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- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Tonegawa Yoshihiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Wed3-4(W641)
- Group
- -
- Course number
- MTH.C211
- Credits
- 1
- Academic year
- 2021
- Offered quarter
- 3Q
- Syllabus updated
- 2021/3/19
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course is intended to introduce basic concepts in the Fourier analysis, in particular, the Fourier series.
The course is followed by Applied Analysis II.
The main objective is to understand the mathematical treatment of Fourier series, which was originally introduced by Fourier himself for the purpose of solving the heat equation.
We study fundamental properties of Fourier series and its convergence, and applications to several fields in mathematics.
Student learning outcomes
Students are expected to understand basic concepts in Fourier series, in particular, mathematical treatment of Fourier series.
We also focus on computations of Fourier series expansion of given functions and applications to differential equations.
Keywords
Series of functions, Fourier series, Bessel's inequality, Riemann-Lebesgue lemma, Dirichlet kernel
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Before coming to class, students should read the course schedule and check what topics will be covered.
Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Fourier's idea and trigonometric series | Details will be provided during each class session |
| Class 2 | Complex-valued functions and series of functions | Details will be provided during each class session |
| Class 3 | Fourier series of a periodic function | Details will be provided during each class session |
| Class 4 | Convergence theorem | Details will be provided during each class session |
| Class 5 | Regularity of a function and the behavior of Fourier coefficients | Details will be provided during each class session |
| Class 6 | Fourier series on intervals | Details will be provided during each class session |
| Class 7 | Applications of Fourier series | Details will be provided during each class session |
Out-of-Class Study Time (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.
Elias Stein, Rami Shakarchi "Fourier analysis" Nippon Hyoron sha
Assessment criteria and methods
Report.
Related courses
- ZUA.C201 ： Advanced Calculus I
- ZUA.C203 ： Advanced Calculus II
- MTH.C212 ： Applied Analysis II
- MTH.C301 ： Complex Analysis I
- MTH.C302 ： Complex Analysis II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed Calculus I/Recitation and Calculus II/Recitation.
