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 has dual aims: 1) to convey mathematical principles relevant to solving fundamental and 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.
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.
Students will find this mathematical methods course helpful in other units such as Quantum Mechanics, Analytical Mechanics, Electricity and Magnetism, as well as in Chemistry, Automotive Engineering and other engineering courses.
This course is a companion course to Mathematical Physics Tutorial I.
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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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 | | • 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
Course Prerequisites | | | Students taking MP1 should have a good understanding of the material in Year 1 mathematics courses Calculus I&II and Linear Algebra Iⅈ 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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関連する科目
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 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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不可(F)と欠席(W)の基準
Criteria for "Fail (F)" & "Absent (W)" grades | | The "Absent (W)" grade is reserved for students who withdraw by the deadline in November. After that day, a letter grade will be awarded based on marks earned from all assessment during the semester.
If Mathematical Physics I is NOT A COMPULSORY SUBJECT and the student plans never to take Mathematical Physics I in the future, then a late Absent (W) grade request will be considered. |
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参考書
Reference Book | | 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.
(Copies of all these books are available in the Science Library.) |
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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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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | • This course is part of your training to be a professional researcher. You are expected to revise the lecture notes, read and work through the textbook, and solve assignment problems outside lecture hours. You cannot learn physics by only attending lectures. The exams will consist of questions covering both lecture notes and assignments.
• Students must be willing to work hard if they wish to achieve a good, internationally competitive level. |
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注意事項
Notice for Students | | Plagiarism (e.g. copying solutions that you have found on the Internet) is an act of academic dishonesty. Cheating in exams (e.g. having lecture notes, assignment solutions or online references open on your computer screen during an online exam) is a serious offence. Copying other people's solutions and claiming them as your own is also an act of academic dishonesty. Nagoya University has a strict policy towards academic dishonesty:
"Acts of academic dishonesty are prohibited during exams, for reports and assignments. If acts of academic dishonesty are discovered, you may be subject to discipline, which may affect your ability to graduate on time."
The punishment for serious breaches (such as cheating in an exam or repeated plagiarism despite a warning) is the loss of all grades from all subjects during the semester and cancellation of any scholarships received.
Even if your course is difficult and it is to be expected that you'll find it hard to finish assignments, it is far better that you submit an honest effort than take the dishonest path. Remember, to be on course for a "B" you only need to score over 70% in the assignments -- and if you paid attention in the tutorials, you would have seen nearly all the problems done for you (in my subjects, at least).
There's no excuse for cheating. |
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他学科聴講の可否
Propriety of Other department student's attendance | | | Students from any department are welcome provided they have a suitable level of prior knowledge. |
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他学科聴講の条件
Conditions for Other department student's attendance | | | Students from any department are welcome provided they have a suitable level of prior knowledge. |
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レベル
Level | | |
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キーワード
Keyword | | |
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履修の際のアドバイス
Advice | | • 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 and Electricity and Magnetism. |
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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) | | All lectures will be live face-to-face and online via MS Teams. Face-to-face attendance is compulsory (barring exceptional circumstances such as COVID infection).
A lecture video will be available immediately after each lecture to help with student revision.
The lecturer will be available to answer questions via Teams chat. |
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