学部・大学院区分
Undergraduate / Graduate
工学部
時間割コード
Registration Code
0819121
科目区分【日本語】
Course Category
専門基礎科目
科目区分【英語】
Course Category
Basic Specialized Courses
科目名 【日本語】
Course Title
[G30]数理物理学演習1
科目名 【英語】
Course Title
[G30]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
酒井 忠勝 ○
担当教員 【英語】
Instructor
SAKAI Tadakatsu ○
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
Seminar
学科・専攻【日本語】
Department / Program
化学生命工学科 化学系プログラム
学科・専攻【英語】
Department / Program
Department of Chemistry and Biotechnology Chemistry Program
必修・選択【日本語】
Required / Selected
選択
必修・選択【英語】
Required / Selected
Elective


授業の目的 【日本語】
Goals of the Course(JPN)
0
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.

Students will master exact and approximate analytical techniques for initial value problems, Fourier series, and Laplace transform that arise in physics, engineering and chemistry.
到達目標 【日本語】
Objectives of the Course(JPN))
0
到達目標 【英語】
Objectives 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.

Students will master exact and approximate analytical techniques for initial value problems, Fourier series, and Laplace transform that arise in physics, engineering and chemistry.
バックグラウンドとなる科目【日本語】
Prerequisite Subjects
0
バックグラウンドとなる科目【英語】
Prerequisite Subjects
Calculus I, Calculus II, Linear Algebra I, Linear Algebra II;or Consent of Instructor
授業の内容【日本語】
Course Content
0
授業の内容【英語】
Course Content
• 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.
成績評価の方法と基準【日本語】
Course Evaluation Method and Criteria
0
成績評価の方法と基準【英語】
Course Evaluation Method and Criteria
Tutorial performance: 30%, Homework score: 60%, Tutorial attendance: 10%.
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.
履修条件・注意事項【日本語】
Course Prerequisites / Notes
0
履修条件・注意事項【英語】
Course Prerequisites / Notes
hybrid
教科書【日本語】
Textbook
0
教科書【英語】
Textbook
None.
参考書【日本語】
Reference Book
0
参考書【英語】
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.)
授業時間外学習の指示【日本語】
Self-directed Learning Outside Course Hours
授業時間外学習の指示【英語】
Self-directed Learning Outside Course Hours
使用言語【英語】
Language used
使用言語【日本語】
Language used
授業開講形態等【日本語】
Lecture format, etc.
授業開講形態等【英語】
Lecture format, etc.
遠隔授業(オンデマンド型)で行う場合の追加措置【日本語】
Additional measures for remote class (on-demand class)
遠隔授業(オンデマンド型)で行う場合の追加措置【英語】
Additional measures for remote class (on-demand class)