授業の目的 【日本語】
Goals of the Course(JPN) | | |
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授業の目的 【英語】
Goals of the Course | | This course is a companion course to Mathematical Physics II. It is a standard "mathematical methods" course. 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 integral, 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 relevant to solving applied problems in physics, engineering and chemistry; 2) to improve students’ technical ability – i.e. ability to express intuition in mathematical terms and ability to solve problems.
Students taking Mathematical Physics I should also enroll in Mathematical Physics Tutorial I. |
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到達目標 【日本語】
Objectives of the Course(JPN) | | |
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到達目標【英語】
Objectives of the Course | | | 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, and applications of these. |
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授業の内容や構成
Course Content / Plan | | 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. |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | Students taking MP1 should have a good understanding of the material in Year 1 mathematics courses Calculus I&II and Linear Algebra Iⅈ or they can obtain the lecturer's permission.
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Related Courses
• Students taking Mathematical Physics I should also enroll in Mathematical Physics Tutorial I. The tutorial course is very important for understanding the lecture course.
• Concurrent registration in Mathematical Physics II is recommended as that unit together with this unit are prerequisites for Electricity and Magnetism I next semester (for students who wish to study Electricity and Magnetism I next semester). |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | For students (e.g. PhysSci) for whom the lecture course and tutorial course count separately towards the graduation requirement, the Mathematical Physics 1 Lecture Course Grade is calculated as follows:
Attendance and class participation: 5%; Weekly Quizzes and/or Assignments: 25%; Mid-term exam: 35%; Final Exam: 35%
For students (e.g. AutoEng) for whom the tutorial course does not count towards the graduation requirement, the reported grade is calculated as follows:
Tutorial Course mark 33%; Lecture Course mark 66%.
The Lecture Course mark is calculated in the same way as for PhysSci students. |
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教科書・テキスト
Textbook | | Boyce W., DiPrima R, Elementary Differential Equations, 7th Ed., Wiley.
You may use a newer edition, but note that the content and question numbers can be different to those in the 7th edition. This means you are likely to submit the wrong questions for assignments and tutorials. |
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参考書
Reference Book | | Reference Books
1. Coddington, E.A., An Introduction to Ordinary Differential Equations, Dover Publications, 1961. (Highly recommended for intermediate/advanced students.)
2. Tenenbaum, M & Pollard, H., Ordinary Differential Equations, Dover Publications, 1963. (Highly recommended for intermediate/advanced students.)
3. Boas M.L., 2006, Mathematical Methods in the Physical Sciences, 3rd ed., John Wiley & Sons.
4. Strang, G., Introduction to Linear Algebra, 4th Edition, Chapter 6.
5. Arfken G.B. & Weber H.J., 2005, Mathematical Methods for Physicists, 6th ed., Elsevier Academic Press.
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | Students from any department are welcome provided they have a suitable level of prior knowledge, which is decided by the lecturer. |
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使用言語
Language Used in the Course | | |
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授業開講形態等
Lecture format, etc. | | Face to face lectures and tutorials are compulsory (other than in exceptional circumstances; e.g. COVID infection). However, in order to record a video of the lecture -- including student interaction with each other and with the lecturer -- the lectures will simultaneously be carried out online using MS Teams. Students are therefore requested to bring their laptop or tablet to the lecture room. Make sure it has a microphone! Bring an electrical cord. For many G30 students, English is a 2nd or even 3rd language, so video recordings are an invaluable learning aid.
Live lectures via MS Teams (face-to-face and online). Before the start of semester students should ensure that they have correctly installed MS Teams using their THERS (国立大学法人東海国立大学機構 ) email account.
NUPACE students should contact Professor John Wojdylo before the start of semester for assistance with installing Teams correctly. |
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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) | | Lecture format, etc.
Face to face lectures and tutorials are compulsory (other than in exceptional circumstances; e.g. COVID infection). However, in order to record a video of the lecture -- including student interaction with each other and with the lecturer -- the lectures will simultaneously be carried out online using MS Teams. Students are therefore requested to bring their laptop or tablet to the lecture room. Make sure it has a microphone! Bring an electrical cord. For many G30 students, English is a 2nd or even 3rd language, so video recordings are an invaluable learning aid.
Live lectures via MS Teams (face-to-face and online). Before the start of semester students should ensure that they have correctly installed MS Teams using their THERS (国立大学法人東海国立大学機構 ) email account.
NUPACE students should contact Professor John Wojdylo before the start of semester for assistance with installing Teams correctly. |
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