2026 (Current Year) Faculty Courses School of Materials and Chemical Technology Common courses
Introduction to Applied Mathematical Methods I
- 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 (WL1-201(W521))
- Class
- -
- Course Code
- XMC.A203
- Number of credits
- 100
- Course offered
- 2026
- Offered quarter
- 1Q
- Syllabus updated
- Mar 5, 2026
- Language
- Japanese
Syllabus
Course overview and goals
This course 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 transform.
They will then learn methods for solving partial differential equations using Fourier transform, 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 transform.
- be able to do calculations on the Fourier transform and the inverse Fourier transform of given functions.
- be able to derive solutions to given partial differential equations using Fourier transform.
Keywords
Fourier transform, convolution, 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 transform |
Computing the Fourier transform / Properties of Fourier transform / Gaussian function |
| Class 2 | Inverse Fourier transform |
Inverse Fourier transform / Fourier inversion formula / Fourier integral formula |
| Class 3 | Convolution |
Definition of convolution / Relationship between Fourier transform and convolution |
| Class 4 | Parseval–Plancherel theorem |
Inner products and norms / Parseval–Plancherel theorem |
| Class 5 | Dirac delta function |
Properties of the Dirac delta function |
| Class 6 | Heat equations and Fourier transform |
Deriving solutions to given heat equations using Fourier transform |
| Class 7 | Wave equations and Fourier transform |
Deriving solutions to given wave equations using Fourier transform / d'Alembert formula |
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.A204 ： Introduction to Applied Mathematical Methods II
Prerequisites
Students are expected to have completed [Calculus I / Recitation], [Calculus II] and [Calculus Recitation II].