Applied Mathematics for Engineering F2
| Numbering Code |
U-ENG25 32065 LJ55 U-ENG25 32065 LJ75 |
Year/Term | 2022 ・ First semester | |
|---|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture | |
| Target Year | Target Student | |||
| Language | Japanese | Day/Period | Tue.2 | |
| Instructor name |
KANOU MANABU (Graduate School of Informatics Professor) OHTSUKA TOSHIYUKI (Graduate School of Informatics Professor) |
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| Outline and Purpose of the Course | Fourier analysis and its application will be described. The major part consists of Fourier series, Fourier transform, and Laplace transform. | |||
| Course Goals | The goal is to understand the basics and applications of Fourier analysis. | |||
| Schedule and Contents |
Preliminaries,1time,The goal and outline of this class are presented. Then, basic knowledge necessary to learn Fourier analysis is briefly reviewed. Fourier series,1time,Fourier series expansion of periodic functions is described. Complex Fourier series,1time,Complex Fourier series, its differential and integral, and spectrum are described. Characteristics of Fourier series,1time,Characteristics of Fourier series are described. Fourier transform,1time,In order to cope with aperiodic functions, Fourier transform is described. Characteristics and applications of Fourier transform is explained together with the Parseval's equation and its applications. Linear systems,1time,Linear systems is described. Solutions of linear differential equations are given by using Fourier series expansion. In addition, impulse responses and transfer functions of linear systems are explained. Summary of the first half,1time,A summary of Fourier series and Fourier transform is provided, and an examination will be given. Parseval's equality and its applications,1time,Parseval's equality, the Wiener–Khinchin theorem, and the relationship between impulse responses and cross-correlation functions in linear systems are described. Introduction to partial differential equations,1time,Basic notions of partial differential equations are described. Solutions of the wave equation and their physical interpretations,1time,The wave equation, one of important partial differential equations, is solved and physical interpretations of its solutions are discussed. Fourier series for solving the wave equation,1time,Another expressions of solutions to the wave equation are derived in the form of Fourier series expansions. Introduction to Laplace transform ,1time,Laplace transform and its characteristics are described aiming at solving ordinary differential equations. Laplace transform for solving ordinary differential equations,1time,Ordinary differential equations are solved by applying Laplace transform and its inverse transform. Discrete Fourier transform and fast Fourier transform ,1time,Discrete Fourier transform for analyzing sampled data is described. Evaluation of achievement,1time,The achievements are evaluated. |
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| Evaluation Methods and Policy | The regular examination, assignments, and attitude in the class will be taken into account. | |||
| Course Requirements | None | |||
| Textbooks | Textbooks/References | Shinichi Ohishi: Fourier Analysis, Iwanami-Shoten isbn{}{9784000077767} | ||
| Related URL | ||||
