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- 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
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- School of Computing
- School of Life Science and Technology
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School of Environment and Society
- Department of Architecture and Building Engineering
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- 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)
- Takiguchi Takashi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(H113)
- Group
- -
- Course number
- MTH.U213
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 3Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
The subject of this course is Fourier analysis. In particular, we learn a method to solve differential equations by using Fourier series. First, we learn the heat equation, the wave equation and the Laplace equation together with their basic properties as typical examples of differential equations. Then, we learn sequences of functions and series of functions as the preparation for the learning of Fourier series. Finally, we learn Fourier series and its basic properties. This course will be succeeded by [Applied Mathematics for Engineers II b] in the fourth quarter.
Fourier analysis is an absolutely essential mathematical basis of science and engineering. In this course, we learn the basic theory of Fourier analysis and a way to use it in an efficient manner.
Student learning outcomes
・Students are expected to understand basic properties of the heat equation, the wave equation and the Laplace equation.
・Students are expected to be able to calculate Fourier series of basic functions.
・Students are expected to be familiar with convergence conditions of Fourier series.
Keywords
the heat equation, the wave equation, the Laplace equation, series of functions, Fourier series
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course mixed with recitation.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | the heat equation and its fundamental properties | Details will be announced during each lecture. |
| Class 2 | the wave equation and its fundamental properties | Details will be announced during each lecture. |
| Class 3 | the Laplace equation and its fundamental properties | Details will be announced during each lecture. |
| Class 4 | sequences of functions and series of functions | Details will be announced during each lecture. |
| Class 5 | Fourier series | Details will be announced during each lecture. |
| Class 6 | properties of Fourier series | Details will be announced during each lecture. |
| Class 7 | convergence of Fourier series | Details will be announced during each lecture. |
| Class 8 | evaluation of progress | Details will be announced during each lecture. |
Textbook(s)
G. Sunouchi, Fourier analysis and applications (Japanese), Saiensu-sha,1995
Reference books, course materials, etc.
None in particular
Assessment criteria and methods
Based on overall evaluation of the results for quizzes, report and final examination. Details will be announced during a lecture.
Related courses
- MTH.U211 ： Applied Mathematics for Engineers Ia
- MTH.U212 ： Applied Mathematics for Engineers Ib
- MTH.U214 ： Applied Mathematics for Engineers Iib
Prerequisites (i.e., required knowledge, skills, courses, etc.)
This is the prerequisite course to take "Applied Mathematics for Engineers Iib".
Students are expected to have completed [Calculus I / Recitation], [Calculus II] and [Calculus Recitation II].
