HC280000 Mathematics for Physics C

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HC280000 Subject Classification Specialized Education

Subject Name 物理数学Ｃ

Subject Name
（Katakana）ブツリスウガクC

Subject Name in
English Mathematics for Physics C

Instructor ISHIKAWA KENICHI

Instructor
(Katakana) イシカワ　ケンイチ

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

Days, Periods, and Classrooms (1st) Tues1-2：SCI E002 AV

Lesson Style Lecture Lesson Style
(More Details) 　

Lecturer shows, demonstrates  and explains the contents on text slides. Detailed algebraic manipulation will be explicitly shown on an electric note. Attendees are required to transcribe, summarize and understand them on your note.
We will use the MS teams and Moodle.  The class materials are distributed via Moodle. A homework will be assigned every class, the homework report should be submitted via Moodle. The class will be recorded in the MS temas and the record will be uploaded on Moodle.

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Semester No. 3

Keywords complex analysis, partial differential equations, Fourier transformations.

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Some mathematics appearing broadly in physics will be presented.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Physics
（Abilities and Skills）
・Mathematical ability to describe physical items.

Class Objectives
/Class Outline To understand complex calculus,  functions, complex analysis,  partial differential equations, and Fourier transformations.

Class Schedule 1. Basic concepts of complex numbers: the calculus, arithmetic, complex plane etc., basic complex functions (polynomial, exponential)
2. Complex functions (cont'd) : elementary functions, some simple examples,  multi-valued functions and branch points, Riemann surface.
3. Analytic and regular functions and contour integrals: Derivative of complex functions, Cauchy-Riemann equation etc.
4. Integral of complex functions: Cauchy's integral theorem, Cauchy's integral representation, and residue theorem.
5. Residue theorem and its application to the evaluation of real function integrals
6. Taylor and Laurent series expansion, analytic continuation
7. Mid-term examination
8. Partial differential equations (PDEs): Classification of Second Order Partial Differential Equations, solution of PDEs with the method o f separation of variables.
9.  Introduction to the Fourier analysis : orthogonal/orthonormal function system
10. Properties of Fourier series and examples of Fourier series: orthogonal functions, completeness, application to solving the PDEs with initial/boundary value problems.
11. Fourier integral and Fourier transformation,  Applications of Fourier transformation to boundary and initial value problems of PDEs
12. Dirac's delta functions
13. Dirac's delta functions II
14. Summary of Chapter I, II and III
15. Final examination

8. Mid-term examination.
15. Final examination.
Attendees are required to solve problems given in the class.
Reports and homeworks will be assigned every week.

The schedule will be adjusted depending on the level of understanding.

Text/Reference
Books,etc. Reference text books:
自然科学者のための数学概論寺沢寛一著岩波書店(約6千円：700頁）;
Mathematical Methods for Physicists， Arfken & Weber
Harcourt/Academic Press(約1万円：1000頁）

PC or AV used in
Class,etc. 　

(More Details) I will share the presentation Slides via Moodle.   Homework will be assigned in the class.
The homework report should be submitted via moodle system. The report manuscript written by hand should be scanned by a smart phone camera or scanner to submit it to moodle.
You have to prepare Note books, pencils...

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review You are required to review concepts lectured and to solve problems given in the lectures.
You have to read text books or exercise books to understand the concepts given in this lecture.

Requirements

Grading Method Homework, reports, mid-term and final examinations.
The following weight ratio will be reflected to your final grade.
mid-term test (about 30%), final exam. (about 50%),
reports and homework (about 20%).
When the mid-term and final exams become on-lined-report due to the COVID-19, I will increase the weight ratio of the reports and homework.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message This field itself has a huge amount of  contents.
This lecture only gives an introductory part of the field
and we will relax the mathematical correctness aiming at
the application in physics problems.

Other I give comments and advices in English for students having not-enough Japanese language skills.

