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Books - Science - Mathematics - Calculus

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    Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra
    by Tom M.Apostol
    Average Customer Review: 5.0 out of 5 stars
    Hardcover (June, 1967)
    list price: $125.95 -- our price: $125.95
    (price subject to change: see help)
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    Reviews (16)

    5-0 out of 5 stars The best math book I have ever read
    This book is extremely well-written and leaves you with the feeling that it couldn't have been better. A tribute to this fact is that it is still in its second edition from 66 and, though it is rather old, has kept its quality.

    It has a good number of exercises (usually between 15-30 per section/topic), which is less than most standard calculus book, but the difference is that the quality of the exercises here is much higher, and you will be surprised when some months later, when tackling some problem for another course, you will remember having done the exercise in Apostol. It also has answers to all the exercises (except for the ones which require a proof, rather than a number as a result). The problems range from easy to very hard, but usually there won't be more than two problems per section that one won't be able to do upon first reading and a little thinking.

    The writing of the book is very good and rigorous, and it covers some topics that are not present in most calculus books. For example it has a small seciton on partial derivatives, it covers the weighted mean-value theorem for integrals and rearrangements of series. There are many other topics that don't usually fit in a calculus course, but the introduction of these when you are still learning it makes the connection between the topics much clearer. After having read the book from cover to cover, it has now become a very useful reference that never leaves my table. Also, because it is rigorous and has a broad number of topics, if you learn this and vol. II now you will save a lot of time later in more advanced courses such as analysis, differential equations, linear algebra and to a lesser extent even differential geometry and probability.

    Because of its nonstandard approach, I think that this book is unsuitable for most people learning calculus for the first time (especially if you are taking a course and not just studying at your own pace). However, it (along with vol. II) is mandatory reading for anyone who wants to study math, in my opinion.

    5-0 out of 5 stars Excellent Text and Useful Reference
    If you're looking for a calculus and linear algebra text with good discussions, useful examples, and challenging-but-doable problems, then this is the text for you.This was my freshman year core math text, and I keep going back to it when I need to refresh or clarify my understanding of the basics.It's the type of text that makes lectures unnecessary.This is one of very few texts that will be irreplacable for decades

    5-0 out of 5 stars take this simple quiz
    if you are the kind of student who thinks the area of a triangle is: "Mmmm...(1/2)BH, or is it (1/3)BH? Oh well, who cares, I can always look it up anyway." then this book is probably not for you. But if you have wondered whether the number given by that formula changes when you change which of the three sides of the triangle you call the base, then this book is exactly what you have been looking for. The author of this book assumes you are bright and curious, the kind of student it was written for at Cal Tech. Professor Apostol has made an enormous and thoroughly successful effort to explain in intellectually honest detail exactly what is going on, and how everything is proven rigorously. In this same vein, Spivak's book is more fun, and Courant's has more physics and applications, but this one is the most scholarly. The linear algebra was an afterthought, added to the original work when that craze swept the subject in the 1960's. In general, great works are best in the first edition before the publisher convinces the author to modify his original vision. In my opinion the linear algebra does nothing to enhance the presentation of one variable calculus, and should have been left out, but it won't hurt you. ... Read more

    Isbn: 0471000051
    Sales Rank: 283242
    Subjects:  1. Calculus    2. Mathematical analysis    3. Mathematics    4. Calculus & mathematical analysis    5. Mathematics / Calculus   


    by Michael Spivak
    Average Customer Review: 4.5 out of 5 stars
    Hardcover (01 September, 1994)
    list price: $70.00 -- our price: $70.00
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    Reviews (58)

    5-0 out of 5 stars Spivak is sometimes misplaced...
    There is a great deal of criticism about Spivak's Calculus here.I believe that the book must be misapplied by institutions using it.Spivak is an excellent introduction to Calculus for an intending mathematician.It introduces a rigourous discourse on Calculus and introductory analysis.It does not fall prey to the exercise/drill ad infinitum of the Stewart/Thomas/Larson variety.The problems in Spivak are hard, even famously hard.They can take hours of deep thought to solve.The people complaining about the problems are missing the point.This book teaches you how to *think* like a mathematician while introducing you to Calculus in a very clear way.

    Spivak is *not* hard to understand but it can take some effort.In short, if you're struggling with this book it might be because your mathematical background isn't quite there yet and you may need to brush up on some precalculus concepts.If you'd like to become a mathematician, get this book then work through Apostol.

    4-0 out of 5 stars The calculus of choice only for future hotshot PhDs
    This is actually hardly what one would call a calculus book. Spivak doesn't care much for actual calculations or the classical physics that was synonymous with calculus for hundreds of years. Instead he takes a polished, modern approach with emphasis on rigour. While it is not impossible to learn the basics of calculus from this book, it could also very well be the course book for what we today would call a first course in analysis. So as a "calculus" book it is only for modern-style pure mathematicians who have little respect for calculations and physics, and instead want to spend their time doing exercises on things like Lipschitz conditions or the Riemann-Lebesgue lemma. I believe it is more valuable as an "analysis" book for those who know their basic calculus already, i.e. compared to Rudin or whatnot; as such it has the advantages of being comparatively chatty and very well illustrated.

