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- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Yanagida Eiji Tanabe Masaharu
- Class Format
- Lecture / Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-8(H103)
- Group
- -
- Course number
- MTH.C204
- Credits
- 2
- Academic year
- 2018
- Offered quarter
- 4Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course is a succession of "Introduction to Analysis III" in the third quarter. We will continue to 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).
The students will learn "divergence theorem" and "Stokes' theorem" on surface integrals. They will also learn differential forms to formalize these theorems in a unified manner, as extensions of the "fundamental theorem of calculus".
Student learning outcomes
At the end of this course, students are expected to:
-- understand the tangent vectors and tangent space of surfaces
-- be able to calculate surface integrals of vector fields
-- understand the meaning of divergence theorem and Stokes' theorem
-- be able to calculate differential forms
Keywords
tangent vector, surface integral, divergence theorem, Stokes theorem,
differential forms, exterior derivative
Competencies that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Parametrization of surfaces and tangent spaces | Details will be provided in class. |
| Class 2 | Recitation | Details will be provided in class. |
| Class 3 | Surface area and surface integrals | Details will be provided in class. |
| Class 4 | Recitation | Details will be provided in class. |
| Class 5 | Gauss' divergence theorem | Details will be provided in class. |
| Class 6 | Recitation | Details will be provided in class. |
| Class 7 | Stokes' theorem | Details will be provided in class. |
| Class 8 | Recitation | Details will be provided in class. |
| Class 9 | Applications of divergence and Stokes' theorems | Details will be provided in class. |
| Class 10 | Recitation | Details will be provided in class. |
| Class 11 | Poisson's equation | Details will be provided in class. |
| Class 12 | Recitation | Details will be provided in class. |
| Class 13 | Differentia forms, wedge product, exterior derivative | Details will be provided in class. |
| Class 14 | Recitation | Details will be provided in class. |
| Class 15 | Integration of differential forms and generalized Stokes' theorem, quiz | Details will be provided in class. |
Textbook(s)
None required
Reference books, course materials, etc.
None required
Assessment criteria and methods
Final exam 50%, assignments and quizzes 50%.
Related courses
- MTH.C201 ： Introduction to Analysis I
- MTH.C202 ： Introduction to Analysis II
- MTH.C203 ： Introduction to Analysis III
- MTH.C204 ： Introduction to Analysis IV
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed
-- Calculus (I/II), Linear Algebra (I/II), and their recitations.
-- Introduction to Analysis I/II.
