2026 (Current Year) Faculty Courses School of Materials and Chemical Technology Common courses

Introduction to Applied Mathematical Methods II

Academic unit or major: Common courses
Instructor(s): Takuya Asayama
Class Format: Lecture (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 3-4 Tue (M-178(H1101))
Class: -
Course Code: XMC.A204
Number of credits: 100
Course offered: 2026
Offered quarter: 2Q
Syllabus updated: Mar 5, 2026
Language: Japanese

Syllabus

Course overview and goals

This course, following [Introduction to Applied Mathematical Methods I], introduces the fundamentals of mathematical methods for analyzing various phenomena that arise in science and engineering.
Students will first acquire the basic concepts and techniques of Fourier series.
They will then learn methods for solving partial differential equations using Fourier series, with the goal of being able to derive solutions to given equations.
A substantial number of practice exercises will be included to promote a thorough and solid understanding of the course material.

Course description and aims

Students are expected to
- understand and be able to explain the concept of Fourier series.
- be able to do calculations on the Fourier series of given functions.
- be able to derive solutions to given partial differential equations using Fourier series.

Keywords

Fourier series, periodic functions, partial differential equations, heat equations, wave equations

Competencies

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

Class flow

This course will be conducted in a face-to-face lecture format, including practical exercises.
Materials and objectives will be provided via Science Tokyo LMS.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Fourier series and Fourier coefficients	Fourier series / Computing the Fourier coefficients
Class 2	Relationship between the Fourier series and the original function	Convergence of Fourier series / Parseval's identity / Leibniz series
Class 3	Basel problem	Sum of the reciprocals of even powers
Class 4	Fourier cosine and sine series and the complex Fourier series	Computing the Fourier cosine and sine series / Computing the complex Fourier series
Class 5	Functions with arbitrary period	Functions with arbitrary period / Computing the Fourier series of functions with arbitrary period
Class 6	Wave equations and the Fourier series	Superposition principle / Separation of variables / Initial value and boundary value problems for wave equations
Class 7	Heat equations and the Fourier series	Initial value and boundary value problems for heat equations

Study advice (preparation and review)

For preparation, students should review the relevant sections of the textbook and lecture materials to confirm their understanding and ensure that they are ready to engage effectively in the practical exercises in each class.
After class, students should work on the exercises in the textbook and lecture materials so that they can independently reproduce and explain the content covered in class.
Both preparation and review are expected to require approximately 100 minutes each per class session.

Textbook(s)

Hideshi Yamane, Te o Ugokashite Manabu Fourier Kaiseki / Laplace Henkan (Japanese) [Fourier Analysis and Laplace Transform Through Writing], Shokabo, 2022. ISBN: 9784785315948

Reference books, course materials, etc.

Shinichi Oishi, Fourier Kaiseki (Japanese) [Fourier Analysis], Rikokei no Sugaku Nyumon Kosu, Shinsoban [Introductory Courses of Mathematics for Science and Engineering, New Edition], Iwanami Shoten, 2019. ISBN: 9784000298889

Evaluation methods and criteria

Grading will be decided based on the quizzes (30%) and the final examination (70%).

Related courses

XMC.A203 ： Introduction to Applied Mathematical Methods I

Prerequisites

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