分析简介 An Introduction to Analysis 英文原版 Robert C Gunning
基本信息
出版社 : Princeton University Press (2018年3月20日)
语言 : 英语
精装 : 384页
ISBN-10 : 0691178798
ISBN-13 : 978-0691178790
商品重量 : 907 g
尺寸 : 185.4 x256.5 x 27.9 mm
页面参数仅供参考，具体以实物为准
书籍简介
一本关于代数、拓扑和微积分的本科基本教科书
对于想要获得高等数学学位的本科生来说，分析导论是代数、拓扑学和微积分基本成果必学的知识。适合在一年的课程中使用，这独特的教科书还引进学生需要加强的技能——严格的证明和正式的数学写作
通过一系列的问题，《分析简介》从一开始处理n维微积分-微分，黎曼积分，级数，微分形式和斯托克斯定理-使学生谁是认真的数学进步更快的更有挑战性的主题。这本书讨论点集拓扑的基本材料，如赋范和度量空间，拓扑空间，紧集，和贝尔范畴定理。它还涵盖了线性代数，包括向量空间、线性映射、约当范式、双线性映射和正规映射。
在课堂上得到证明，《分析简介》是第一本把这些主题集中在一个易于使用的大主题下的教科书。
提供了一个严谨的微积分入门在一个和几个变量
向学生介绍基本的拓扑结构
涵盖线性代数的主题，包括矩阵、行列式、约当范式，以及双线性和正规映射
讨论了n维的微分形式和斯托克斯定理
也涵盖黎曼积分，可积性，反常积分，和级数展开
An essential undergraduate textbook on algebra, topology, and calculus
An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.
With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning―differentiation, the Riemann integral, series, and differential forms and Stokes's theorem―enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.
Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.
Provides a rigorous introduction to calculus in one and several variables
Introduces students to basic topology
Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings
Discusses differential forms and Stokes's theorem in n dimensions
Also covers the Riemann integral, integrability, improper integrals, and series expansions
名人推荐
Gunning的书是一本很棒的分析入门书，它准确地介绍了一门荣誉分析课程应该包括哪些内容。写作严谨而生动，其中包含了许多有趣的数学知识。——wilhelm Schlag，芝加哥大学
"Gunning's book is a great introduction to analysis that presents precisely what an honors analysis course should include. The writing is rigorous but lively, and much interesting mathematics is packed in it."―Wilhelm Schlag, University of Chicago
“每个未来的硕士学生都应该通过这本奇妙的书，以掌握分析的基础知识。”Donninger，国际数学新闻
"Every prospective master’s student should work through this fantastic book in order to acquire a sound background on the fundamentals of analysis."---R. Donninger, International Math News
作者简介
Robert C. Gunning是普林斯顿大学的数学教授。他的著作包括关于黎曼曲面的讲座和关于复杂分析变体的讲座(都在普林斯顿大学)。
Robert C. Gunning is professor of mathematics at Princeton University. His books include Lectures on Riemann Surfaces and Lectures on ComplexAnalytic Varieties (both Princeton).
