学部・大学院区分理学部
時間割コード0680100
科目区分専門基礎科目
Basic Specialized Courses
科目名　【日本語】数理物理学演習１
科目名　【英語】Mathematical Physics Tutorial I
コースナンバリングコード
担当教員　【日本語】久野　純治 ○ 北原　鉄平
担当教員　【英語】HISANO Junji ○ KITAHARA Teppei
単位数1
開講期・開講時間帯秋 火曜日 ４時限
Fall Tue 4
授業形態演習
Lecture
学科・専攻
G30 Physics
必修・選択
* See "Remarks"


授業の目的　【日本語】
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 master exact and approximate analytical techniques for initial value problems that arise in physics, engineering and chemistry. Questions of existence, uniqueness and convergence are also discussed. Fourier series follow naturally from the 2nd-order theory and these are investigated, too.
授業の目的　【英語】
到達目標　【日本語】
到達目標　【英語】
授業の内容や構成
? 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
Calculus I, Calculus II, Linear Algebra I, Linear Algebra II;or Consent of Instructor
関連する科目
Mathematical Physics Tutorial I, Mathematical Physics II
成績評価の方法と基準
tutorial Attendance: 50%; Class performance: 50%
教科書・テキスト
None.
参考書
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）
注意事項
*See "Course List and Graduation Requirements" for your program for your enrollment year. Concurrent registration in Mathematical Physics I is advised.
他学科聴講の可否
他学科聴講の条件
レベル
キーワード
履修の際のアドバイス
授業開講形態等
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