5 comments about Calculus and Analytic Geometry (9th Edition).

1. This is a good, thorough, well-written text. There are no errors that I have found. We used it for a few years for Freshman college calculus.



2. I used the 5th edition.
   This is a standard textbook. It is a bit more detailed than the competition (because it was written by mathematicians, I guess).
   Calculus books all cover standard topics. Where they differ is in the quality of the exposition and the bag of tricks they teach. You want a book with both, and this might be it.
   It's on the recommended reading list of the Mathematical Association of America as the first choice - as in "***" - for introductory Calculus (i.e., not "advanced") (see: http://www.maa.org/BLL/calculus.htm).



3. The approach to the self study of calculus that I've adopted involves working through every problem in each section. This text is excellent for that technique. The authors present the material in sections that usually build upon on another and can be read in about thirty to forty five minutes while working through the examples. The writing is for the most part clear and easy to follow. Every now and then a section seems disjointed. The progress through differential and integral calculus of functions of a single varible (Chapters 1-7) is very thorough and smooth. The approach is both intuitive and mildly rigorous so that the student is not left thinking that calculus is not without rigor. The emphasis is on applications hence engineering and applied physics students will benefit most from this text. The introduction of transcendental functions is divided into two parts with most material in chapter six. The best aspect of this text is the problem set found at the end of each section. The authors have worked hard to build into the problems the material put forward in the text of the section. The problems are designed to reinforce both calculations as well as to provide stimulation to deeper thought (Theory and Examples section). Problems are divided into sets of problems reflecting the divisions in the section. These problems start as computational exercises and progress into applications and thought problems. Every concept can be looked at from different perspectives and the problems are designed to bring out this understanding of the ideas that are presented in the text. The emphasis is of course on the board applications of the concept. In addition the problems vary in the type of function so that there is a constant review of the techniques of approaches to solving the functions.
   An average classroom problem set for a section would be fifteen to twenty problems that would take about an hour and a half for the average student. To work all the problems in a section (range 40-100) takes about six to eight hours.
   I bought this text four years ago and a new edition has since been published. I am very satisfied with both the content and approach. I can pick up most texts on the subject and find that my working knowledge as learned from Thomas and Finney is more than adequate to follow the study.



4. To easily make myself understood in the most important of technical and scientific circles, I have so far found two scenarios that work. One is first thinking through a concept on an emotional, gut, intuitive level (body as vector, particle, motion, mass, or what not) and then just sharing with the APPROPRIATE, well-behaved AUDIENCE. The other approach is to prepare a massive amount of simple, yet accurate terminology and then make brief, accurate statements to the APPROPRIATE, well-behaved AUDIENCE. For either situation where such scientific explanation is needed, this book has proven itself again and again.
   
   Whether I'm imagining myself traveling along a three dimensional surface or learning exactly how the words "rise" and "run" can be used in relation to the concept of a derivative, this book makes it easy to look up concepts by index or table of contents and then review, refresh, and better understand the terminology and symbols.
   
   Of all the required course materials purchased during my 6 year pursuit of a bachelor's and master's, out of the 5-6 thousand dollars spent, this book has proven itself the most worthy, above all others. In comparison, the rest of the required course materials come off as part of some sort elaborate book-store, department, publisher money-making kick-back scheme. With only a few exceptions.
   
   Bottom Line: For learning about functions of one or more variables including calculus vector analysis, this is THE one-stop shopping experience. The selection and presentation topics are its best features. (If a little more depth in problem solving is truly needed, just pick up one of the great Schuam's like the one on Vector Analysis.)



5. Words cannot explain how good this book is. This must be one of the best books ever written. This is the book that helped me understand the MEANING OF CALCULUS to the point where I can apply it anywhere. I came across this book 8 years ago and to be honest without this book, I would not have been able to understand all the EE theory that I learned afterwards. The chapters on multivariable calculus helped me understand undergrad EM.
   So I conclude "A POWERFUL TOOL BOOK FOR ENGINEERS / PHYSICISTS"

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 Introduction to Analysis.

