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**About this book :- **
**Advanced Calculus A Geometric View ** written by
** James J. Callahan **

With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. This invites geometric visualization; the book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps, such as the role of the derivative as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. Advanced Calculus: A Geometric View is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. It avoids duplicating the material of real analysis. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.

**Book Detail :- **
** Title: ** Advanced Calculus A Geometric View
** Edition: **
** Author(s): ** James J. Callahan
** Publisher: ** Springer-Verlag New York
** Series: ** Undergraduate Texts in Mathematics
** Year: ** 2010
** Pages: ** 543
** Type: ** PDF
** Language: ** English
** ISBN: ** 1441973311,9781441973313
** Country: ** US

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**About Author :- **

The author ** James Callahan ** is Professor Emeritus of Department of Mathematics and Statistics, Clark Science Center,
** Smith College ** , Northampton, MA 01063, US.

In 1975, James Callahan received the Lester R. Ford Award of the Mathematical Association of America and at Smith he has received the Faculty Distinguished Teaching Award and the Sears–Roebuck Foundation Award for Teaching Excellence and Campus Leadership. He has made research trips to England and France.

Callahan was the director of the Five College Calculus Project (funded by the National Science Foundation), and co–author of Calculus in Context (W. H. Freeman & Co, 1995). He wrote The Geometry of Spacetime (Springer–Verlag, 2000) an undergraduate text in mathematics about relativity, as well as Advanced Calculus: A Geometric View (Springer–Verlag, 2010).

Callahan's interests include geometry, dynamical systems, chaos and fractals, catastrophe theory, relativity, most areas of applied analysis and building things.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Advanced Calculus A Geometric View by James Callahan **

** • Download PDF Advanced Calculus A Geometric View (Solution) by James Callahan **

** • Download PDF Calculus in Context by James Callahan, Kenneth Hoffman **

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**Book Contents :- **
**Advanced Calculus A Geometric View ** written by
** James J. Callahan **
cover the following topics.

1. Starting Points

2. Geometry of Linear Maps

3. Approximations

4. The Derivative

5. Inverses

6. Implicit Functions

7. Critical Points

8. Double Integrals

9. Evaluating Double Integrals

10. Surface Integrals

11. Stokes’ Theorem

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