| 学部・大学院区分 | | 理学部 | | | 時間割コード | | 0680080 | | | 科目区分 | | 専門基礎科目
Basic Specialized Courses | | | 科目名 【日本語】 | | 数理物理学１ | | | 科目名 【英語】 | | Mathematical Physics I | | | コースナンバリングコード | | | | | 担当教員 【日本語】 | | WOJDYLO John Andrew ○ | | | 担当教員 【英語】 | | WOJDYLO John Andrew ○ | | | 単位数 | | 2 | | | 開講期・開講時間帯 | | 秋 火曜日 ５時限
Fall Tue 5 | | | 授業形態 | | 講義
Lecture | | | 学科・専攻 | | | | | 必修・選択 | | | |
| 授業の目的 【日本語】 | | | This course is a companion course to Mathematical Physics II. Students master analytical techniques for problems that arise in physics, engineering and chemistry. This course introduces first order and second order ordinary differential equations and their solution methods. Questions of uniqueness of solutions and convergence are also discussed. Students are also introduced to Fourier series, the Fourier transform, convolution, Laplace transform, and the Dirac delta function. Students will find this mathematical methods course helpful in other units such as Quantum Mechanics, Analytical Mechanics, Electricity and Magnetism, as well as in Automotive Engineering and other engineering courses. This course has dual aims: 1) to convey mathematical principles; 2) to improve students’ technical ability ? i.e. ability to express intuition in mathematical terms and ability to solve problems. |
| | | 授業の目的 【英語】 | | | | | 到達目標 【日本語】 | | | At the end of this course, students will have mastered a variety of first order linear and nonlinear ODEs, second and arbitrary order linear ODEs and their solution methods, Fourier series, the Fourier transform, convolution and the Laplace transform together with applications. |
| | | 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 and engineering.
? 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.
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| | | 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 | | | Attendance: 5%; Weekly Quizzes and Assignments: 25%; Mid-term exam: 35%; Final Exam: 35% |
| | | 教科書・テキスト | | | Boyce W., DiPrima R, Elementary Differential Equations, 7th ?10th Ed., Wiley. |
| | | 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.)
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| | | 課外学習等（授業時間外学習の指示） | | | | | 注意事項 | | ? Students taking Mathematical Physics I should also take Mathematical Physics Tutorial I.
? Concurrent registration in Mathematical Physics II is recommended as that unit is a prerequisite for Electricity and Magnetism I.
? The book by Boas is also useful for Mathematical Physics II, Electricity and Magnetism, as well as many other areas of physics.
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| | | 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 | | | | | 遠隔授業（オンデマンド型）で行う場合の追加措置 | | | |
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