学部・大学院区分 Undergraduate / Graduate		農学部

時間割コード Registration Code		0910824

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		Mathmatical 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		2

開講期・開講時間帯 Term / Day / Period		秋火曜日４時限 Fall Tue 4

対象学年 Year		２年 2

授業形態 Course style		演習 Seminar

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・関連する科目
Course Prerequisites and Related Courses

Calculus I, Calculus II, Linear Algebra I, Linear Algebra II; or Consent of Instructor

成績評価の方法と基準
Course Evaluation Method and Criteria

Tutorial performance: 30%, Homework score: 60%, Tutorial attendance: 10%.

教科書・テキスト
Textbook

None.

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.)

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.

使用言語
Language Used in the Course

授業開講形態等
Lecture format, etc.

In person if possible. Online, remote class (using Microsoft Teams), otherwise.

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)