Derivatives and Integrals of Multivariable Functions (PDF)
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 text, "Continuous Functions of Vector Variables": specifically, elementary results...
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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 text, "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.
- Autor: Alberto Guzman
- 2012, 2003, 319 Seiten, Englisch
- Verlag: Birkhäuser Boston
- ISBN-10: 1461200350
- ISBN-13: 9781461200352
- Erscheinungsdatum: 06.12.2012
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- Dateiformat: PDF
- Größe: 19 MB
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