| Derivatives and Integrals of Multivariable Functions 2003 Edition Contributor(s): Guzman, Alberto (Author) |
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ISBN: 0817642749 ISBN-13: 9780817642747 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Paperback Published: August 2003 Annotation: This work provides a systematic examination of derivatives and integrals of multivariable functions; it is suitable for a one-semester course in what is usually called advanced calculus of several variables. The approach taken here is similar to that of the author??'s previous text, "Continuous Functions of Vector Variables": specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. The elementary material in the single- and several-variable case leads naturally to significant advanced theorems about functions of multiple variables. Topics covered include differentiability and its relation to partial derivatives; directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. The development of the vector-field theorems ties together material from many of the chapters and emphasizes the physical applications of the theory. Prerequisites for the reader include background in theoretical linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line. Written in a definition-theorem-proof format, "Derivatives and Integrals of Multivariable Functions" has a conversational style and is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. Ideal for upper-level undergraduates whose next course will be real analysis, this book is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations inanalysis and differential geometry. |
| Additional Information |
| BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Calculus - Mathematics | Mathematical Analysis |
| Dewey: 515 |
| LCCN: 2003052489 |
| Physical Information: 0.66" H x 6.06" W x 9.32" (1.06 lbs) 319 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This text is appropriate for a one-semester course in what is usually called ad- vanced calculus of several variables. The approach taken here extends elementary results about derivatives and integrals of single-variable functions to functions in several-variable Euclidean space. The elementary material in the single- and several-variable case leads naturally to significant advanced theorems about func- tions of multiple variables. In the first three chapters, differentiability and derivatives are defined; prop- erties of derivatives reducible to the scalar, real-valued case are discussed; and two results from the vector case, important to the theoretical development of curves and surfaces, are presented. The next three chapters proceed analogously through the development of integration theory. Integrals and integrability are de- fined; properties of integrals of scalar functions are discussed; and results about scalar integrals of vector functions are presented. The development of these lat- ter theorems, the vector-field theorems, brings together a number of results from other chapters and emphasizes the physical applications of the theory. |