2020/2021
Research Seminar "Geometric Foundations of Analysis"
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Instructors:
Mikhail V. Finkelberg
Language:
English
ECTS credits:
6
Contact hours:
60
Course Syllabus
Abstract
We introduce and study the basic notions of analysis: metric spaces, continuity, differentiation and integration. We also prove some applications, such as the mean value theorem, and Cauchy inequality.
Learning Objectives
- The goal of the course is to teach the students to handle the basic notions of analysis: metric spaces, continuity, differentiation and integration.
Expected Learning Outcomes
- The students learn the notion of metric spaces
- The students learn the notion of continuous maps
- The students learn the notion of complete metric spaces
- The students learn the notion of compactness
- The students learn the notion of absolutely convergent series
- The students learn the notion of differentiation
- The students learn the mean value theorem and its applications
- The students learn the notion of integration
Course Contents
- Metric spacesWe define metric spaces and study their basic properties
- Continuous mapsWe define continuous maps and study their basic properties
- IntegrationWe define integration and study its basic properties
- The mean value theoremWe prove the mean value theorem and discuss its applications.
- DerivativesWe define derivatives of functions of one real variable and study their basic properties.
- Absolutely convergent seriesWe define absolutely convergent series and study their properties
- CompactnessWe define compact metric spaces and study their basic properties
- Complete metric spacesWe define complete metric spaces and study their basic properties
