▶Japanese
Post to SNS
- Home
- > School of Science
- > Undergraduate major in Mathematics
- > Applied Analysis I
- 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 Onodera Michiaki Yoneda Tsuyoshi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Wed3-4(H112)
- Group
- -
- Course number
- MTH.C211
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 3Q
- Syllabus updated
- 2017/1/11
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
The main subject of this course is basic concepts of complex analysis and Fourier series. After introducing such basic facts, we explain some typical examples of Fourier series. This course will be followed by Applied Analysis II.
Complex analysis is one of the fundamental tools in mathematics, and is applicable to a wide variety of objects. On the other hand, it is not easy to comprehend without suitable training. To that end, rigorous proofs will be given for most propositions, lemmas and theorems. Moreover, we study typical examples of complex series.
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
complex number, holomorphic function, Cauchy-Riemann relations, d'Alembert's ratio test, power series, trigonometric series, Fourier series expansion
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 | Introductory to Complex Analysis, Four arithmetic operations, complex plane, Euler's formula | Details will be provided during each class session |
| Class 2 | Power series, trigonometric series | Details will be provided during each class session |
| Class 3 | Fourier series expansion | Details will be provided during each class session |
| Class 4 | Convergence, Gibbs phenomenon | Details will be provided during each class session |
| Class 5 | sine and cosine series expansions | Details will be provided during each class session |
| Class 6 | Fourier series expansion of complex form | Details will be provided during each class session |
| Class 7 | Fourier series on general interval | Details will be provided during each class session |
| Class 8 | Fourier series of multi-variable function, comprehension check-up | Details will be provided during each class session |
Textbook(s)
to be determined
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.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.
