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Derivatives and Integrals of Multivariable Functions by Alberto Guzman

Derivatives and Integrals of Multivariable Functions

by Alberto Guzman
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Book cover type: Paperback
  • ISBN13: 9780817642747
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 319
  • Original Price: EUR 49.99
  • Language: English
  • Edition: 2003
  • Item Weight: 502 grams
  • BISAC Subject(s): Functional Analysis, Calculus, and Mathematical Analysis

This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author's previous "Continuous Functions of Vector Variables" specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, 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. Prerequisites include background in 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, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. "Derivatives and Integrals of Multivariable Functions" is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry.

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