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Derivatives And Integrals Of Multivariable Functions,Used
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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 authors previous text, 'Continuous Functions of Vector Variables': specifically, elementary results from singlevariable calculus are extended to functions in severalvariable 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, onevariable calculus, and some acquaintance with continuous functions and the topology of the real line.Written in a definitiontheoremproof 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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