1. I don't know about you, but I'm not a fan of large books. His presentation is terse, and very readable. I bought this for self study and was initially concerned with the lack of solutions. But as I continued my studies I actally found it aided learning, I stuck through problems that I would have normally just looked up the solutions for. If you want to teach yourself, its length and writing style is for you. My only complaint is the lack complex analysis, he does however present you with some of the basic results as exercises.



2. This is an excellent book. I'm a mechanical engineer and i found this book very useful for all kind of engineers. Don't hesitate, just buy it. If you want more complex books, buy the Apostol's mathematical analysis, but only if you have all the necesary knowledge as a background, because is very difficult to asimilate.



3. Introduction to Analysis by Rosenlicht is a lovely introduction to advanced undergraduate, and beginning graduate mathematical analysis.
   *Topics covered*: The fundamentals of analysis, including measure theory, Fourier series, Fourier integrals, function spaces, including Hilbert spaces.
   Book Comparison:
   Walter Rudin's "Real and Complex Analysis is a classic graduate level text book. The level is somewhere between two popular books by W. Rudin: Principles of Math Analysis ("Baby-Rudin") and "Real and Complex."
   Here is a brief comparison: Rosenlicht vs Rudin: Rudin's 'Real and Complex' has become an institution, but conventional wisdom will have it that Rosenlicht is a lot gentler on students, and easier to get started with; more warm-up exercises: Rosenlicht stresses motivation a bit more, the exercises are easier, and finally Rosenlicht gets to touch upon a few applications; fashionable these days. Rudin's book is more advanced, goes more in depth, and it has stood the test of time.
   The material in Rosenlicht is somewhat flexible, and it can be tailored to a variety of introductory analysis courses, from function theory to integration, to functional analysis. Review by Palle Jorgensen, August 2007.



4. For $[...] you will get an unbelievably clear explanation of metric spaces, continuous functions, differentiation and Riemann integration. This text is a tremendous accompaniment to Baby Rudin (this book along with Apostol's Mathematical Analysis (buy it used) will take you over the hump in a real analysis class using Rudin). Also, Rosenlicht taught at a time when real analysis was presented using diagrams - a pedagogical tool that has fallen out of some favor. While not numerous, the diagrams presented are very helpful in describing the concept (e.g., connectivity, the nested set property...). I found these to be invaluable. The writing is clear and the proofs are straightforward. The extremely useful information in this book will set you back around 6 cents per page - do the math on some other texts and you will see what a bargain this book is.



5. This is a good book in that it synopsizes the things that you would need for some type of Economics study (the point of my reading this book was to learn enough math to be able to intelligently read some economic articles that I had seen before). It was not quite enough math, but it did show you what you should know by the time you get to the level of needing analysis.
   
   There are no problems/ solutions in this book, and so if you wanted to test your skills/ knowledge, then this is not the book for you.
   Take it for what it is: A reference, but not a proper math book.

5 comments about An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements.

1. This book is written for the introductory physics student, but it helped me get a good understanding of experimental error in my chemistry lab. The author presents error analysis using simple scenerios and without going too deep into calculus and statistics.



2. This book is boring and basically is just another statistics book. if you have some sick twwisted interest in estimating error, buy this book otherwise find something more interesting. if you have to use this for a class, Im sorry, i feel your pain.



3. This book is perfect for somebody who was never properly introduced to formal probability and statistics. The language is easy to understand and each chapter not only explains the "what," but makes sure you understand the "why" as well. Also introduces you to more complicated aspects of the subject--binomial & poisson distributions, chi-squared analysis, etc.



4. This book does an excellent job of starting from the basics and then building on them at a comfortable pace until the reader has been taken to the more advanced and useful points of error analysis. This book is clearly written, with appropriate and helpful examples throughout. The practice problems at the end of the chapters are relevant and straightforward, further aiding the learning process. The author not only understands the subject of error analysis inside and out, he also knows the right way to teach it. Though the book approaches error analysis from a physics point of view, I found it very applicable to all of my scientific coursework, including biochemistry and (especially) analytical chemistry.



