63100701 Introduction to physical mathematics

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School Liberal Arts Education Program

Lecture Code 63100701 Subject Classification Area Courses

Subject Name Introduction to physical mathematics

Subject Name
（Katakana）

Subject Name in
English Introduction to physical mathematics

Instructor TANAKA SHINPEI

Instructor
(Katakana) タナカ　シンペイ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  1Term

Days, Periods, and Classrooms (1T) Thur9-10,Fri7-8：IAS J303

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

The course is in principle given as face-to-face lectures.

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

Course Level 1 : Undergraduate Introductory

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 06 : Physics

Eligible Students

Keywords Physical mathematics, Applied mathematics

Special Subject for Teacher Education 　 Special Subject 　

Class Status within
Liberal Arts Education Area Courses（Courses in Natural Sciences)　Category：Physics / Astronomy / Applied Physics
Expected Outcome Learning how to use basic mathematics to deal with basic physical problems.

Class Objectives
/Class Outline In natural science, mathematics is used as a language. You will learn how to use mathematics as a skill to solve basic physical problems. I will focus more on the intuitive understandings of mathematical concepts than on the exactness.

Class Schedule 1. Physics modeling and graphs: “change” and “total”
2. Derivative as slope and instantaneous rate
3. Basic differentiation rules
4. Using derivatives in physics: extrema and stability intuition
5. Integral as area and accumulated quantity
6. Fundamental link: derivative ↔ integral
7. Integration in 1D physics: work and energy
8. What is an ODE? From “law” to equation
9. Balance laws (conservation mindset) → first-order ODEs
10. Exponential relaxation: the most common first-order ODE
11. Drag and terminal velocity
12. Newton’s 2nd law as a second-order ODE
13. Simple harmonic motion
14. Damping and forcing (real oscillators + resonance)
15. Numerical solution and conclusions

Final examination

Text/Reference
Books,etc. Handouts are given. Text books will be assigned in the class.

PC or AV used in
Class,etc. Text, Handouts, Visual Materials

(More Details) Textbooks and handouts

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Read the handout before the lecture. When exercises are given, finish them either in the class or after class. Ask whenever you have questions.

Requirements

Grading Method Understandings of each chapter are evaluated by both final examination and reports on exercises.

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	2026Year	School/Graduate School	Liberal Arts Education Program
Lecture Code	63100701	Subject Classification	Area Courses
Subject Name	Introduction to physical mathematics
Subject Name （Katakana）
Subject Name in English	Introduction to physical mathematics
Instructor	TANAKA SHINPEI
Instructor (Katakana)	タナカ　シンペイ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Thur9-10,Fri7-8：IAS J303
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
The course is in principle given as face-to-face lectures.
Credits	2.0	Class Hours/Week	4	Language of Instruction	E : English
Course Level	1 : Undergraduate Introductory
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	06 : Physics
Eligible Students
Keywords	Physical mathematics, Applied mathematics
Special Subject for Teacher Education		Special Subject
Class Status within Liberal Arts Education	Area Courses（Courses in Natural Sciences)　Category：Physics / Astronomy / Applied Physics
Expected Outcome	Learning how to use basic mathematics to deal with basic physical problems.
Class Objectives /Class Outline	In natural science, mathematics is used as a language. You will learn how to use mathematics as a skill to solve basic physical problems. I will focus more on the intuitive understandings of mathematical concepts than on the exactness.
Class Schedule	1. Physics modeling and graphs: “change” and “total” 2. Derivative as slope and instantaneous rate 3. Basic differentiation rules 4. Using derivatives in physics: extrema and stability intuition 5. Integral as area and accumulated quantity 6. Fundamental link: derivative ↔ integral 7. Integration in 1D physics: work and energy 8. What is an ODE? From “law” to equation 9. Balance laws (conservation mindset) → first-order ODEs 10. Exponential relaxation: the most common first-order ODE 11. Drag and terminal velocity 12. Newton’s 2nd law as a second-order ODE 13. Simple harmonic motion 14. Damping and forcing (real oscillators + resonance) 15. Numerical solution and conclusions Final examination
Text/Reference Books,etc.	Handouts are given. Text books will be assigned in the class.
PC or AV used in Class,etc.	Text, Handouts, Visual Materials
(More Details)	Textbooks and handouts
Learning techniques to be incorporated
Suggestions on Preparation and Review	Read the handout before the lecture. When exercises are given, finish them either in the class or after class. Ask whenever you have questions.
Requirements
Grading Method	Understandings of each chapter are evaluated by both final examination and reports on exercises.
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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