Continuous Functions of Vector Variables

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Product Description

This is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. The author covers boundedness, extreme values, and uniform continuity of functions, along with connections between continuity and topological concepts such as connectedness and compactness. The order of topics mimics the order of development in elementary calculus, with analogies and generalizations from such familiar ideas as the Pythagorean theorem.

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Continuous Functions of Vector Variables Review

I think this is one of the best introduction book to analysis and to multivariable calculus at the same time. it is more intesive than ross elementary analysis but less intensive than spivak and rudins. one reading this book will not need a multivariable calculus background to study this advance topic. though it is reserve for students who lack a some what mathematical maturity, it is still an excellent book, because it makes the students understand the subject.from there a student can advance further. the only problem with this book is that the problems are a bit routine. Guzman should have put nonclassic problems i.e. challenging problems.

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