Engineering Mathematics B2
| Numbering Code |
U-ENG23 33173 LJ73 U-ENG23 33173 LJ55 |
Year/Term | 2022 ・ First semester | |
|---|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture | |
| Target Year | Target Student | |||
| Language | Japanese | Day/Period | Fri.1 | |
| Instructor name | GOTOU HIROYUKI (Disaster Prevention Research Institute Associate Professor) | |||
| Outline and Purpose of the Course | This course lectures Fourier analysis and solution of the partial differential equations as its application. Students learn definitions and characteristics of Fourier series for periodic functions and Fourier transform for integrable non-periodic functions. The course aims to develop the ability to apply the Fourier analysis to various engineering problems. In addition, the course introduces discrete Fourier transform and its application to engineering problems. | |||
| Course Goals | Students understand Fourier series and Fourier transform together with the mathematical and physical background. Students analyze various problems on the Fourier series and the Fourier transform, and solve the partial differential equations. | |||
| Schedule and Contents |
+Day 1: Introduction What is Fourier Analysis? How to apply it? Clarify the necessary background knowledge. +Day 2-3: Fourier series A periodic function which is expanded into an infinite series of trigonometric functions is called a Fourier series. +Day 4-5: Partial differential equation I Second order partial differential equations (Laplace equation, wave equation, thermal equation, etc.) are discussed. The applications of Fourier series to initial-boundary problems are discussed. +Day 6-8: Convergence of Fourier series and Functional space Convergence behavior of Fourier series are discussed. Functional space (L2) is introduced as an application of the Fourier series. +Day 9-10: Fourier transform Fourier analysis of non-periodic function leads to the Fourier transform. The various properties of the Fourier transform is derived. +Day 11-12: Partial differential equation II Second order partial differential equations with infinite domain are discussed as the applications of Fourier transform. +Day 13: Supplement of Fourier transform Supplement contents of Fourier transform are lectured, i.e. uncertainty principle, etc. +Day 14: Discrete Fourier transform Discrete Fourier transform for digital signals is explained. +Day 15: Exercise Exercise the typical problems about Fourier analysis and partial differential equations. |
|||
| Evaluation Methods and Policy | Attendance, homeworks, midterm exam, and term-end exam. The details are introduced in the first class. | |||
| Course Requirements | Calculus, Linear Algebra, Engineering Mathematics B1. | |||
| Study outside of Class (preparation and review) | Students need to review the lecture for preparation to quiz. | |||
| Textbooks | Textbooks/References | None. | ||
| References, etc. | Useful material is introduded during the lecture. | |||
| Related URL | ||||
