## Course Title : Engineering Mathematics B2

Code 31730 3rd year Friday・1 Kyotsu155 2 No Restriction Lecture Japanese H. Gotoh,

### Course Description

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.

### Grading

Attendance, homeworks, midterm exam, and term-end exam.

### Course Goals

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.

### Course Topics

Theme Class number of times Description
Introduction 1 What is Fourier Analysis? How to apply it? Clarify the necessary background knowledge.
Fourier series 5 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.
Fourier transform 3 Fourier analysis of non-periodic function leads to the Fourier transform. The lecture discusses how to represent the non-periodic functions and shows the various properties of the Fourier transform using examples. The relationship to the Laplace transform is further discussed.
Application to Partial Differential Equations 4 Second order partial differential equations (Laplace equation, wave equation, thermal equation, etc.) are discussed. The applications of Fourier series and Fourier transform to initial-boundary problems are discussed.
Achievement confirmation 1 A qestion-and-answer meeting is carried out. The answer of the term-end exam is posted on KULASIS after the exam.
1
1

None.

### Textbook(supplemental)

Useful material is introduded during the lecture.

### Prerequisite(s)

Calculus, Linear Algebra, Engineering Mathematics B1.

KULASIS