Course title
V03107001
Fundamentals of mathematical analysis

 enomoto yuko Click to show questionnaire result at 2018
Course description
This is a course on basic analysis. Student will learn concept in basic analysis including Archimedean property, Bolzano-Weierstrass theorem, Cauchy sequence, epsilon-delta definition and Uniform continuous functions.
Purpose of class
The purpose of this class is to understand basic theory of analysis, to be able to prove a limit of real sequence using epsilon-N definition and to be able to prove continuity of function using epsilon-delta definition.
Goals and objectives
  1. To understand continuity of real number
  2. To understand epsilon-N definition and to be able to prove a limit of real sequence using epsilon-N definition
  3. To understand epsilon-delta definition and to be able to prove continuity of function using epsilon-delta definition
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Dedekind cut Review of the high school mathematics and Mathematics 1 240minutes
2. upper bound and lower bound, Archimedean property Review of a previous lecture 240minutes
3. Limit of real sequence 1: epsilon-N definition Review of a previous lecture 240minutes
4. Limit of real sequence 2: property of a limit Review of a previous lecture 240minutes
5. Monotone sequences Review of a previous lecture 240minutes
6. Subsequence Review of a previous lecture 240minutes
7. Limit of real sequence 3: Bolzano-Weierstrass theorem Review of a previous lecture 240minutes
8. Limit of real sequence 4: Cauchy sequence Review of a previous lecture 240minutes
9. Limit of real sequence 5: upper limit and lower limit Review of a previous lecture 240minutes
10. Limit of function: epsilon-delta definition Review of a previous lecture and Mathematics 1 240minutes
11. Continuous function 1: epsilon-delta definition and mean value theorem Review of a previous lecture and Mathematics 1 240minutes
12. Property of continuous funtions Review of a previous lecture and Mathematics 1 240minutes
13. Uniform continuous functions Review of a previous lecture 240minutes
14. Examination Review of a previous lecture 240minutes
Total. - - 3360minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Examination Report Total.
1. 10% 10% 20%
2. 30% 10% 40%
3. 30% 10% 40%
Total. 70% 30% -
Evaluation method and criteria
Examination and report
Textbooks and reference materials
I introduce textbooks in the first lecture.
Prerequisites
Mathematics 1
Office hours and How to contact professors for questions
  • Before or after the lecture
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Education related SDGs:the Sustainable Development Goals
    Last modified : Sat Mar 21 13:03:15 JST 2020