COURSE IN ANALYSIS, A - VOLUME I: INTRODUCTORY CALCULUS, ANALYSIS OF FUNCTIONS OF ONE REAL VARIABLE

Jacob, Niels; Evans, Kristian P

ISBN 10: 9814689084 / ISBN 13: 9789814689083

Editore: World Scientific Publishing Company, 2015

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Dati bibliografici

• Titolo: COURSE IN ANALYSIS, A - VOLUME I: INTRODUCTORY CALCULUS, ANALYSIS OF FUNCTIONS OF ONE REAL VARIABLE
• Editore: World Scientific Publishing Company
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 9814689084
• ISBN 13: 9789814689083
• Rilegatura: Rilegato
• Condizione: New

Descrizione articolo

Riassunto

Volume 1 covers the content of two typical modules in undergraduate course for mathematics: Part 1: Introductory calculus Part 2: Analysis of functions of one variable These two parts are divided into 32 chapters. Part 1 begins with an overview of a set of real numbers: rational and irrational. This is accompanied by a discussion of arithmetic rules, inequalities, absolute values. Doing this, the authors, in a clever way, introduce elements of a set theory using Cantor's approach. This is followed by the definition of a function and discussion of operations on functions. From this they move to differential and integral calculus and their applications.Part 2 contains rigorous proofs of theorems from Part 1. In particular, they introduce the order structure on a real line using axioms of an ordered field. It is worth mentioning that Part 2 contains elements of topology obviously on real line and a good insight on convex functions. The convex functions relate Analysis to linear spaces equipped with norm. Finally, to close Part 2 the authors supply a number of Appendices, among them Appendices on logic, set theory and Peano axioms.Remarkably, Volume 1 contains 360 problems with complete solutions.

Recensione

This is a very good book for anyone interested in learning analysis. I highly recommend this book to anyone teaching or studying analysis at an undergraduate level. --Zentralblatt MATH

What I find interesting and appealing about Jacob and Evan's book is the philosophy or spirit of mathematical curriculum that the authors promote. --MAA Reviews

The writing style is generally quite clear, and students should have little difficulty reading this book. The full seven-volume collection will no doubt be an indispensable reference for analysts and non-analysts alike, and this volume is an excellent start. --Mathematical Gazette