学部・大学院区分
Undergraduate / Graduate | | 農学部 | | 時間割コード
Registration Code | | 0910810 | | 科目区分
Course Category | | 専門基礎科目
Basic Specialized Courses | | 科目名 【日本語】
Course Title | | [G30]数理物理学１ | | 科目名 【英語】
Course Title | | [G30]Mathmatical Physics I | | コースナンバリングコード
Course Numbering Code | | | | 担当教員 【日本語】
Instructor | | WOJDYLO John Andrew ○ | | 担当教員 【英語】
Instructor | | WOJDYLO John Andrew ○ | | 単位数
Credits | | 2 | | 開講期・開講時間帯
Term / Day / Period | | 秋 火曜日 ５時限
Fall Tue 5 | | 対象学年
Year | | ２年
2 | | 授業形態
Course style | | 講義
Lecture | |
授業の目的 【日本語】
Goals of the Course(JPN) | | | | 授業の目的 【英語】
Goals of the Course | | This course is a companion course to Mathematical Physics II. Its content similar to standard "mathematical methods" courses taught in mathematics departments around the world at second year level to students majoring in STEM subjects. Students are given the opportunity to master analytical techniques for problems that arise in physics, engineering, chemistry and any area utilizing applied mathematics. This course introduces first order and second order ordinary differential equations and their solution methods. Uniqueness of solutions and convergence are emphasized. 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 lecture courses such as Quantum Mechanics, Statistical Physics, Analytical Mechanics, Electricity and Magnetism, as well as lecture courses in the Agricultural Sciences, Automotive Engineering and other engineering courses.
It is strongly recommended that students taking Mathematical Physics I also enroll in Mathematical Physics Tutorial I, because mastering the assignments in both courses is essential for performing well in the MP1 lecture course exams. You should view assignment work in both the MP1 lecture course and the MPT1 tutorial course as preparation for the exams in the MP1 lecture course.
Assignment exercises are an essential part of both the lecture course and the associated tutorial course (Mathematical Physics Tutorial I). Students are thereby given the opportunity to master a wide variety of technical variations encountered in solving concrete examples of the basic theory, as well as a variety of simple extensions of the basic theory, and simple analytical techniques related to the lecture content but not mentioned in lectures, that extend the scope of problems that students can solve. Mastery of these aspects makes students more attractive to employers.
Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 到達目標 【日本語】
Objectives of the Course(JPN) | | | | 到達目標【英語】
Objectives of the Course | | Objectives of the Course
The overriding objective of this course is to foster the student's scholarly independence. In order to succeed in this course, students must understand the content sufficiently to have the ability to potentially critique and evaluate the correctness of the output from group work, and generative AI if they use it, relevant to the lecture and assignment content. This is a transferable, real-world skill and, more importantly, mindset: the habit of checking before believing, while possessing the knowledge and technical ability to make the judgement.
Students will have the ability to solve problems such as creative variations of assignment exercises and lecture content with no help, and thereby demonstrate that they are capable of learning STEM knowledge and techniques, and are therefore potentially useful to future employers or university research groups.
This course has dual practical aims: 1) to convey mathematical principles relevant to solving applied problems in physics, engineering, chemistry and other STEM areas; 2) to improve students’ technical ability – i.e. ability to express intuition in mathematical terms and ability to solve problems.
Students master analytical techniques for problems that arise in STEM areas such as physics, engineering and chemistry. 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 emphasized. Students are also introduced to Fourier series, the Fourier transform, convolution, Laplace transform, and the Dirac delta function, and applications of these. |
| | 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. |
| | 履修条件・関連する科目
Course Prerequisites and Related Courses | | 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 or they can ask for the lecturer's permission.
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).
Advice
• 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.
• More advanced students should concurrently study the book by Coddington. |
| | 成績評価の方法と基準
Course Evaluation Method and Criteria | | Course Evaluation Method and Criteria, Procedure for Withdrawal, Criteria for Absent (W) grade, Warning with regards to use of AI and Plagiarism
Attendance and class participation: 5%; Weekly Quizzes and/or Assignments: 20%; Midsemester exam: 37.5%; End of Semester Exam: 37.5%.
Some exam questions in the lecture course are simple repetitions of either tutorial or lecture assignment questions with minor changes or simple creative variations. If the student is unable to make meaningful progress with such exam questions during the exam, while in the assignment they presented quite a good solution, then the entire assignment corresponding to that question will be deemed to have a mark of 20%.
Be aware that mastering the assignments is essential for performing well in the exams. You should view assignment work as preparation for the exams.
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Necessity / Non-necessity to submit "Course Withdrawal Request Form"
If the student plans to withdraw then a formal withdrawal form must be signed by the lecturer and submitted to the Student Office by the official deadline in November.
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Conditions for Course Withdrawal
A withdrawal request made after the official deadline in November will be rejected unless the circumstances are very exceptional. 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 withdrawal request will be considered.
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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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Notice to Students Regarding Use of AI, Academic Honesty and Plagiarism
1. WARNING ABOUT THE USE OF AI
Despite any rules and better ethical judgment, many of you will rely on AI (ChatGPT, Gemini, Sonnet, Claude etc.) to solve your assignment problems. Be aware that besides constituting academic misconduct and dishonesty, such use of AI is detrimental to your learning: among other things, you will lack the experience of getting stuck and digging your way out of a problem using your own knowledge, tenacity, ingenuity and creativity. You will not learn resilience in the field of study. The examinations are designed to test the quality of your learning, your ability to bring together multiple threads dealt with in lectures and assignments, your ability to interpret the equations and unify your understanding, to seek connections and dig your way out of a seeming dead end when solving a problem. You will not learn this by relying on AI. You will do very well in assignments but very poorly in the exams.
2. PLAGIARISM and other forms of cheating.
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. |
| | 教科書・テキスト
Textbook | | Boyce W., DiPrima R, Elementary Differential Equations, 7th Ed., Wiley.
You may use a newer edition for clearer presentation and arguments, 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. |
| | 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.
(Copies of all these books are available in the Science Library.) |
| | 課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | 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. |
| | 使用言語
Language Used in the Course | | | | 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. |
| | 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) | | Face to face lectures and tutorials are compulsory. 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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