A concise introduction to analysis [electronic resource] / Daniel W. Strook.
Strook, Daniel W., author.
2015
QA300
Available Online

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Title A concise introduction to analysis [electronic resource] / Daniel W. Strook.
Author Strook, Daniel W., author.
ISBN 9783319244693 electronic book
3319244698 electronic book
9783319244679
3319244671
DOI https://doi.org/10.1007/978-3-319-24469-3
Published Cham : Springer, [2015]
Language English
Description 1 online resource.
Item Number 10.1007/978-3-319-24469-3 doi
Call Number QA300
Dewey Decimal Classification 515
Summary 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 Includes index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed December 22, 2015).
Available in Other Form Print version: 3319244671
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Record Appears in Online Resources > Ebooks
All Resources
Analysis on The Real Line
Elements of Complex Analysis
Integration
Higher Dimensions
Integration in Higher Dimensions
A Little Bit of Analytic Function Theory.

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