A Concise Introduction to Analysis

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book A Concise Introduction to Analysis by Daniel W. Stroock, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Daniel W. Stroock ISBN: 9783319244693
Publisher: Springer International Publishing Publication: October 31, 2015
Imprint: Springer Language: English
Author: Daniel W. Stroock
ISBN: 9783319244693
Publisher: Springer International Publishing
Publication: October 31, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book The New Generation of Computable General Equilibrium Models by Daniel W. Stroock
Cover of the book The EU's Common Security and Defence Policy by Daniel W. Stroock
Cover of the book The United Kingdom’s Defence After Brexit by Daniel W. Stroock
Cover of the book Russia’s Domestic Security Wars by Daniel W. Stroock
Cover of the book Soluble Bio-based Substances Isolated From Urban Wastes by Daniel W. Stroock
Cover of the book Developing Language Teachers with Exploratory Practice by Daniel W. Stroock
Cover of the book Competition and Conflicts on Resource Use by Daniel W. Stroock
Cover of the book Electric Vehicle Systems Architecture and Standardization Needs by Daniel W. Stroock
Cover of the book Web and Big Data by Daniel W. Stroock
Cover of the book Macrophages by Daniel W. Stroock
Cover of the book Spin and Charge Ordering in the Quantum Hall Regime by Daniel W. Stroock
Cover of the book Education in Post-Conflict Transition by Daniel W. Stroock
Cover of the book Yeasts in Natural Ecosystems: Diversity by Daniel W. Stroock
Cover of the book Avalanches in Functional Materials and Geophysics by Daniel W. Stroock
Cover of the book Towards the Implementation of the New Urban Agenda by Daniel W. Stroock
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy