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. Review of predicate logic,
Exercises1:predicate logic 		Review of the high school mathematics 240minutes
2. Continuity of real numbers Review of a previous lecture 240minutes
3. upper bound and lower bound, Archimedean property Review of a previous lecture 240minutes
4. Exercises 2: upper bound and lower bound Review of a previous lecture 240minutes
5. Definition of Limit for real sequences (epsilon-N definition) Review of a previous lecture 240minutes
6. Property of Limit for real sequences,
Exercises 3: Limit of real sequence 		Review of a previous lecture 240minutes
7. Monotone sequences, method of diminishing intervals Review of a previous lecture 240minutes
8. Bolzano-Weierstrass theorem, Cauchy sequence Review of a previous lecture 240minutes
9. upper limit and lower limit for real sequence Review of a previous lecture 240minutes
10. Property of limit for real function Review of a previous lecture and Mathematics 1 240minutes
11. Definition of continuous function (ε-δ) Review of a previous lecture and Mathematics 1 240minutes
12. Mean value theorem Review of a previous lecture and Mathematics 1 240minutes
13. Exercises 4: continuous function 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 Exercises Total.
1. 15% 10% 5% 30%
2. 20% 10% 10% 40%
3. 15% 10% 5% 30%
Total. 50% 30% 20% -
Evaluation method and criteria
Examination, report and exercises
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
I introduce textbooks in the first lecture.
Prerequisites
Differential and Integral Calculus 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 applicable
N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sat Sep 09 06:06:37 JST 2023