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	2024Year	School/Graduate School	School of Science
Lecture Code	HC280000	Subject Classification	Specialized Education
Subject Name	物理数学Ｃ
Subject Name （Katakana）	ブツリスウガクC
Subject Name in English	Mathematics for Physics C
Instructor	ISHIKAWA KENICHI
Instructor (Katakana)	イシカワ　ケンイチ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, First Semester
Days, Periods, and Classrooms	(1st) Tues1-2：SCI E002 AV
Lesson Style	Lecture	Lesson Style (More Details)
Lecturer shows, demonstrates and explains the contents on text slides. Detailed algebraic manipulation will be explicitly shown on an electric note. Attendees are required to transcribe, summarize and understand them on your note. We will use the MS teams and Moodle. The class materials are distributed via Moodle. A homework will be assigned every class, the homework report should be submitted via Moodle. The class will be recorded in the MS temas and the record will be uploaded on Moodle.
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Semester No. 3
Keywords	complex analysis, partial differential equations, Fourier transformations.
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Some mathematics appearing broadly in physics will be presented.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Physics （Abilities and Skills）・Mathematical ability to describe physical items.
Class Objectives /Class Outline	To understand complex calculus, functions, complex analysis, partial differential equations, and Fourier transformations.
Class Schedule	1. Basic concepts of complex numbers: the calculus, arithmetic, complex plane etc., basic complex functions (polynomial, exponential) 2. Complex functions (cont'd) : elementary functions, some simple examples, multi-valued functions and branch points, Riemann surface. 3. Analytic and regular functions and contour integrals: Derivative of complex functions, Cauchy-Riemann equation etc. 4. Integral of complex functions: Cauchy's integral theorem, Cauchy's integral representation, and residue theorem. 5. Residue theorem and its application to the evaluation of real function integrals 6. Taylor and Laurent series expansion, analytic continuation 7. Mid-term examination 8. Partial differential equations (PDEs): Classification of Second Order Partial Differential Equations, solution of PDEs with the method o f separation of variables. 9. Introduction to the Fourier analysis : orthogonal/orthonormal function system 10. Properties of Fourier series and examples of Fourier series: orthogonal functions, completeness, application to solving the PDEs with initial/boundary value problems. 11. Fourier integral and Fourier transformation, Applications of Fourier transformation to boundary and initial value problems of PDEs 12. Dirac's delta functions 13. Dirac's delta functions II 14. Summary of Chapter I, II and III 15. Final examination 8. Mid-term examination. 15. Final examination. Attendees are required to solve problems given in the class. Reports and homeworks will be assigned every week. The schedule will be adjusted depending on the level of understanding.
Text/Reference Books,etc.	Reference text books: 自然科学者のための数学概論寺沢寛一著岩波書店(約6千円：700頁）; Mathematical Methods for Physicists， Arfken & Weber Harcourt/Academic Press(約1万円：1000頁）
PC or AV used in Class,etc.
(More Details)	I will share the presentation Slides via Moodle. Homework will be assigned in the class. The homework report should be submitted via moodle system. The report manuscript written by hand should be scanned by a smart phone camera or scanner to submit it to moodle. You have to prepare Note books, pencils...
Learning techniques to be incorporated
Suggestions on Preparation and Review	You are required to review concepts lectured and to solve problems given in the lectures. You have to read text books or exercise books to understand the concepts given in this lecture.
Requirements
Grading Method	Homework, reports, mid-term and final examinations. The following weight ratio will be reflected to your final grade. mid-term test (about 30%), final exam. (about 50%), reports and homework (about 20%). When the mid-term and final exams become on-lined-report due to the COVID-19, I will increase the weight ratio of the reports and homework.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	This field itself has a huge amount of contents. This lecture only gives an introductory part of the field and we will relax the mathematical correctness aiming at the application in physics problems.
Other	I give comments and advices in English for students having not-enough Japanese language skills.
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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