OXFORD UNIVERSITY PRESS

Fundamentals of Mathematical Analysis

ISBN : 9780198868798

参考価格(税込): 
¥7,304
著者: 
Adel N. Boules
ページ
480 ページ
フォーマット
Paperback
サイズ
153 x 234 mm
刊行日
2021年03月
メール送信
印刷

Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and aims to achieve excellent breadth and depth and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.

目次: 

1 Preliminaries
2 Set Theory
3 Vector Spaces
4 The Metric Topology
5 Essentials of General Topology
6 Banach Spaces
7 Hilbert Spaces
8 Integration Theory

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