## Engineering Mathematics B2

JA | EN

 科目ナンバリング U-ENG23 33522 LE55 U-ENG23 33522 LE73 開講年度・開講期 2020・前期 単位数 2 単位 授業形態 講義 対象学生 学部生 使用言語 英語 曜時限 金1 教員 SCHMOECKER，Jan-Dirk（工学研究科 准教授） 授業の概要・目的 This course deals with Fourier analysis and with the solution of partial differential equations as its application. It discusses Fourier series for periodic functions and its relation to integrable non-periodic functions. Once the student gets familiar with its characteristics, the course aims to develop the ability to apply Fourier analysis to various engineering problems. The lecture emphasises the relationship between the numerical analysis and today’s applications. 到達目標 To get students acquainted with an understanding of Fourier series analysis and its basic concepts. Further, to get students familiar with the various types of partial differential equations and their applications. 授業計画と内容 Week 1: Introduction, What is Fourier Analysis? How to apply it? Clarify the necessary background knowledge.Weeks 2-5: Fourier series, A periodic function which is expanded into an infinite series of trigonometric functions is called a Fourier series. Convergence behaviour and series properties are discussed with specific example calculations.Weeks 6-10: Fourier transform, Fourier analysis of non-periodic function leads to the Fourier transform. The first class of functions is the actual Fourier integral. The lecture discusses how it represents the non-periodic functions and shows the various properties of the Fourier transform. Students ability to use the Fourier transform is improved through examples. The relationship to the Laplace transform is further discussed.Weeks 11-13: Application to Partial Differential Equations,4回,In the last part of this course well known partial differential equations (Laplace equation, wave equation, heat equation, etc.) are discussed. The application of Fourier series and Fourier transform is discussed to obtain specific solutions to boundary value.Week 14: Numerical Fourier analysis, Fast Fourier transform (FFT) is a basic Fourier transform algorithm. In this lecture it is explained and a software illustration provided.This is followed by final exam in feedback class 成績評価の方法・観点 Participation, assignment and 2 tests (mid and end) 履修要件 Calculus, Linear Algebra, Engineering Mathematics B1. 授業外学習（予習・復習）等 Regular homeworks will be given that review the class content. 教科書 Handouts will be given in class. Textbooks and other material are introduced in class. 参考書等 Pinkus, A. and Zafrany,S.: Fourier Series and Integral Transforms, Cambridge University Press. isbn0521597714 Further material is introduced during classes. 