▶Japanese
Post to SNS
- Home
- > School of Science
- > Undergraduate major in Mathematics
- > Applied Analysis II
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Yoneda Tsuyoshi Yoneda Tsuyoshi Onodera Michiaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Wed3-4(H112)
- Group
- -
- Course number
- MTH.C212
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 4Q
- Syllabus updated
- 2017/1/11
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
In this course, we re-consider Fourier series in the functional analysis framework, and we explain important inequalities and orthonormal system. We also explain definition and properties of Fourier transform which can be obtained as continuous limit of Fourier series. Lastly we consider several partial differential equations as applications of Fourier series and Fourier transform. This course is a continuation of Applied Analysis I.
The notions of Fourier series and Fourier transform are fundamental not only in mathematics but also in science, and are applicable to describe a wide variety of objects. On the other hand, these abstract notions are not easy to comprehend without suitable training. To that end, rigorous proofs will be given for most propositions, lemmas and theorems. Moreover we study the most fundamental PDEs such as wave, heat and Laplace's equations.
Student learning outcomes
Students are expected to study basic concepts of complex analysis. More precisely, we study Fourier series, Fourier transform, these definitions, properties and method of these calculations. These have important roles in science and technology.
Keywords
Bessel's inequality, Parseval's equality, Fourier transform, wave equation, heat equation, Laplace's equation
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 | Function spaces, Orthonormal system | Details will be provided during each class session |
| Class 2 | Bessel's inequality, Parseval's equality | |
| Class 3 | Fourier 's integral formula | |
| Class 4 | Fourier transform and Fourier inverse transform | |
| Class 5 | properties of Fourier transform | |
| Class 6 | application to wave equations | |
| Class 7 | application to heat equations | |
| Class 8 | application to Laplace's equation, comprehension check-up |
Textbook(s)
None required
Reference books, course materials, etc.
None required
Assessment criteria and methods
Students' course scores are based on final exam 50% and midterm exam 50%.
Related courses
- ZUA.C201 ： Advanced Calculus I
- ZUA.C203 ： Advanced Calculus II
- MTH.C211 ： Applied Analysis I
- 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.
