Applied Mathematics for Engineers Ila

Academic unit or major

Common courses

Instructor(s)

Tomoro Asai

Class Format

Lecture (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

3-4 Tue (M-110(H112))

Class

-

Course Code

XMC.A203

Number of credits

100

Course offered

2025

Offered quarter

3Q

Syllabus updated

Sep 26, 2025

Language

Japanese

Syllabus

Course overview and goals

This course allows students to learn the basics for mathematical analysis of phenomena captured through experiments and observation on the basis of the calculus and linear algebra completed in the first year.

The subject of this course is Fourier analysis. In particular, we learn a method to solve differential equations by using Fourier series. First, we learn the heat equation, the wave equation and the Laplace equation together with their basic properties as typical examples of differential equations. Then, we learn sequences of functions and series of functions as the preparation for the learning of Fourier series. Finally, we learn Fourier series and its basic properties. This course will be succeeded by [Applied Mathematics for Engineers II b] in the fourth quarter.

Fourier analysis is an absolutely essential mathematical basis of science and engineering. In this course, we learn the basic theory of Fourier analysis and a way to use it in an efficient manner.

Course description and aims

・Students are expected to understand basic properties of the heat equation, the wave equation and the Laplace equation.
・Students are expected to be able to calculate Fourier series of basic functions.
・Students are expected to be familiar with convergence conditions of Fourier series.

Keywords

the heat equation, the wave equation, the Laplace equation, series of functions, Fourier series

Competencies

• Specialist skills
• Intercultural skills
• Communication skills
• Critical thinking skills
• Practical and/or problem-solving skills

Class flow

Standard lecture course mixed with recitation.

Course schedule/Objectives

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Nakamura,”Fourier Analysis” (Asakura Publishing) (in Japanese)

Reference books, course materials, etc.

None in particular

Evaluation methods and criteria

Based on overall evaluation of the results for quizzes, report and final examination. Details will be announced during a lecture.

Related courses

• XMC.A201 ： Applied Mathematics for Engineers Ia
• XMC.A202 ： Applied Mathematics for Engineers Ib
• XMC.A204 ： Applied Mathematics for Engineers Ilb

Prerequisites

This is the prerequisite course to take "Applied Mathematics for Engineers Iib".

Students are expected to have completed [Calculus I / Recitation], [Calculus II] and [Calculus Recitation II].