No comments about Computational Methods for Multiphase Flow.

3 comments about A Practical Guide to Splines.

1. This is a very nice book about splines for all who needs interpolation of data and are getting a bit nervous about the somewhat improper behaviour of normal cubic splines, i.e., the ones you learned about in your undergrad exam. The author provides both illustrative examles with computer codes (in FORTRAN) and describes the necessary theoretical background. Compared with many other books, it is readable also for a non-mathematician, although some experience with numerical analysis will be most helpful.



2. This is absolutely the most excellent book on the subject ever written. It is rigorous, accessible to those who are not professional mathematicians, and full of examples. Using de Boor's public domain software is a cinch, but you need to read the book to fully understand how to do it properly. I really wonder how I got along without it all these years.



3. Excellent content but is typewritten. Hard to read using "modern"-eyes. Aside from the presentation, the content is well written (as usual for de Boor) and complete. A very good introduction to splines and applications.

No comments about Geospatial Analysis (2nd Edition).

5 comments about Applied Differential Equations (3rd Edition).

1. This was the required text when I took differential equations back in the early 80s. As a sophomore engineering student, I found the book to be easy to read and easy to learn from. It is especially nice that the book has very few errors/typos in it. I have gone back to this book many times in the intervening years (in graduate school and beyond) and I continue to go back to it as an excellent reference. In fact, the copy that I purchased back in 1982 is starting to come apart and I was happy to see that it is still available.

   I am currently an engineering professor and I teach an applied mathematics course to senior level honors students. I find that I frequently go back to Spiegel's book for examples and explanations that I can present to my class when I am covering differential equations. This is still one of the best introductory texts on differential equations that I have come across.




2. Saying "good-bye" to my wonderfully and beautifully illustrated Calculus(Ron Larson)textbook and having to say "hello" to this plain and terribly boring-looking black and white book (absolutely no other colors, refering to the paperback copy), initially I found the text to be very dry and I thought it was going to be a good sleep aid. But after some weeks of studying I fall in love with it.
   For each kind of d.e. it supplies more methods than some other books on the same subject. It introduces theorems that I do not see in other books, for example, the convolution theorem. The author at times, depite his plain and dry disguise, tells you how a math idea was formulated and tries to guess how the discoverer was thinking when originally working on the problems. If you read closely you will find the author can be witty too. It also has good exercises expecially in the B and C section. There are a lot of wonderfully catogerized applied problems.
   This may be an old fashion book, but I have found a lot of value in it. I wish the publisher will make a new edition of the book with dressed up colors and better paper (The cover of the paperback 3rd edition is too thin and too weak to be a good cover).



3. This book is nicely written for anyone who is trying to self-learn ODE in a fast, nice and comfortable way.
   The best book on the subject.



4. the best applied math book I have ever read



5. If you think differential equations is an inaccessible topic, then this book's for you. Spiegel has a way of making the theory very real for "applied" folks such as practicing engineers as well as for mathematicians. The text also defines many of the special functions useful in engineering disciplines such as Bessel, Gamma and Legendre functions. The third edition hardcover also has an extremely attractive burgundy cover, with interesting histories of renowned people of math, science, and engineering on the inside.

5 comments about Calculus: Concepts and Contexts.

1. This book was actually my textbook for 3 semesters in a row, and, throughout that time, I've been basically forced to live with this book next to me at almost all times. There are certainly some good points and bad, but I'll start with the good.

   First off, the book does an excellent job, in my opinion, of giving every student of (almost) all ability levels a chance to grasp some deep calculus theories. For the math majors, that includes theoretical proofs (though most are just sketched in there!) and some good proof problems near the end of each section, and, for the non-math people, many applied problems (both "textbook" and "real-world" applied problems) combined with many routine drill-type problems to drive the concepts home. I also liked the numerous amounts of graphs and pictures drawn in the book, especially for 3-D graphing and surfaces, where it's not as easy to construct those by hand. His review of algebra and trigonometry is also very helpful, as my high school did not cover some of the topics in my precalc class before I took calculus I in college.

