This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one theorem upon the other, enriching the development with numerous explanatory remarks and historical footnotes. In this title, a number of well chosen illustrative examples and counterexamples clarify the theory and teach the reader how to apply it to solve problems in mathematics and other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Brouwer's fixed point theorem, Picard's theorem and the Weierstrass approximation theorem are discussed in stared sections.
About Martin Moskowitz
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Author  :  Martin Moskowitz 
Publisher  :  World Scientific Publishing Co Pte Ltd 
Data Published  :  04 January 2020 
ISBN  :  9814299278 
EAN  :  9789814299275 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  450 pages 
Age +  :  18 years 
Language  :  English 
Rating  : 
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