an exam, or a great way to get "another viewpoint" that might help you figure out what you're not getting from your dry, dessicated textbook. You should know that this book covers more advanced material than the very simple stuff, but frankly, it handles it so well that I didn't need to review the simple stuff to understand what I needed to. Imagine that -- a math book so clear that you can pretty much pick it up anywhere and just start reading! If you're a student taking "calculus I" in high school, much of this book will be beyond what you want, but you'll be able to understand it.
   
   What's more, I'd recommend it to anyone who is in a field who might stumble across a Calculus idea or problem, such as computer geeks (such as myself), or engineering professionals, etc. Pick it up & if you can't read it now, put it on the shelf -- you'll be glad it's there when the need arises. An excellent book, that "hits" just the right level of review and learning so you can really understand it, and use it.



2. This book deserves 10 stars. It is simply the clearest and easiest to understand math book on a difficult topic that I've ever seen. Out of the over 1300 things that I have reviewed on Amazon, I would give this book the highest rating. I completely agree with Darkman in his earlier review, that the book is so good that you can just pick up anywhere and understand what is being said. I've seen a lot of math books over the years that purported to be what this one is, and were not, most of them not by any stretch of the imagination. As he says, most just cover proofs, which isn't that useful for most people, or try to teach the applied practical side but just make it too difficult.
   
   The problem is that most people who are good at math, good enough to get a Ph.D. and write a book like this, are so good at it that they just don't understand the average college student who doesn't. For some amazing reason, Bachman does, and if all math teachers were like him, math would actually be, if not a popular subject, at least far more than it is now. If you are considering this book, just pick it up and start reading anywhere and you'll see what we mean. It's truly an amazing feat of writing and math teaching and the book is worth 10 times the actual purchase price, in my opinion, in all the time it will save you and all the hassle you'll avoid trying to understand difficult concepts.
   
   Not only that, but the way Bachman presents the subject, despite the overall technical level, he is still able to show you the beauty and elegance of the language of advanced calculus despite that.
   
   Finally, the worked problems are well chosen and very clearly solved and illustrated. I just can't say enough good about this book. I've looked for a math book this clear for advanced calculus and other advanced math topics for almost 35 years. I'm so excited by this book that words don't really do justice, and at my age there's not a whole lot that I get really excited about anymore. They should inaugurate a new Nobel Prize for teaching excellence and give the first one to Bachman so he can retire from day to day college teaching and continue to write books like this.



3. When you're studying Advanced Calculus on your own you need three things (apart from work and the right mindset, of course:)
   -A good intuition about the nuts and bolts of the problems.
   -Many, many exercises.
   -A source for formalism and other theorems that are important.
   
   David Bachman's book is amazing in that it is the first book i know that can give you the first point and a bit of the second. But! Do not expect to learn Adv. Calculus using this book alone.
   
   Firstly there simply are not enough exercises. Secondly, it has some important omissions (there is nothing about the Implicit Function and Envelope Theorems, which are essential in Differential Calculus).
   
   But if you arm yourself with this wonderful little book (They DO say it's a companion for more advanced texts in the cover), with a good source of solved problems and any regular Calculus textbook and work them over you should be in good shape.



4. I took a course in vector calculus and linear algebra 15 years ago but was forced to drop out of college and have forgotten most of the material. I am preparing to go back to college and complete a degree, so I want to get caught up. This is not a bad book as a supplement to a good text, but it's not a good text book on its own. I thought I'd be able to use this by itself, but I ended up using my calculus textbook to actually learn the subject matter, then I used this text to fill in the gaps and review.

5 comments about Schaum's Outline of Calculus (Fourth Edition).

1. not that great, if you have a good text, you'll notice that the examples are pretty much the same



2. In order to take an advanced statistics course (since I have been out of college awhile) I have to take a calculus test. They gave me a sample of 60 questions from prior years and recomended a text that cost $180!!!
   