   But, for the bad, my first gripe is with the organization. You can obviously tell that the book was written in two volumes as there is a clear shift from single-variable to multi-variable in the style of presentation (less examples in the multi-variable, no CD-ROM help available) and language (he shifts from a "let's be nice to the student" point of view in the beginning to skipping some essential steps in exercises and writing like a math professor as you go along!). Also, I felt that some of the sections were out of place where they were, like the l'Hospital's Rule section being right in-between a bunch of sections on physical applications of dervatives? While I can certainly see it as being an application of derivatives, I see it as much more of a theoretical topic than an application; in my opinion, it should come near the end of techniques of differentiation (chapter 3). Also, I felt that he should've included more examples with the solids of revolution sections, one of the hardest parts of calculus for me (and MANY other people in my class); it's one of the only sections in single-variable that considers 3-D problems; therefore, it should be taken slowly, in my opinion. One other gripe: the cost! That's a lot of money to be shelling out on a single book! Luckily, I knew I would use it for three semesters, so it was worth it. If you're not planning on taking multi-variable calculus, then only buy the single-variable volume to save yourself some money!

   So, my final thought: If you're looking for a book with a lot of exercises for all levels, then this is definitely a good book. If you're looking for a book to essentially replace a teacher, then this book won't do that. A good teacher will most likely need to accompany this book to really get something out of it.




2. First off, I had no choice but to buy this book.

   What can I say about this book that hasn't already been said? Is this the only book on Calculus? I like to think I am adequet in mathmatics, my number one gripe was I did not take advantage of Amazon before I shelled out the full 150 dollars for this book, I could have had this crad for $50. I have a precalulus book by Michael Sullivan (whom I wish was writing this book), his explanation are pretty good, especially when he refers you back to solving a problem after he has gone over the examples, without that book I would have never done well in precalculus class, I basically thought myself from his book.

   Buying this book I thought James Stewart wrote a little like Michael, boy was I wrong, there are hardly any examples to refer back to when working out problems from the book, its just like "okay here are some numbers and theorems, now heres the answer!" The only reason I gave this a second star, was because of the CD-ROM that comes accomodated with this book giving hints on how to solve some selected problems. This book feels more like a text book (reading) than a typical math book, I understand that once you get to Calculus 1 one should be fluent in math, but still there's no reason for this. Maybe he wrote this book for student who like to skip class, because the only way to understand this book is with the help of a math professor.




3. I have to have this book for my calculus classes at the college I attend. This is my first semester in Calculus II (hopefully, I won't have to repeat it like I did Calc I) and this book is completly horrid for anyone who is shaky in math at all. The examples the book uses are next to useless (I mean, really, Calculus for Dummies is a better book than this is), the organization is atrocious (having two or more names for the SAME thing, even if it occurs later on in the book, is absurd), and the CDROM is useless. Seeing as how this is now my third semester with this book, I can fairly say (since there is no way I will change my mind) that this is the WORST math book I have ever had the misfortune to use and I have told that to all three of my professors. I have also, on the semester evaluations, failed this book with the lowest grade possible. Of course, I have also literally pitched it at the wall on numerous occasions and have spent many nights frustrated beyond belief to the point where, if I had had matches, I would have burned it to ash. I cannot begin to stress what a god awful book this is and I beseach all of the prospective professors to think long and hard before commiting your classes to suffer through calculus with this monstrosity.
   
   To say that I hate this book does not do justice to my feelings of animosity towards it.



4. I am attempting to learn calculus for the first time. I did wonderfully in pre-calculus, but this horrible book (and my thickly accented disorganized professor) have forced me to withdraw from the class and try again later.
   
   The author appears to be writing for other calculus teachers who already understand the material. The writing is incredibly confusing. The examples are not very helpful. The questions at the end of the sections are too few, and do not do a good job of building up difficulty. I find that it is easier to learn math concepts if you have a large quantity of problems to work on that start simple and progressively add more difficult aspects to them.
   
   If you are a professor thinking about using this book for your class, PLEASE RECONSIDER! If you are student with the misfortune of having to use this book for your class, hopefully your professor speaks so that you can understand him/her and maybe get another calc book to actually LEARN SOMETHING FROM.



5. I have read (almost) nothing but negative reviews about this book. I used this book for Single and Multi-Variable Calculus and had no problem with it at all.
   This book isn't the end-all Calculus book, but I will say that being someone who always thought of himself as "non-mathematically inclined," I had no trouble at all with the theorems, proofs or examples Stewart provides.
   It's not too complex, it doesn't skip steps (usually) and it is very thorough.

2 comments about Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics).

1. Thomas wrote a good book on a quite specialized subject. Although finite difference schemes have been traditionally viewed as a game field for physicists, they are given today much more commercial attention as financial option market evolves. Those who seek standard numerical recipes are advised to read this book. You will enjoy it (easy reading) and learn. But the book may not satisfy quests of a more rigorous readership. It abuses the Fourier method in stability analysis while considering only PDEs with constant coefficients. The bibliographical work has not been done at all. In addition, the cover does not state that this is the first book of two. I'd also advise to read G.Marchuk "Methods of Numerical Mathematics" (Springer, 1982) where a more general approach for stability of numerical schemes is developed.



