## Course Title : Engineering Mathematics B2

Code 35220 3rd year Thursday・2 kyotsu4 2 Lecture English Schmöcker,

### 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

Participation, assignment and 2 tests (mid and end)

### 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 4 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 5 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.
Application to Partial Differential Equations 4 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.
Numerical Fourier analysis 1 Fast Fourier transform (FFT) is a basic Fourier transform algorithm. In this lecture it is explained and a software illustration provided.

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### Textbook(supplemental)

Pinkus, A. and Zafrany,S.: Fourier Series and Integral Transforms, Cambridge University Press. Further material is introduced during classes.

### Prerequisite(s)

Calculus, Linear Algebra, Engineering Mathematics B1.

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