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功能分析2010
Functional analysis 2010 |
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| 课程网址: |
http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c9eec1dc...
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| 主讲教师: |
信息不详。欢迎您在右侧留言补充。
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| 开课单位: |
诺丁汉大学
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| 开课时间: |
信息不详。欢迎您在右侧留言补充。
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| 课程语种: |
英语
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| 中文简介: |
这是一个模块框架。它可以在线观看或下载为zip文件。2010年秋季学期。泛函分析从线性代数和度量拓扑的结合开始。这些工作以一种非常有效的方式来阐明微分方程所产生的问题。在函数的无限维空间中寻找解。这个模块通过建立主要定理(部分归功于伟大的波兰数学家Stefan Banach)和探索它们的不同结果为我们铺平了道路。所涉及的主题包括:–范数拓扑与拓扑同构;mdash;算子的有界性;mdash;紧性和有限维数;mdash;泛的扩展;mdash;弱*密实度;mdash;序列空间和对偶性;mdash;巴拿赫代数的基本性质。适合:本科四年级学生Dr . Joel F. Feinstein数学科学学院Dr . Joel Feinstein是诺丁汉大学纯数学副教授。在剑桥大学读完数学之后，他在利兹大学攻读博士学位。他在利兹做了一年的博士后，然后在梅努斯(爱尔兰)做了两年的讲师，然后在诺丁汉找到了一个固定的职位。他的主要研究兴趣是泛函分析，特别是交换巴拿赫代数。范斯坦博士发表了两篇关于他在本科生数学教学中使用信息技术的案例研究。2009年，范斯坦博士因在这一领域的成功创新而获得诺丁汉大学迪林勋爵教学奖。
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| 课程简介: |
This is a module framework. It can be viewed online or downloaded as a zip file. As taught Autumn semester 2010. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include: – norm topology and topological isomorphism; – boundedness of operators; – compactness and finite dimensionality; – extension of functionals; – weak*-compactness; – sequence spaces and duality; – basic properties of Banach algebras. Suitable for: Undergraduate students Level Four Dr Joel F. Feinstein School of Mathematical Sciences Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.
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| 关 键 词: |
模块框架; zip文件; 功能分析
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| 课程来源: |
信息不详。欢迎您在右侧留言补充。
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| 最后编审: |
2018-12-17：wrq
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| 阅读次数: |
20
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