2024 Faculty Courses Liberal arts and basic science courses Basic science and technology courses
Calculus II M(1～10)
- Academic unit or major
- Basic science and technology courses
- Instructor(s)
- Masaharu Tanabe
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon / 1-2 Fri
- Class
- M(1～10)
- Course Code
- LAS.M105
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Based on "Calculus I", this course focuses on more rigorous mathematical analysis of the limit of sequences of numbers and functions, applications of differentiation of functions of a single variable and partial differentiation of multivariate functions, series of numbers and sequences of functions.
The aim of this course is to provide knowledge about analysis which will be important for
science and engineering.
Course description and aims
Following "Calculus I", this course aims for a deeper understanding and development of the theory of calculus.
Keywords
Limit, continuity, Taylor's theorem, series, sequence of functions
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Besides lectures, a recitation class is held every week in accordance with the progress of the lectures.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Continuity of the real numbers, supremum, infimum | Understand basic properties of real numbers. |
| Class 2 | Limits of sequences, monotone sequences, Cauchy sequences | Understand basic facts related to sequences. |
| Class 3 | Limits of functions of a single variable, continuity, maximum, intermediate value theorem | Understand the properties of continuous functions. |
| Class 4 | Differentiation, mean value theorem, limits of indeterminate forms | Understand the properties of differentiable functions. |
| Class 5 | Taylor's theorem, extremal values | Understand Taylor's theorem. |
| Class 6 | Definite integral | Understand the definition of the definite integral. |
| Class 7 | Point sets on a plane, sequences of points | Understand point sets and their properties. |
| Class 8 | Limits of multivariate functions, continuity | Understand the limit and continuity of multivariate functions. |
| Class 9 | Differentiation of multivariate functions, total derivative and partial derivative | Understand the differentiation of multivariate functions. |
| Class 10 | Taylor's theorem for multivariate functions, extremal values | Understand Taylor's theorem and extremal values. |
| Class 11 | Series, absolute convergence, conditional convergence | Understand series of numbers and their convergence. |
| Class 12 | Sequences of functions | Understand sequences of functions. |
| Class 13 | Series of functions, power series | Understand series of functions and, as a special case of them, power series. |
| Class 14 | Advanced topics | Understand some advanced topics in analysis. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None in particular.
Reference books, course materials, etc.
See the Japanese reference book above.
Evaluation methods and criteria
Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.
Related courses
- LAS.M101 ： Calculus I / Recitation
- LAS.M107 ： Calculus Recitation II
Prerequisites
Students are supposed to have completed Calculus I / Recitation (LAS.M101).
Students are recommended to take Calculus Recitation II (LAS.M107) at the same time.