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derivatives and integrals of multivariable functions (in English)
Guzman (Author)
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derivatives and integrals of multivariable functions (in English) - guzman
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Synopsis "derivatives and integrals of multivariable functions (in English)"
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 in analysis and differential geometry.
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The book is written in English.
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