    5-0 out of 5 stars Excellent
    In my opinion this is one of the best single variable calculus textbooks out there. It is pretty big in size and contains proper and precise explanations for all the topics in calculus and beyond. The excercises in this text will really make you think when you do them. Another great thing is that this text contains topics that you would not normally see in the first year calculus book, such as complex power series, fields, construction of real numbers. I understand that in a first year of university one might not be serious about studying (heck, that's how I was!), but if you are, you will find this book rewarding. So if you are serious about learning and UNDERSTANDING intro to analysis, buy it. This is one of the few books to keep. ... Read more

    Isbn: 0914098896
    Sales Rank: 243330
    Subjects:  1. Calculus    2. Mathematics   


    Introduction to Calculus and Analysis, Volume 1 (Classics in Mathematics)
    by Richard Courant, Fritz John
    Average Customer Review: 5.0 out of 5 stars
    Paperback (22 December, 1998)
    list price: $49.95 -- our price: $41.04
    (price subject to change: see help)
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    Reviews (9)

    5-0 out of 5 stars Absolutely beautiful!
    I give 5 stars to this book because in contrast with the majority of the calculus textbooks it gives the reader the perfect combination between rigor and intuiton. Another thing that I also like a lot is the fact that volume 2 has solutions to almost all the excercises, which is great because some of the problems are very difficult. I really think this book is a "must have".

    5-0 out of 5 stars simply the Best Calculus Book
    An intuitive, rigorous and a beautifully conceptual approach to calculus is what distinguishes this book from the thousands of run-of-the-mill "Calculus I" textbooks published every year.

    This is not surprising because 1) Courant and John were both important German-born mathematicians, both schooled in that great mathematical mecca, Gottingen, both making fundamental contributions to many classical branches of pure and applied mathematics.Courant is an especially important mathematician since he not only studied under the greats Minkowski and Hilbert - even serving as the latter's assistant - but founded the Courant Institute of Mathematical Sciences in New York, modelled on the Gottingen Mathematical Institute. 2) That typical German thoroughness and emphasis on the mastery of the "fundamental concepts", so dear to German textbooks, is evident in all sections of the book, particularly in the introductory material on the number continuum, functions, continuity etc.

    The exercises at the end of chapters are substantial and excellent, and help to develop proof skills in students as well as a subtle mathematical intuition.

    Mathematics is best learnt by studying books written by important mathematicians.Classic books like these should always serve to prove the truth of Abel's dictum that to master mathematics one should 'study the masters and not the pupils'.

    5-0 out of 5 stars You must have this.
    My review of the first volume pretty much applies here as well.How many *calculus* texts have an introduction to complex variables, and the theory of analytic functions?This is the only one I've ever seen, and I don't think anyone else could make it more enriching than Courant.Useful material on vector calculus, the theory of matrices, and even introductory material on the *calculus of variations* (something we usually don't see at *all* in the undergrad curriculum) is included.It is refreshing to have an instructor like Courant, who doesn't assume we can't follow higher mathematical roads, but also doesn't sit at the other end of the spectrum, just waving a wand and "poof, here is the result".

    Courant also published a standard reference work (also two volumes, I believe) on Mathematical Physics.While the level of mathematics required is post-grad, I was still able to read sizeable sections of it without getting lost.

    We can only hope Dover decides to publish Courant's works one day, to make them a little more affordable.But still, you can buy both volumes of Courant's intro to calculus for about the same price as a modern calculus text that waters down the material, and on top of that, provides inadequate explanation for the material it does cover. ... Read more

    Isbn: 354065058X
    Sales Rank: 181625
    Subjects:  1. Calculus    2. Functional Analysis    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Fourier series    7. Mathematics / Mathematical Analysis    8. Real analysis    9. numerical methods   


    A First Course in Calculus (Undergraduate Texts in Mathematics)
    by Serge Lang
    Average Customer Review: 4.5 out of 5 stars
    Hardcover (16 March, 1998)
    list price: $69.95 -- our price: $55.46
    (price subject to change: see help)
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    Reviews (2)

    5-0 out of 5 stars simple, but not unsophisticated

    As a high school teacher, I used this text with great success several times for both AP Calculus BC and AP Calculus AB courses. It is my favorite calculus text to teach from, because it is very user-friendly and the material is presented in such an eloquent way. There are no gratuitous color pictures of people parachuting out of airplanes here. Opening this book is like entering a temple: all is quiet and serene. Epsilon-delta is banished to an appendix, where (in my opinion) it belongs, but all of the proofs are there, and they're presented in a simple (but not unsophisticated) way, with a minimum of unnecessary jargon or obtuse notation. He doesn't belabor the concept of "limit"; most calculus books beat this intuitively obvious concept into the ground. Even though it doesn't cover all of the topics on the AP syllabus, I would rather supplement and use this text rather than any other.

    4-0 out of 5 stars Calculus for beginning college students
    I needed to bring my high school calculus up to speed for first year physics studies and found this to be the only book which covered the necessary ground. The material is presented in a thorough manner with the great majority of topics shown with proofs. The book is very well organized and there are abundant worked examples. Some problems are offered which deal with matters not covered in the text, but usually there is a worked example given among the answers. Lang deals with the material in a clear fashion so that the subject matter is usually not difficult to follow.On the negative side I can say that there is no human touch between the covers. His sole attempt at humor is an item following a list of problems in which he notes "relax". In the foreword he exhibits his firm belief that many freshmen arrive unprepared for college calculus, which may be true. But nowhere in the book is there a note of encouragement, so it cannot be described as reader friendly. Finally the index is pathetic--just three pages for a book of 624 pages, so that finding things can be frustrating. ... Read more

    Isbn: 0387962018
    Sales Rank: 743697
    Subjects:  1. Calculus    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Mathematical Analysis   


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