KA131001 Mathematical Analysis

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Informatics and Data Science

Lecture Code KA131001 Subject Classification Specialized Education

Subject Name 数理解析

Subject Name
（Katakana）スウリカイセキ

Subject Name in
English Mathematical Analysis

Instructor AIZAWA HIROAKI

Instructor
(Katakana) アイザワ　ヒロアキ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Mon9-10,Thur7-8：ENG 220

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Lecture

Credits 2.0 Class Hours/Week 4 Language of Instruction B : Japanese／English

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Differential Equations, Fourier Analysis, Laplace Transforms, and Physics-Informed Neural Networks

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) In this course, students are expected to learn the concept of mathematical analysis as a basis for data science, and to develop the ability to create programs to realize them.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Computer Science Program
（Knowledge and Understanding）
・D1. Knowledge and ability to understand the theoretical framework underlying computer science and to collect and process high-dimensional data through full use of information processing technology based on scientific logic.
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.

Data Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Intelligence Science Program
（Knowledge and Understanding）
・D1. A deep systematic understanding of the advanced intelligence of human beings and its realization by computers.
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.

Class Objectives
/Class Outline We discuss the concept of mathematical analysis, including ordinary differential equations, Fourier analysis, Laplace transforms, and Physics-Informed Neural Networks. For better understanding, we make the programs using Python.

Class Schedule Lesson 1. Introduction
Lesson 2. Function, derivative, and series expansion
Lesson 3. Differential equations
Lesson 4. First-order ordinary differential equations
Lesson 5. First-order linear differential equations
Lesson 6. First-order differential equations
Lesson 7. Second-order differential equations
Lesson 8. Periodic function, orthogonal functions, and inner product spaces
Lesson 9. Fourier series expansion
Lesson 10. Complex Fourier series expansion
Lesson 11. Fourier transform
Lesson 12. Laplace transform
Lesson 13. Fourier and Laplace transforms for differential equations
Lesson 14. Numerical methods for ordinary differential equations
Lesson 15. Physics-informed neural networks

Text/Reference
Books,etc. Textbook: 向谷博明，下村哲，相澤宏旭　「基礎履修応用数学」，培風館
Reference Book: 神永正博著　「Pythonで学ぶフーリエ解析と信号処理」，コロナ社
Reference Book: 金谷健一著  「これなら分かる応用数学教室--最小二乗法からウェープレットまで--」，共立出版
Reference Book: A. Boggess, F.J. Narcowich, A First Course in Wavelets with Fourier Analysis

PC or AV used in
Class,etc. Text, Handouts, Microsoft Teams

(More Details) Lecture materials are available on the support page (https://aizawan.github.io/mathematical-analysis/intro.html)  in Jupyter Notebook format. Announcements, as well as assignment and submission, will be handled via Teams.

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Reference books and textbooks will be introduced in the first lecture. Links to additional reference materials are also compiled on the support page.

Requirements Jupyter Notebook will be provided. Additionally, since assignments must be created in Jupyter Notebook, please set up a Python environment either locally or using Google Colaboratory.

Grading Method Evaluation will be based on reports and assignments.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2025Year	School/Graduate School	School of Informatics and Data Science
Lecture Code	KA131001	Subject Classification	Specialized Education
Subject Name	数理解析
Subject Name （Katakana）	スウリカイセキ
Subject Name in English	Mathematical Analysis
Instructor	AIZAWA HIROAKI
Instructor (Katakana)	アイザワ　ヒロアキ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Mon9-10,Thur7-8：ENG 220
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Lecture
Credits	2.0	Class Hours/Week	4	Language of Instruction	B : Japanese／English
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Differential Equations, Fourier Analysis, Laplace Transforms, and Physics-Informed Neural Networks
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	In this course, students are expected to learn the concept of mathematical analysis as a basis for data science, and to develop the ability to create programs to realize them.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Computer Science Program （Knowledge and Understanding）・D1. Knowledge and ability to understand the theoretical framework underlying computer science and to collect and process high-dimensional data through full use of information processing technology based on scientific logic. （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. Data Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. Intelligence Science Program （Knowledge and Understanding）・D1. A deep systematic understanding of the advanced intelligence of human beings and its realization by computers. （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
Class Objectives /Class Outline	We discuss the concept of mathematical analysis, including ordinary differential equations, Fourier analysis, Laplace transforms, and Physics-Informed Neural Networks. For better understanding, we make the programs using Python.
Class Schedule	Lesson 1. Introduction Lesson 2. Function, derivative, and series expansion Lesson 3. Differential equations Lesson 4. First-order ordinary differential equations Lesson 5. First-order linear differential equations Lesson 6. First-order differential equations Lesson 7. Second-order differential equations Lesson 8. Periodic function, orthogonal functions, and inner product spaces Lesson 9. Fourier series expansion Lesson 10. Complex Fourier series expansion Lesson 11. Fourier transform Lesson 12. Laplace transform Lesson 13. Fourier and Laplace transforms for differential equations Lesson 14. Numerical methods for ordinary differential equations Lesson 15. Physics-informed neural networks
Text/Reference Books,etc.	Textbook: 向谷博明，下村哲，相澤宏旭　「基礎履修応用数学」，培風館 Reference Book: 神永正博著　「Pythonで学ぶフーリエ解析と信号処理」，コロナ社 Reference Book: 金谷健一著「これなら分かる応用数学教室--最小二乗法からウェープレットまで--」，共立出版 Reference Book: A. Boggess, F.J. Narcowich, A First Course in Wavelets with Fourier Analysis
PC or AV used in Class,etc.	Text, Handouts, Microsoft Teams
(More Details)	Lecture materials are available on the support page (https://aizawan.github.io/mathematical-analysis/intro.html) in Jupyter Notebook format. Announcements, as well as assignment and submission, will be handled via Teams.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Reference books and textbooks will be introduced in the first lecture. Links to additional reference materials are also compiled on the support page.
Requirements	Jupyter Notebook will be provided. Additionally, since assignments must be created in Jupyter Notebook, please set up a Python environment either locally or using Google Colaboratory.
Grading Method	Evaluation will be based on reports and assignments.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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