A Concise Introduction to Analysis

Daniel W. , Stroock


anglais | 10-11-2015 | 232 pages

9783319244679

Livre de poche


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Couverture / Jaquette

This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions.
Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text.
A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.

Note biographique

Before he retired, Stroock had been on the faculty of several universities, most recently M.I.T. The majority of his work has to do with analytic aspects of probability theory, especially the application of probability theory to partial differential equations. He is a member of the American Mathematical Society, the American Academy of Arts and Sciences, the National Academy of Sciences, and the Polish Academy of Arts and Sciences.

Fonctionnalité

Unique owing to its conciseness and brevity of the subject matter

Contains topics unusual in other texts at this level, such as the proof of the prime number theorem

Covers polar coordinates and the divergence theorem, applying these to derivation of Cauchy's integral formula

Table des matières

Analysis on The Real Line.- Elements of Complex Analysis.- Integration.- Higher Dimensions.- Integration in Higher Dimensions.- A Little Bit of Analytic Function Theory.

Détails

Code EAN :9783319244679
Auteur(trice): 
Editeur :Springer International Publishing-Springer Nature Switzerland-Springer International Publishing
Date de publication :  10-11-2015
Format :Livre de poche
Langue(s) : anglais
Hauteur :235 mm
Largeur :155 mm
Epaisseur :13 mm
Poids :359 gr
Stock :Impression à la demande (POD)
Nombre de pages :232
Mots clés :  Analytic Function Theory; Cauchy's Formula; Cauchy's integral formula; Divergence Theorem; Fubini's Theorem; Polar Coordinates; Real Analysis; Riemann Integration Theory; advanced calculus; analytic functions; mathematical analysis