   Well for 1/15 of the price of the expensive text, I can get about 55 out of 60 questions answered through this one. The ones that are not covered in this book pertain to complex integrations - I'll buy the Schaum's Advanced Calc text and get my answers and still have tons of money left over.
   
   *** Another thing is that the first few chapters are an excellent review of pre-calc, something I did not think I would need but it turns out to be more useful than I thought. ****
   
   The covering of some topics, like LaHopital's rule is better than most texts.
   
   I have not encountered typos yet - when I have that that I did - once I plunge into it more - turns out he is right and I was mistaken.
   
   ****Having numberous worked out problems and problems with at least the solutions to check yourself is GREAT FOR SELF STUDY ****



3. This book does provide coverage of all major material in traditional calculus,however the manner in which the material is presented is similar to that of a condensed textbook, which is neither entertaining nor completely clear. If you want a quick study guide then this is the book for you,provided you understand most information you read in a textbook. All in all, this book is alright, but I wouldn't depend solely on it.



4. I bought this book to supplement my class textbook when I was having trouble in Calculus I. I chose this book over the many other supplements available because I knew I could carry forward into Calculus II and Multivariable Calculus.
   As mentioned in many other reviews, this book provides plenty of practice problems, so if you're having an issue in one particular area in class or in the class's textbook, this is a good place to go to really thoroughly understand it. They provide a decent number of examples and solutions. Within each chapter are explanations of the lesson, followed by example problems with step-by-step solutions, and finally "Supplementary Problems" for you to solve on your own (though there are no answers in the back for you to check your work). It's also got some really good lists of trig formulas, geometric formulas, common integrals, and common derivitives.
   The only thing I dislike about the book is that the explanations are rather poor compared to a textbook, but it's hardly surprising seeing as how this is an outline and that it covers topics from the beginning of Calc I all the way through differential equations of first and second order in under 600 pages.
   I would totally recommend this book for the student looking to supplement a confusing textbook, or looking to brush up on concepts that have gotten a little rusty.



5. This book is great for when you're beginning Calculus, but it doesn't give intense hard problems for it. Great study guide to review the basics but isn't the hardcore stuff.

5 comments about A Mathematician's Apology (Canto).

1. As Hardy himself makes clear in the beginning, he would never have written such a book if his mathematical powers had not failed him in old age. I do feel like this book is more an apology for not being a mathematician anymore than for having been one. As for all true loves, the time for judging and summings things up comes only when the joyful days of passion are over. I was hoping this book would give me an inspired first person view of what is higher mathematics and what is like to be a real mathematician. I found that it is not a good book for that, it doesn' t even try it. What it accomplishes instead is giving a precise, objective, cruel, marhematically clear picture of the drive, the ambition, the passion for excellence in any activity, be it a sport or a science that makes the life of the ones who dedicate their life to it so more pure and meaningful. It also poses some tough, fundamental questions regarding how much of your life one can dedicate to one single "abstract" passion without having to go trough some really bitter times and regrets in old age. My personal answer is that what really counts, in the end, is how much you loved and, what was sorely missing in Hardy's life, how much you express that love. But for some people, gifted and cursed at the same time, that is still not enough.



2. One of the most scholarly books that has been written in the 20th century, G.H. Hardy's thrilling memoir tells a story that other people are too afraid to discuss. Hardy's depressing transition from mathematical genius to near vegetable is a telling example of the archtypical fear of cerebral atrophy that resides among even the most resilient and foolhardy among us. This concise "novel" reads fluidly and especailly so for when written by a mathematician and serves to enlighten the world of the multi-talented nature of a world class mathematician. All in all this book is a rare find and should be read by people of all ages: whether a young aspiring mathematician or an old decrepit intellectual.



3. This short book has long been one of my favorites. Hardy's philosophical musings may depress some but they ring so very true. Hardy is quite honest about life, art, mathematics, and his failing abilities. For example, his statement, that a very small minority of us are really good at what we do may sound depressing today. But the fact is true.
   