2. This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM). The theory and practice of FDM is discussed in detail and numerous practical examples (heat equation, convection-diffusion) in one and two space variables are given. In particular, Alternating Direction Implicit (ADI) methods are the standard means of solving PDE in 2 and 3 dimensions.
   In almost all cases model problems are taken in order to show how the schemes work for initial value problems, initial boundary value problem with Dirichlet and Neumann boundary conditions.
   This book is a *must* for those in science, engineering and quantitative financial analysis. It digs into the nitty-gritty of mapping a PDE to a FDM scheme while taking nasty boundary conditions into consideration. The resulting algorithms are documented are are easily programmed in C++ or other language.
   The book does not cover topics that are also important: operator splitting (Marchuk/Janenko), non-constant coefficient PDEs, nonlinearities. Finally, the book uses von Neumann analysis as a means of proving stability (getting a bit long in the tooth). There are more robust methods that use monotone schemes, M-matrices and the maximum principle. You should consult other specialised references.
   This is Volume I of a two-volume set (Volume II deals with Conversation Laws and first-order hyperbolic as well as Elliptic problems.

   (...)

4 comments about Advanced Calculus for Applications (2nd Edition).

1. This is a one of the best introductions to advanced calculus out there, in my opinion. Once you've read it, you'll have enough background to start work on serious PDEs and analysis. Further, the book has an rather extensive set of problems for the reader to work, with solutions provided.

   There are several flaws, however, which is why I gave it 4 stars. In particular, the first couple chapters are an excrutiating read. It was so boring, in fact, that I quit reading the book and shelved it for three years (math was just a hobby at the time). Once you get past those initial few series-choked chapters, the book picks up the pace quite a bit; the book actually becomes quite the page turner once you get to chapter 6 and for the rest of the text --- took only three weeks to soak up the last half of the book, and that without rushing (versus three years for the first fourth ;) ).

   This book is, however, an introductory text --- I'd say probably Junior level. Thus, many points are not explicitly proven. Calculus of variations, for example, only gets a couple pages, and as I recall, they only prove the necessity of d/dx(df/du') - df/du = 0, omitting any discussion of sufficiency: many other similar examples occur throughout the text. This shouldn't be a problem, however, as such issues are often discussed in the literature or in more advanced (graduate-level or advanced undergraduate) texts.

   Another potential problem is that the text is fairly old. As such, it doesn't address the use of numerical methods on computers, although it does discuss numerical methods (somewhat outdated ones at times, however, as reflected in the strong emphasis on series solutions thoughout). Personally, I didn't find this to be a problem; there are plenty of mathematical methods texts out there that address these issues, so let them handle it.

   So, overall, I'd say Hildebrand is a pretty good book if you're looking for a way to extend your knowledge of elementary calculus. After Hildebrand, you should do pretty well reading graduate-level texts, monographs and journal/conference proceedings, although the going might be pretty rough at first.




2. This book helped me get a High Pass in Applied Mathematics here at the Thayer School of Engineering of Dartmouth College. It's not a great intro text to this material and it skips alot of details but it's a fantastic additional reference book.

   For example there is a solved problem of a wave function PDE, which involves Bessel functions. Earlier sections of the text refer to how the ODE's are solved by Bessel, which many books leave out.

   Later sections of the text contain an intriguing treatment of the Laplace transform.

   This book is not for beginners but is a good stepping stone to more advanced concepts such as the Calculus of Variations. Beyond this you are wise to consider additional texts such as Hildebrand's Methods of Applied Mathematics which contains a more rigorous section on C of V, Bender and Orszag's Advanced Mathematical Methods for Scientists and Engineers, Wunsch's Complex Variables, and even a good review on PDE's such as Haberman's Elementary Applied PDE's is not a bad idea if you are in a review situation like I was (having spent 8 yrs in Dot Com's and then back to grad school in engineering).




3. I've been using this book to supplement an intense course on mathematical methods of physics that I'm currently taking correspondence in Germany, and it's been a real help to me thus far. It doesn't seem to be super mathematical (in the pure theoretical sense), but it is most definitely useful for applications, particularly for physical problems. Anyone who has had the calculus I-III sequence at a mediocre American university, along with differential equations and linear algebra, should be able to make great use of this book. It's been 17 years since I finished my undergrad math degree, and I feel that this book is just my speed!



