Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) : Book

Search ISBN:0486683362 offer from Abebooks or used books from Alibris. Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) Reference Book. Classifications : Calculus Pure Mathematics Mathematics Professional Science Professional & Technical Subjects Books General AAS Mathematics Professional Science Professional & Technical Subjects Books Mathematical Ana . Click the following link to view the cover of Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics).

1) Paperback Book Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) by Dover Publications. Be prepared for a lot of "connecting the dots". You should be constantly on the look-out for implied preconditions and missing proof steps. The requisite Linear Algebra can´t be picked up entirely from the book. I stopped reading after section IV.3, when i realized the value i extracted from the book didn´t compensate for the effort i needed to expand on gap-filling.

Definitions are, more often than not, introduced inline, rather than set apart and given a number. Some important theorems, specifically the Inverse Mapping Theorem and the Implicit Function Theorem, aren´t marked distinctively. This makes for an unwieldy reference.

Some important proofs and examples are relegated to the exercise sections. Section III.5 (Higher Derivatives), for instance, is entirely exercise-based. Section II.2 cites exercise 2.5 as a counter-example to theorem 2.5 (i.e. as demonstrating how, when one of the theorem´s preconditions is broken, the conclusion fails to hold), but the exercise is actually an example, not a counter-example (in other words, the exercise explores a function, which fulfills both the theorem´s preconditions and conclusion).

On the up side, the proofs are concise (when not too terse) and the pace is upbeat (when not galloping). Some of the topics (specifically, Lagrange Multipliers) are dealt with in generality that i dare you find in other books.

The book could be excellent, if submitted to a thorough content-wise and graphical editorial review. As it stands, it must be supplemented with other titles, and demands more than it gives.¤

2) Paperback Book Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) by Dover Publications. I don´t know how good this book will be for someone who is not comfortable with proofs, because it takes a somewhat more abstract, less computational and visual approach to the subject. Nevertheless, if you already learned multivariable calculus in a computational/visual style in an early undergraduate class, and now find yourself more comfortable with the abstract approach of higher mathematics, this book will help you re-learn the concepts of multivariable calculus in the proper abstract setting. Everything clicks at reasonable reading speed so you don´t need to spend a lot of time stopping to remind yourself of what he´s doing. An easy, smooth read that will leave you with a good perspective on the subject. Highly recommended for the right kind of reader.¤

3) Paperback Book Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) by Dover Publications. This is a wonderful book. The exercises are interesting and resolvable: you do not need to be a genius. In rigorous style, it covers differential manifolds, differential forms, etc.. Buy it!¤

4) Paperback Book Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) by Dover Publications. This is a clear, well motivated discussion of advanced calculus (2nd year, multivariable) using the machinery and vocabulary of the differential mapping and differential forms. This discussion takes place within Rn and all manifolds are explicitly within Rn. So this lets you get a good grounding in the ideas that are generalized in the more abstract differential geometry/Reimannian setting. There is mothing you lead to "unlearn" to adapt to the more abstract world of bundles. It gives a clear roadmap of the ideas that will need to be adapted to the new setting.

This is also a great book if you just want to learn 2nd year calculus but want to see more than div,grad, curl.

More suited for mathematicians and physicists than engineers.

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5) Paperback Book Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) by Dover Publications. Some people think Dover books, being cheap, ought to be bad. In fact, this Dover series specializes in "salvaging" great titles that went out of print and are of great intellectual/pedagogical value. Such is the case again for this title.
Very well written. Of course, C.H. Edwards is notorious for his book on the history of calculus.
Exceedingly clear. I started reading it while taking Calculus II, in search of some more elaborate perspectives. It is that clear.
Chapter 1 is a brief incursion in some topological aspects. Chapter 2 directional derivatives, differentials. Ch3. Chain rule. Ch.4 Critical points. Ch. 5 MANIFOLDS (patches ?! ) and Lagrange multipliers (and this is around a bit over page 100!). Ch 6 Taylor´s in one and Ch. 7 several variables. Ch 8 Classification of critical points. Part III begins with Newton´s method and contraction mappings. Then goes to Multivariable mean theorem, Inverse and Implicit Mapping Theorem. Ch 4 (III) is Manifolds in Rn and finishes with higher derivatives. Part IV is Multiple Integrals, n-dimensional integrals, Riemman sums, Fubini´s theorem, Change of Variables, Improper Integrals, Path Lenght and Line Integrals, Green´s theorem, some applied problems, Line and Surface Integrals. Book end with Differential Forms, Stoke;s theorem, Classical Theorems of Vector Analysis, Closed and Exact Forms, Normed Vectors Spaces, Variational Calculus the Isoperimetric problem.
Lots, lots of bangs for your bucks. Because of the breadth of the exposition, clarity and price, it´s a must-have.
You can kind of draw a parallel between this and Hubbard´s Vector Calculus, Linear Algebra and Differential Forms. Both kind of span the same space. Of course, being older, it doesn´t have the same computational flavor as Hubbard´s (but then again, it´s not really about numerical methods, is it?).¤

6) Paperback Book Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) by Dover Publications.

Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

Page Updated: Robert N. Goolsby, 1-Dec-2008, 04866833629780486683362, 8X0-070-320-0X0-620-200-8

Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics)

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