5. If you have ever had to read or study a book on probability and find yourself saying, "what did he say?" and find yourself rereading the page a second or third time, buy this book. it is well written and understandable. it covers everything i need to know about error analysis and probability, and probably everything you will need to know too.

5 comments about Calculus With Analytic Geometry.

1. It definitly helps one who want to master Calculus or join the Calculus competiton of any kinds.

   It better than "Calculus With Analytic Geometry, Seventh Edition" for it give you some useful appendixs and very simplify than it. It does not includ differential equation for as the author said that it is not useful when there is a full course on differential equation!!!




2. Another MIT student here... unfortunately not all calc. classes at MIT has stopped using this book. As a result the majority of our class is hopelessly lost... and this is at MIT!!!... now that's a testament to how bad the book is... Things aren't explained well, the examples have nothing to do with the actual problems, and without the "space wasting" graphics that so many other books have it's difficult to visualize what Simmons is talking about, and despite popular opinion visualizing what you are doing is very important to calculus. I'm relying on my HS calc book to get me through the course.



3. This book is perfect if you are looking for a book that has a nice balance between theory and application. Theory is presented on an as-needed basis and there is more in the appendix if the reader is so inclined. This was an excellent book for me my freshman year and it has been a good reference for me throughout my math career. It is a nice stepping stone on the way to spivak.



4. I have a big, dirty secret: I needed three tries to get through calculus. Needless to say, I went through (or at least started) three calculus books. The third of these was Simmons' first edition of the current volume. Dr. Simmons takes a historical approach to the material, following discovery after discovery. While today we define the derivative in terms of the limit, this definition (and the delta-epsilon proof machinery beneath the limit concept) came after the geometric notion of the tangent of a curve. I found it enormously helpful to know where I was going before I started. And why not? The great mathematicians that built the rigorous foundations beneath the calculus all knew where they had to end up.
   
   One other topic that Dr. Simmons enjoys is arithmetic series. This topic unfolded like a flower during its presentation. As I moved into computer science, this provided valuable background to some of the iterative methods of calculation I was exposed to.
   
   I might have a different perspective, though; George Simmons was my Calc 2 prof :-)



5. This book virtually made me love mathemathics. It's a book with an unique set of features in it's appendix, and the writing style of the author is almost like you are actually reading a great novel about calculus.

5 comments about Proofs from THE BOOK.

1. We used it for an undergraduate statistics seminar series; and that was largely a success. PFTB contains many of the most elegant proofs I have ever seen. Reading through it is, by itself, an enjoyable journey through some aspects of many branches of mathematics. A few of its chapters may not address the average undergraduate math population quite well, due to its depth of reasoning and assumption of prior knowledge in Abstract Algebra and Geometry; but those who reads it are likely to be more advanced anyway. In general, an excellent book.



2. One of the most important mathematicians in the last quarter of a century was, arguably, Paul Erdos. At least we could say he was the one who travelled the most, and who had more collaborations with other mathematicians in the areas of Graph Theory, Combinatorics, etc.
   
   One of his dreams was to assemble a collection of all the most beautiful proofs in Mathematics, in which God would maintain the perfect proofs in mathematical theorems. This collection would be called The Book. Unfortunately, he didn't see his dream fulfilled while among us, but after his death Agner and Ziegler wrote this excellent book, "Proofs from THE BOOK", as a nice excerpt of what The Book could have been.
   
   Topics in this book range from Number Theory to Analysis, and also discussing Combinatorics and Graph Theory. Most of the proofs are accessible to everybody with some mathematical training, they are beautiful and surprisingly simple.
   
   I just love this book, in the last five years or so I have bought several copies of it, as it has been my favorite gift for people who want to discover a little more about the beauty of Mathematics.



3. NOTE: This review is JUST for the Kindle edition.
   
   The Kindle edition is completely worthless, because it is missing many symbols. It appears to have been done using OCR, and it was confused by mathematical symbols. For example, there are some places where I THINK it was supposed to be the greek letter phi, but it comes out as a left parenthesis and a right parenthesis. At least with that you can figure out what it was supposed to be. There is much worse--places where symbols are completely gone. E.g., there is a place where you just get a capital sigma with a subscript giving a summation limit, a blank space, a less than sign, and another blank space. So, the proof is saying the some of *something* is less than *something else*.
   
