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

Goals of the Course(JPN)

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.

Objectives of the Course(JPN)

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.

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 differencesbetween 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 singularpoint; 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 ofconvergence. Integration and differentiation of Fourier series.• Fourier transform, convolution, Dirac delta function. Laplace transform.

Course Prerequisites and Related Courses
 Calculus I, Calculus II, Linear Algebra I, Linear Algebra II; or Consent of Instructor

Course Evaluation Method and Criteria
 Tutorial performance: 30%, Homework score: 60%, Tutorial attendance: 10%.

Textbook
 None.

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.)

Study Load(Self-directed Learning Outside Course Hours)
 There are assignments for each tutorial.

Language Used in the Course

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

Additional measures for remote class (on-demand class)