2025 (Current Year) Faculty Courses School of Science Undergraduate major in Mathematics
Introduction to Analysis III
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Hideyuki Miura / Masaharu Tanabe
- Class Format
- Lecture/Exercise
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MTH.C203
- Number of credits
- 110
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
In this course we will teach "vector calculus", that is a calculus for scalar fields (single-valued functions) and vector fields (multivalued functions) . Each lecture will be followed by a recitation (a problem-solving session). This course will be succeeded by "Introduction to Analysis IV" in the fourth quarter.
The students will learn basic operations of vector fields, such as "divergence" or "rotation". They will also learn "Green's theorem", which is a multivariable analogue of "the fundamental theorem of calculus".
Course description and aims
At the end of this course, students are expected to:
-- be able to calculate inner and outer products
-- be able to calculate line integrals of vector fields along curves
-- be familiar with parametrization of curves and surfaces
-- understand the meaning of gradient, divergence, and rotation, and be able to calculate them
-- understand what Green's theorem means and know how to use it
Keywords
Outer product, vector fields, line integral, gradient, divergence, rotation, Green's theorem on the plane
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course with recitation sessions. Homework will be assigned every week. There will be occasional quizzes.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Outer product of vectors and derivatives of multivalued functions | Details will be provided in class. |
| Class 2 | Recitation | Details will be provided in class. |
| Class 3 | Curves and surfaces in the space | Details will be provided in class. |
| Class 4 | Recitation | Details will be provided in class. |
| Class 5 | scalar fields and gradient vectors | Details will be provided in class. |
| Class 6 | Recitation | Details will be provided in class. |
| Class 7 | Line integrals of vector fields | Details will be provided in class. |
| Class 8 | Recitation | Details will be provided in class. |
| Class 9 | Green's theorem and its application | Details will be provided in class. |
| Class 10 | Recitation | Details will be provided in class. |
| Class 11 | Divergence and rotation of vector fields | Details will be provided in class. |
| Class 12 | Recitation | Details will be provided in class. |
| Class 13 | Surface integrals and divergence theorem | Details will be provided in class. |
| Class 14 | Recitation | Details will be provided in class. |
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 required
Reference books, course materials, etc.
None required
Evaluation methods and criteria
Based on the final exam, quizzes, and the problem solving situation in the recitation sessions. Details will be provided in the class.
Related courses
- MTH.C201 ： Introduction to Analysis I
- MTH.C202 ： Introduction to Analysis II
- MTH.C204 ： Introduction to Analysis IV
Prerequisites
Students are expected to have passed
-- Calculus (I/II), Linear Algebra (I/II), and their recitations.
-- Introduction to Analysis I/II.