4. This book is definitely geared to the applied mathematics student; the topics in this book are strictly for pratical applications and not theory. It isn't too difficult but takes quite a lot of mathematical manipulation. Also, this book is quite old: to give you an idea, the first edition of this book was used by John Nash in his undergraduate calculus class in the early 1950s. Although many topics have been added in the 2nd edition, much of the material hasn't changed since its first publication in 1948. Nevertheless, you can still learn a tremendous amount from this book, even if you happen to be a 16 year old.

5 comments about Calculus: One and Several Variables, Ninth Edition.

1. If you dread taking calculus and aren't into math theory, I wouldn't recommend using this book. It'll only increase your headaches. The examples are sometimes too simple for the homework problems and will require an additional supplement. The chapters are horribly structured. A new chapter usually begins directly underneath exercises--a definite eye sore, given all the theorems shown. I, however, think the chapter on "Limits" is by far the best section. If the book implemented this method of teaching throughout the whole book, I'd give the book a better rating.
   
   A college calculus book I can stand behind is "Calculus" by Smith and Minton. They work out several examples in simple terms to help you understand Calculus without all the frustration. I wish I would have discovered it earlier during my course.



2. The important theorems are proved, and most everything is worked out in a very straightforward manner. For those who want theory, this text has it. For those who don't, there are a great many examples that guide the student through nearly any problem. The exercises are challenging and relevant.



3. Having used this book throughout my undergraduate education in calculus (Calc 1-3), I can attest to the effectiveness of this edition. What I truly love about this edition is the effort put forth to actually explain why, and not just give a "that's the way it is" analysis of concepts. After meeting other people exposed to calculus in high school where you're expected just to take concepts like the connection between the definite and indefinite integral at face value, it was amazing to actually come across a calc book that takes time to explain things logically, which is kind of the whole point.
   Word to the wise, this isn't a calc for business or calc for life sciences version. This is calculus, pure, pulling no punches. I'm giving it four stars because I think there could have been better organization concerning the proofs for some of the ideas and concepts presented.



4. This is an excellent textbook as a classroom text or for self-study. I
   have read other reviews where the reviewer complains about too much theory. This is nonsense. If you only want formulas then take only that
   from the book. If you want more it is there. This book is an excellent
   precursor to analysis and differential equations. The authors don't baby
   the reader but you better come well versed in precalculus. Please don't
   try to study calculus if you can't do inequalities, logs, etc. and then
   blame the author and your instructors for your failures.



5. This is a very decent calculus book.
   
   One of my favorite features is the complete lack of stock photos -- instead, they decided to fill the space with USEFUL information, and diagrams related to the topic being discussed (no baseball players and businessmen...).
   
   The book has a fairly good balance of theory and applications, and does a good job at using elegant but INSTRUCTIVE proofs.
   
   It is a gentler introduction that something like Apostol or Spivak -- less theory ... which depending on what you plan to use it for can be a good or bad thing. I personally used it before trying to tackle Apostol's book, and it made reading the latter much easier.
   
   All in all, I'd recommend this book over most other calculus books geared towards this audience.

1 comments about Measure Theory: A First Course.

1. Mathematics is like mountaineering: its hard to get to the summit, good mountaineers real teachers aren't easily found and, at the end, all newcomers will search for help in the books. Kubrusly never forgets he once was at the mountain's basis and the hardway he tooks. This is the kind of book he wondered in his Math beginning. This book is something like a very friendly version of "Elements of Integration and Lebesgue Measure" from Bartle. Beside clarity, Kubrusly has honesty: he don't proposes problems that can't be solved by a real interested student and when the things get more difficult, he helps with hints. There are a lot of books and pedantics authors who puts theorems, from others books, maked-up like problems. Luckily for the students, there are good Math writers, like Kubrusly, struggling for teaching.

2 comments about The Illustrated Wavelet Transform Handbook.

1. This book provides a comprehensive overview of wavelet transform methodologies and applications. The emphasis is on practical applications which are illustrated with many detailed figures and examples from Science and Engineering. A particular interesting chapter on medical applications is provided. In the introductory chapters, Addison gives a clear account of the theory for both continuous and discrete wavelet transform and associated post-processing techniques. Unlike many of the other books in this area, Addison communicates the concepts with a level of detail, sufficient for the applied engineer and scientist, but without becoming bogged down in a fog of mathematical gymnastics (a feature of many of the books in this area). A welcome addition to the growing number of books on this important signal analysis technique.



2. Very good introduction to wavelet analysis. Not for someone looking for casual reading but for someone who wants to be able to dig in and start doing actual analysis it will get you going.