   I can recall when words such as super, excellent, awesome etc. were used judiciously and very rarely to describe truly significant achievement. Today, doing one's job, albeit poorly, is described as excellent.
   
   What I most like about Hardy's book is it's honesty and respect for the reader. A suggestion. Read the book proper BEFORE wading through C.P. Snow's forward. After about the second read tackle the forward.
   
   A must have.



4. Hardy was a giant among early 20th century mathematicians. It is difficult to overstate his importance. He was one of the first to show that mathematics is as much art as science without having to have interpretation (such as Dunham's "Journey Through Genius...").
   
   This is what makes this book so poignant. Hardy realizes that he no longer is Hardy. In today's mathematics world that may not have been the case given the immediate communications possible between humans which may have kept him going. However, it may have been that he was suffering from the onset of dementia or Alzheimer's - it is difficult to tell given his admissions of not being up to the task - regardless, this book is overwhelmingly sad.
   
   Anyone who cares about math should read this and thank Hardy for his contributions - plus they should have a copy of "A Course in Pure Mathematics".



5. I learned about this book while reading another book, "Prime Obsession" and it awoke my curiosity mainly for two reasons: because it was a interesting subject, an apology for being a mathematician, trying to explain the purpose and usufulness of mathematics, and because I wanted to know more about Hardy's life, since I knew a few things about the nice story of this mathematician and Ramanujan. This is a brief book, there is a foreword that serve as a brief biography before enjoying Hardy thoughts, which by the way really grab your attention, even you learn a few lessons of simple mathematics proofs that try to show the beauty of it. I consider this book valuable for everyone.

5 comments about Schaum's Mathematical Handbook of Formulas and Tables.

1. tables are concise with out missing any important integrals. the table is my constant companion for undergrad physics and mathematics.



2. It is a good quick reference to getting formulas for math problems.



3. A very useful book that gathers all the mathmatical formals 'as the title states. As an Engineering Student it is very helpful to have everything in one text instead of getting your old books and digging through them to find them.



4. This book has everything in it as far as formulas. If you are looking for examples, this is not the book for you. I had some difficulty remembering Integration by Parts for my current Grad class. This book helped out. It also helps out for all those pesty integrals and derivatives as well. I've been using this book for 2 months in my classes. Although I don't always use it, I never leave home without it.
   
   Also covers Taylor and Fourier Series, Laplace Transforms, Statistics, and other stuff as an engineer I've never had to learn and never plan to. ;)



5. This handbook is a must have for any junior level or higher engineering major or any major that deals with advanced mathematics. It contains detailed and easy to understand charts and tables ranging from College Algebra and Trigonometry to Advanced Calculus and Differential Equations. It is also a must have reference book to anyone needing to access to advanced mathematics formulas.

5 comments about Calculus of Variations.

1. Ok, not everyone needs to (or wants to) know calculus of variations. But if you are among the ones who, this is a great book to get started with (assuming you are in grad school and have a decent handle on calculus and some basis in dealing with differential equations). The text is clear and concise, and the financial investment is minimal. A good buy!



2. This is a classic text and I would recommend it to graduate students and mathematicians who need a review of the subject. Great for us physicists as well.



3. As a physicist I want to find a book to refresh my memory on theoretical mechanics. I came across this one, and after reading its first 4 chapters in continuation, I kow I don't need any other book. What a treat! Written by a past master, the book costs you next to nothing; yet as it's written by sure hand, it hasn't slightest pretention, just plain and insightful, natural and smoth flow, leads you almost effortlessly fowward. Even though I learned the subject before, I don't know of or even imagine a better exposition. Wow, I started to love Russian mathematicians.



4. This book is a "must have" for those wanting to study topics in functional analysis.



5. I like this book, certainly what I have read of it. I'm now digging around near page 75, and it struck me that for the first time I really "get it" - In particular, this was about the use of the Legendre transform. The authors start with a very gentle introduction of it, and then, while things become more abstract, the text never jumps too far and never leaves the reader too much in puzzling. It's ought to be studied though, and it's not "easy".