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Rating: 
Summary: Odd
Review: A very odd book in my opinion; the order of the chapters makes it different from other books on the subject. For one, partial differentiation is treated before vectors, which is a significant deviation from most other advanced calculus texts out there. If you want to know the geometrical significance instead of analysis, buy another text this is after all a text on ADVANCED calculus. On the other hand, I don't know why the author calls it an advanced calculus text. Cross products and dot products are used instead of the inner product space; definitely not advanced. If you want a real advanced calculus text, buy "Advanced calculus of several variables" by C. H. Edwards. And Rojelio, learn some english. I had no idea what you were talking about.
Rating: 
Summary: Lucid with good notation
Review: An excellent reference work, with some thoughtful choices of notation, which always helps. I thought the differential geometry sections were a bit thin, so if that is what you after look elsewhere. If you want a good book on the core of multi-variate calculus this one will serve you well. He proves everything, which is nice too.
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Summary: Old style Advanced Calculus
Review: First of all, Mr. Heyward's review would be very difficult to improve upon. However, I would like to supplement his remarks by emphasizing that this text is a classic work ... albeit from a substantially different time and place. Despite the required Carbon dating, Dr. Widder does an excellent job overall and he introduces a format that many more modern books could profit from.The last time I saw this text used in an Advanced Calculus course was in the early '70's. I was a grad student TA for the course and had to work with the material in detail. I found it to be clear, complete, and very useful ... especially for one interested in a more applied approach. Every student of analysis should at least take a look at the book. The Dover edition is, as usual, very inexpensive ... another big plus.
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Summary: Suitable for certain Subjects
Review: I bought this textbook as a supplementary resource book for an advanced calculus class I once took although I ended up using it for a Differential Equations II class instead (in particular the partial differential equation and fourier series sections). This book does not present proofs as one might expect from many of today's Advanced Calculus classes. It does not present abstract theorems but rather applied Calculus and Differential Equations. You will not find logical connectives, quantifiers, techniques of proofs, set operations, induction, or completeness axioms in this book. What you will find is partial differentiation, line and surface integrals, definite integrals, fourier series, infinite series, etc. Electrical and Computer Engineers will find that they may benefit from the Vector, Fourier Series, and Laplace Transform chapters of this book. Physics majors are more likely to profit from the chapters on Partial Differentiation and Fourier Series. Here's the textbooks chapter titles: 1) Partial Differentiation, 2) Vectors, 3) Differential Geometry', 4) Applications of Partial Differentation, 5) Stieltjes Integral, 6) Multiple Integrals, 7) Line and Surface Integrals, 8) Limits and Indeterminate Forms, 9) Infinite Series, 10) Convergence of Improper Integrals, 11) The Gamma Function. Evaluation of Definite Integrals, 12) Fourier Series, 13) The Laplace Transform, 14) Applications of the Laplace Transform. The book may be considered as being written in the ole' school style. It was written by a former Professor of Mathematics at Harvard and was first printed in 1947. The relatively low cost of the textbook may be attributed to it not having been `updated' for a while, being devoid of any color, and being softbound. It has some worked out examples but focuses more on established theorems and lemmas to solve problems. The book is fairly well organized and is overall a good reference book.
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Summary: GREAT BOOK
Review: I really believe that this book does an excellent job at teaching such a difficult topic. "Advanced Calculus" is just packed with proofs and stimulating problems. This should be the text used to teach the subject. If you intend to tutor yourself on the topic or you are actually taking the class, this book is a must. I am currently using this as a secondary text to an advanced calculus class I am taking, and, as far as I'm concerned, this is the only text I need. This book does, in such a small package, more than you'll ever need. I recommend one purchases this book at the multi-varialbe calculus level and use it through your time in analysis courses. This is a must have for all math majors.
Rating:
Summary: Their small price overcome to those more expensives
Review: This is a Classic "old" Text. One of the best among the classics of Advanced Calculus. In fact this is not an advanced book. But being advanced or not does depend on who is located in front of the book. It is, but rather, a continuation of the classic Calculus texts like Thomas, Leithold, Taylor, etc. This as for the content, that includes topics like Stieltjes Integral, line and surface Integrals, Fourier Series and Laplace Transformed (Stieltjes Integral can be included in the non advanced Calculus courses after treating the parametric equations in a Calculus course that is not considered advanced). What makes special this book it is the easiness with which the author introduces the topics, without necessity of entering in rodeos. He goes once and for all to the grain and it presents the whole content without creating doubts in the reader. It selects their exercises very well, leaving very undoubtedly that any student that has read each section of the book carefully, they can carry out them. The answers are at the end of the book. It presents the theorems with a nomenclature without complications, facilitating the reader's understanding. This book deserves to be in our shelves for future references, and anyone can have it without fear to lose its money, since it is very cheap....
Rating:
Summary: GREAT BOOK
Review: This is a classic text and a great book. I found that this book helped me truly understand many concepts which other books simply made confusing.
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Summary: A bit of a hodge podge but still a useful reference
Review: This text is very definitely written in the grand old non-geometrical style which some might find a bit more difficult to follow but the theory is sound with very good coverage of differentiation and integration including the essential elements of topology (it discusses compact sets without referring to them as such). My main complaint is that evidently in this era, it was stylish to omit certain details of the proofs. Other than that, it is still a serviceable text if used as a reference (especially considering the low price). I feel fortunate to have inexpensively purchased my copy of this text and have no intention of selling it or my copy of "Elements of Calculus" by Granville, Smith and Longley. But I also feel fortunate that I didn't have to learn the subject from either text. One of the best part of buying a used math book is in the reading of the notations made by previous owners 8-)
Rating:
Summary: Great book
Review: Yes, a bit oldfashioned and black and white, but if you want attention to detail and rigorous proofs of all the theorems (gets to be quite advanced) this is a book for you. I taught myself after learning basic diff/int calculus. If you ever read a calc. book and get annoyed by those "..it can be shown.." lines, look in this little text and chances are it IS shown here.
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