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所在平台: Udemy |
课程主页: https://www.udemy.com/course/functional-analysis-1/
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课程名称：功能分析（第一部分） 课程概述：该课程主要关注度量空间，为深入理解功能分析的后续部分（功能分析第二部分）奠定基础。课程采用著名的《功能分析及其应用》一书，作者为埃尔温·克雷斯齐格。课程主要内容包括：度量空间的定义及其性质，诱导度量、广义三角不等式等基本概念，以及常见的度量空间示例，如：普通度量空间、欧几里得平面ℝ²、欧几里得空间ℝ³、函数空间C[a,b]、空间ℓ∞（L-infinity）、空间Lᵖ、界限函数空间B(A)、序列空间等。 课程还涵盖了几条有用的不等式，包括霍尔德不等式、明科夫斯基不等式、柯西-施瓦茨不等式以及辅助不等式。此外，课程中包含了习题及其解答，帮助学生巩固所学知识。 课程中还会探讨以下主题（目前以印地语/乌尔都语附英文字幕上传，之后将提供英文版）：可分离空间和完备度量空间。第一章的所有小节、示例和习题均以简单易懂的方式进行解释，希望学生能从视频讲座中学习到很多，并给予积极反馈。完成本课程后，建议学生学习功能分析第二部分，其中将通过视频讲解教材的第二章内容。
This course Functional Analysis (part1) mainly focuses on Metric spaces. It provides a good material to understand the ideal of metric spaces to start Functional Analysis-2. The Book followed for this course is the famous text on Functional Analysis and its Applications written by Erwin Kreyszig.Main contents of the course are as follows:Definition of Metric Spaces with Properties Some Basic Ideas including, induced metric, generalized triangle inequalityBasic Examples of Metric Space The usual metric space The Euclidean Plane ℝ² The Euclidean Space ℝ³ The Function Space C[a,b] The Space ℓ∞ (L-infinity) The Space Lᵖ The Space B(A) of Bounded Functions The Sequence Space 's'Some useful Inequalities are derived Holder Inequality Minkowski Inequality Cauchy - Schwarz Inequality An Auxiliary InequalityStudent Exercises with solutions are explained.Following topics are being worked (They are uploaded in Hindi/Urdu with english subtitles, soon they will be available in English)Separable spacesComplete metric spaces All of the sections, Examples and Exercises from the first chapter of this book are explained by me in simple way. i hope the students will learn much from my video lectures and will give me positive feed back. After completing this course the students are recommended to take Functional Analysis-2 in which second chapter of the textbook is explained in videos.