   This is a shame, because the book itself, from what I can see, is EXCELLENT.



4. The Kindle edition of the book is missing or misrepresenting math symbols in so many places it makes it completely unreadable.



5. This is a different kind of math book. It is not a textbook. Neither is it a monograph on a special math topic. It is a eclectic collection of proofs largely from number theory, combinatorics, graph theory and discrete mathematics in general. It is inspired by what the famous peripatetic mathematician Paul Erdos would like to see in God's BOOK. In my view, this book is best appreciated by dipping in occasionally when you are in the mood or when you have read a proof in another book and would like to see how it is done in this book. Most of the proofs are accessible to undergraduates or even college students.

5 comments about Who Is Fourier?: A Mathematical Adventure.

1. This book gives a clear explaination of Fast fourier transform. Although there are many books with lot of mathematics to explain fast fourier transform, this book explains without much math. Some explainations are too wordy, but overall this is a very good book to buy for yourself if you are new to Fourier domain and were wondering what is FFT.



2. This book was originally written to convey the experiences of the Transnational College of LEX (TCL), also known as Torakare, to as many members of the Hippo Group as possible. The college was founded in Tokyo in 1984 as a place where people could study the relationships between human beings and languages. People of all ages, from recent high school graduates to grandparents, study there. It is a school with no homework or exams and no taking of attendance, although people do graduate. Senior fellows, scientists and academicians are also there to lecture and help direct the people in their studies. The Hippo Family Club is the name that the group went by before the LEX name was taken, so the members and graduates are often referred to by that legacy title.
   The language studies conducted at LEX are amazing, the Hippo members practice speaking eleven different languages at the same time. Their approach is that every form of human endeavor, mathematics included, has its' own specific language. Therefore, the idea behind this book was to write a description of Fourier series that would be understandable by as many people as possible.
   In that capacity, they have succeeded very well, they start with the basic idea that all speech is a set of waveforms that can be described by sine and cosine curves. Moving slowly from this point, the plotting of complex waveforms by combining different curves is demonstrated. The calculus operations of differentiation and integration are included and the final stop is at the Fast Fourier Transforms (FFTs).
   Many diagrams are used along this journey, reflecting the incremental nature of the presentation. The slow speed of coverage makes it inappropriate as a textbook, but it would be an excellent book for individual study. However, if you knew some of the math, you would find those sections boring. In many ways, this book has the appearance of a children's workbook, only there are not very many exercises to work through.
   While I often found the pace tedious, I remain impressed by the concept of LEX and this book. It is readily admitted early on that it is the work of amateurs, but the authors clearly had fun in writing it and they do explain the topic in complete detail.



3. Some weeks ago I had the opportunity to read the entire book. It has 456 pages and is divided into 3 parts with a total of 13 chapters. There is an appendix (12 pages) with a few exercises.
   
   What author explains here is very well done, with plenty of illustrations, but Fourier analysis is treated very superficially, with a few practical applications. There is a lack of a set of exercises (problems to be solved) in the end of each chapter, in order to help readers to practice what was learned previously.
   
   If you need to acquire a deep knowledge on Fourier transform and intend to apply it in some important areas of Telecommunications (microwave engineering, digital signal processing, etc.), don't expect to become an expert just reading this book. Here you will find a few basic concepts, only.



4. This companion to the "Transnational College of Lex's other book "What is Quantum physics?" is an equally facile, user friendly, un-scary, gentle introduction to Fourier Analysis. Step-by-increasingly difficult-step it take the reader deeper and deeper into the substance, until he awakes deep into Fourier analysis without even knowing how he got there. The main heuristics are carefully chosen and demonstrative diagrams and equally careful explanations as to what the diagrams mean.
   
   While I would have been happier with a wider range of, and more robust applications of, Fourier analysis to problems other than just "the wave-particle duality problem," I understand why this was done: as preparatory and a build up to the later book on quantum mechanics, and I am thus nevertheless very much satisfied. The Lex series is to be commended and highly recommend. Its pedagogy is a craft unto itself. Amen
   
   Five Stars



5. A great book, which explains this intimidating top in a hands on light hearted. I would recommend this book to anyone. The best way I can describe the writing style is that it is similar to the O'Reilly Head First series.

