| Course title | |||||
| フーリエ解析および演習 [Fourier Analysis & Practices] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 3 | |
| Department | Year | 2～4 | Semester | 1st | |
| Course type | 1st | Course code | 022703 | ||
| Instructor(s) | |||||
| 田中 洋介 [TANAKA Yosuke] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
| This course provides the students with an introduction to Fourier analysis. It covers Fourier series, Fourier transform, and Laplace transform as well. |
| Expected Learning |
|
Learners who successfully complete this course will be able to understand the concept of Fourier analysis and apply it to solve various types of mathematical problems in the field of electrical and electronic engineering including electric circuits, communication system, coding, encryption, and wave analysis. See the Curriculum maps. |
| Course schedule |
|
1.Mathematical preparation □ Periodic function □ Complex number and complex expression □ Even and odd functions 2.Fourier series(I) □ Fourier sine and cosine series 3.Fourier series(II) □ Complex Fourier series 4.Fourier transform □ Fourier integrals □ Characteristics of Fourier transform 5.Hyperfunctions(I) □ Delta function □ Fourier transform of delta function 6.Hyperfunctions(II) □ Fourier transform of periodic function □ Fourier transform of unit-step function 7.Convolution □ Convolution □ Convolution theorem and Parseval's theorem □ Nyquist-Shannon sampling theorem 8.Correlation □ Correlation □ Fourier transform of correlation function 9.Application to linear differential equation □ Linear differential equation 10. Linear system □ Linear system 11. Application to electrical circuit □ Electrical circuit equation □ Electrical circuit equation with sinusoidal source □ Electrical circuit equation with periodic non-sinusoidal source □ Electrical circuit equation with non-periodic non-sinusoidal source 12.Laplace transform □ Laplace transform □ Characteristics of Laplace transform □ Inverse Laplace transform 13. Application of Laplace transform to differential eequation □ Differential equation □ Relation between Fourier and Laplace transforms 14. Summary 15. Term Exam. |
| Prerequisites |
|
High-school- level knowledge of mathematics including calculus, trigonometric function, and complex numbers. Students are expected to have the standard amount of time to prepare for and review the lecture as specified by the University. |
| Required Text(s) and Materials |
| 黒川・小畑著：演習で身につくフーリエ解析（共立出版） |
| References |
|
H.P.スウ著、佐藤訳「フーリエ解析」森北出版 松尾著「やさしいフーリエ変換」森北出版 小暮著「なっとくするフーリエ変換」講談社 |
| Assessment/Grading |
|
Homework assignments, quizzes, and term exam |
| Message from instructor(s) |
| Course keywords |
| Office hours |
| Tuesday 15:00-16:00 (@N1-206A) |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/14/2019 2:42:52 PM |