英文原版 An Introduction to Analysis 分析导论 精装 Robert C. Gunning 英文版 进口英语原版书籍
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作者Robert C. Gunning
出版社Princeton University Press
ISBN9780691178790
出版时间2018-03
装帧精装
定价548元
货号YB-59570
上书时间2024-03-31
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内容摘要
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
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