Multivariate Calculus and Geometry (Springer Undergraduate Mathematics Series) (Paperback)

~ Sean Dineen (Author) " We introduce differentiable functions, directional and partial derivatives, graphs and level sets of functions of several variables..." (more)
Key Phrases: toroidal polar, unit speed parametrized curve, unit speed parametrization, Parametrized Surfaces (more...)

Editorial Reviews

Review

From the reviews of the second edition:

"The author has taken the sensible approach of giving an adequate formulation of the theories, backed up by geometric insight and accompanied by reasonable explanations."
The Mathematical Gazette

"It is rare to find a text on multivariate analysis where the geometrical intuition is preserved so well."
Zentralblatt für Mathematik und ihre Grenzgebiete

"This is a nice introduction to multivariate calculus for higher level undergraduates. ... The text contains many worked out examples and a collection of additional exercises with solutions given in the appendix of the book." (F. Haslinger, Monatshefte für Mathematik, Vol. 139 (3), 2003)

"In this revised edition, which includes additional exercises and expanded solutions, Seán Dineen gives a solid description of the basic concepts, via simple familiar examples, which are then tested in technically demanding situations. The author recognizes the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a comprehensive and unified understanding of the differential, integral and geometric calculus of several variables. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems." (L’Enseignement Mathematique, Vol. 47 (3-4), 2001)

"Dineen deals with many of the topics you would find in a typical text on advanced calculus but he does so in a much more sophisticated way. ... All the new terms are defined as they appear and all the necessary theorems are stated ... . The book is ... very clearly written, and there are lots of useful diagrams and worked examples. The approach ... is one that students who are going on will want to learn sooner or later." (Peter Saunders, The Mathematical Gazette, Vol. 86 (505), 2002)

"Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with an understanding of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning." (Zentralblatt für Didaktik der Mathematik, August, 2001)

Product Description

Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with a deep understanding of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems. In this revised edition, which includes additional exercises and expanded solutions, Seán Dineen gives a solid description of the basic concepts, via simple familiar examples which are then tested in technically demanding situations. The author recognises the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a comprehensive and unified understanding of the Differential, Integral and Geometric Calculus of Several Variables.

Product Details

• Paperback: 254 pages
• Publisher: Springer; 2nd edition (May 11, 2001)
• Language: English
• ISBN-10: 185233472X
• ISBN-13: 978-1852334727
• Product Dimensions: 9.8 x 7 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #561,302 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

2 of 3 people found the following review helpful:

4.0 out of 5 stars A neat book, August 6, 2009

By	Pedro Tomas Hasdeu (capital federal Argentina) - See all my reviews (REAL NAME)

This is not an elementary textbook, it is in fact aimed at higher level undergraduates. This means you shouldn't be afraid of theorems & their proofs, you should know some linear algebra, including some familiarity with n-dimensional euclidean space, as well as partial derivatives and elementary calculus. The author's Functions Of Two Variables could be profitably read before tackling the present book.

The book is about the differential and integral calculus of multivariable functions, including a very nice introduction to the classical elementary diffential geometry of curves & surfaces. A bent on differential geometry can be perceived all along.

The style is elegant and crisp and rather intuitive. All in all it is a very nice book. I didn't give it five stars because some of the stuff you'd expect to find in an advanced calculus book, such as series (including Taylor's series) and a careful discussion of differentiability, are missing.(This review is about the first 1998 edition).

1 of 7 people found the following review helpful:

2.0 out of 5 stars Too Technical. Good for Students maybe..., April 6, 2008

By	Nicolas Miari (Tokyo, Japan) - See all my reviews (REAL NAME)

But not for someone who wants to learn at his own pace.
It starts with the Matricial definition of derivatives and assumes
a complete knowledge of Matrix Theory.

This, at least for me, is neither intuitively nor psychologically
friendly. Other math books, which are not even targetted at
undergraduates are easier and more fun to follow
(e.g. Algebra by B.L. van der Waerden Algebra: Volume I)

Boring, maybe good for someone at college who has a teacher and
need to pass an exam.

If you are a math nerd who can follow books like:

Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
Corollary
Theorem
Proof
Corollary
...
[Some Explanatory Text]
...
Theorem
Proof
Corollary
Proposition
Proof
Corollary
Proposition
Lemma
Proof
...
[Figure]
...

Then this is the book for you.