学部・大学院区分
Undergraduate / Graduate
理学部
時間割コード
Registration Code
0680100
科目区分
Course Category
専門基礎科目
Basic Specialized Courses
科目名 【日本語】
Course Title
数理物理学演習1
科目名 【英語】
Course Title
Mathematical Physics Tutorial I
コースナンバリングコード
Course Numbering Code
担当教員 【日本語】
Instructor
久野 純治 ○ 北原 鉄平
担当教員 【英語】
Instructor
HISANO Junji ○ KITAHARA Teppei
単位数
Credits
1
開講期・開講時間帯
Term / Day / Period
秋 火曜日 4時限
Fall Tue 4
授業形態
Course style
演習
Lecture
学科・専攻
Department / Program
G30 Physics
必修・選択
Compulsory / Selected
See "Course List and Graduation Requirements" for your program for your enrollment year.


授業の目的 【日本語】
Goals of the Course(JPN)
授業の目的 【英語】
Goals of the Course
Students taking Mathematical Physics I should also take this tutorial class. This course introduces first-order and second-order ordinary differential equations and their solution methods. Students will master exact and approximate analytical techniques for initial value problems that arise in physics, engineering and chemistry. Questions of existence, uniqueness and convergence will also be discussed. Fourier series follow naturally from the second-order theory and these are investigated, too.
到達目標 【日本語】
Objectives of the Course(JPN))
到達目標 【英語】
Objectives of the Course
Students will master exact and approximate analytical techniques for initial value problems, Fourier series, and Laplace transform that arise in physics, engineering and chemistry.
授業の内容や構成
Course Content / Plan
• First order ordinary differential equation (ODE) initial value problems. Integration factor; separable equations;
systems of ODEs (Hamiltonian systems); phase plane, flow. Uniqueness and existence theorems. Some differences
between linear and nonlinear ODEs.

• Second order linear ODE initial value problems. Homogeneous solution. Proving linear independence (Wronskian).
Method of Undetermined Coefficients; Variation of Parameters. Series solutions: ordinary point, regular singular
point; convergence tests; Method of Frobenius. Examples from physics, engineering and chemistry.

• Fourier series. Dirichlet conditions. Role of symmetry. Gibbs phenomenon. Effect of jump discontinuity on speed of
convergence. Integration and differentiation of Fourier series.

• Fourier transform, convolution, Dirac delta function. Laplace transform.
履修条件
Course Prerequisites
Calculus I, Calculus II, Linear Algebra I, Linear Algebra II; or Consent of Instructor
関連する科目
Related Courses
Mathematical Physics I
成績評価の方法と基準
Course Evaluation Method and Criteria
Tutorial performance: 30%, Homework score: 60%, Tutorial attendance: 10%.
不可(F)と欠席(W)の基準
Criteria for "Fail (F)" & "Absent (W)" grades
The “Absent/W” grade is reserved for students who withdraw by November 30.
After that day, grade (A+ to F) will be awarded based on marks earned from all assessments during the semester.
参考書
Reference Book
1. Boas M.L., 2006, Mathematical Methods in the Physical Sciences, 3rd ed., John Wiley & Sons.
2. Strang, G., Introduction to Linear Algebra, 4th Edition, Chapter 6.
3. Arfken G.B. & Weber H.J., 2005, Mathematical Methods for Physicists, 6th ed., Elsevier Academic Press. (Copies are available in the library.)
教科書・テキスト
Textbook
None.
課外学習等(授業時間外学習の指示)
Study Load(Self-directed Learning Outside Course Hours)
There are assignments for each tutorial.
注意事項
Notice for Students
Concurrent registration in Mathematical Physics I is advised.
他学科聴講の可否
Propriety of Other department student's attendance
他学科聴講の条件
Conditions for Other department student's attendance
レベル
Level
キーワード
Keyword
履修の際のアドバイス
Advice
授業開講形態等
Lecture format, etc.
Online, remote class (using Microsoft Teams)
遠隔授業(オンデマンド型)で行う場合の追加措置
Additional measures for remote class (on-demand class)