A course in mathematical analysis

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A course in mathematical analysis / D.J.H. Garling

資料種別:: 電子ブック
形態:: 1 online resource (xvi, 300 p.)
著者名:: Garling, D. J. H.
ISBN:: 9781139424493 [1139424491] (: electronic bk)
書誌ID:: EB00000276

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Title from publisher's bibliographic system (viewed on 05 Oct 2015).
The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.

主題:

Mathematical analysis

言語:

英語

目次情報:

Foundations and Elementary Real Analysis / Volume 1：

Introduction

Prologue: The Foundations of Analysis: / Part I：

The axioms of set theory / 1：

Number systems / 2：

Functions of a Real Variable: / Part II：

Convergent sequences / 3：

Infinite series / 4：

The topology of R / 5：

Continuity / 6：

Differentiation / 7：

Integration / 8：

Introduction to Fourier series / 9：

Some applications / 10：

Appendix: Zorn's lemma and the well-ordering principle

Index

Foundations and Elementary Real Analysis / Volume 1：

Introduction

Prologue: The Foundations of Analysis: / Part I：

The axioms of set theory / 1：

Number systems / 2：

Functions of a Real Variable: / Part II：

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