5 comments about Introduction to Partial Differential Equations with Applications.

1. From just basic usage of the book, and with almost no introduction to PDEs, I found the book to be very helpful. This book starts out the way any PDE book should, a review of ODEs and then a careful, systematic approach to PDEs with very helpful illustrations. After the PDE is introduced, many different examples of PDE application are shown (such as the heat equation, Laplace's equation, and the wave equation), and with very careful demonstration of the use of the PDEs. I would have to say that any math or physics (especially in mechanics) person would benefit greatly to have either read or own this book.



2. I am a sophomore student in computer engineering, and my professor used this book as a supplement to his notes (http://www.aei.mpg.de/~horst/math4999-2pdf.pdf) while doing a course on introductory differential equations, and it came in quite handy



3. This book is a good book from the mathematical point of view and a good overview of the overall mathematical framework. For example, looking at a PDE, what can one say about the solution? Does it exist? Is it unique? What properties does the solution have? The book's emphasis is on presenting the various types of PDE's and then using physics to illustrate its usefulness. For example, the section of the book on quasi-linear and linear equations of the first order first looks at all of the mathematical underpinnings of this kind of equation. Only afterwards does the book look at the applications of such PDEs for solving problems in traffic flow and gas dynamics. In contrast "Partial Differential Equations for Scientists and Engineers" by Farlow assumes you have a specific physics problem you are attempting to solve and then goes about showing you how PDE can help.
   Thus, my advice for someone who wants to study PDE and learn the practical applications is that they should first read and study this book for the theory and some of the applications. Then, buy and read Farlow's book. See if you can determine how to solve each physics problem presented in that book with PDEs. If you can, you are on your way to saying you know Partial Differential Equations from both a theoretical and practical standpoint.



4. I use it as a reference for a Boundary Value Problems course at the college level. Not a beginner level text, you need a background in DEs and linear algebra.
   
   Inexpensive and a classic.



5. poorly organized complicated explanation where it can be written in easier way. I would look for something else to learn PDEs

5 comments about Elementary Analysis: The Theory of Calculus.

1. 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



2. 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 ...



3. 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.



4. 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. This book is pretty good. I bought the online version to be able to copy extended formulas into a word program. It doesn't do it. After several attempts with Amazon customer service's suggested fixes, it still doesn't work.

5 comments about Matrix Analysis.

1. I bought this book hoping to learn about matrix analyis. I did not. This book is simply a reference manual with plenty of theorems, axioms etc. with little explanation. They give it to you rough and row. NOT A SINGLE SOLVED EXAMPLE, and not even solutions for the exercises given in the book are provided. If you intend to learn about matrix analysis, as I did, let not the 5 stars review mislead you. Don't make the same mistake, this book is not for you.



2. I agree with other commentators who remarked that the book is better suited for someone already versed in linear algebra. For the student new to all this, the text can be, shall we say, too formidable?
   
   A good usage is when you have studied the subject, perhaps several years ago, and need a concise refresher.
   
   The strong aspect of the book is the emphasis on numerical calculations. Rather than about proving theorems. Don't worry that it was printed in 1990! While computers have heavily improved, thanks to Moore's Law, the maths of course has not. All the algorithms explained here are still germane to number crunching of linear systems. As another take, look at the Amazon page for the book, for the section about other books that cite this one. Notice the preponderance of computational books.



3. THis book covers some key aspects in matrix analysis.
   
   Would certainly recommend this book.



4. Definitely, not a lot of attention has been paid to pedagogy by the authors of this book. However it forms an excellent summary of most of the theory and is very good for one who understands it and one who wants a ready reference in the subject.



5. No matter what the blurb says this is a graduate level book. You cant teach yourself linear algebra using this book. Having said that this is a fantastic book for the initiated. Concise. Consistent. Well-written. A very helpful index. I refer to it regularly and it rarely disappoints. This is a must have. Absolutely 5 stars.