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 | | 数理物理学１ | | 科目名 【英語】
Course Title | | 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 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.
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 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, and applications of these.
• 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. |
| | 到達目標 【日本語】
Objectives of the Course(JPN) | | | | 到達目標【英語】
Objectives of the Course | | 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.
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 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, 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 | | Calculus Iⅈ Mathematical Physics I&II or Consent of Lecturer.
Students MUST have previously performed strongly in a vector calculus course. |
| | 成績評価の方法と基準
Course Evaluation Method and Criteria | | PhysSci and all other students for whom the tutorial course Mathematical Physics Tutorial I counts towards their graduation requirement:
Attendance and class performance, attitude: 5%; Weekly quizzes or other written assessment: 30%; Midterm exam: 32.5%; Final Exam: 32.5%
Automotive Engineering Students and all other students for whom the tutorial course Mathematical Physics Tutorial I DOES NOT count towards their graduation requirement:
Lecture Course mark: 2/3; Tutorial Course Mark: 1/3.
A formal withdrawal form must be signed by the lecturer and submitted to the Student Office by the official withdrawal deadline in November.
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. |
| | 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. |
| | 参考書
Reference Book | | 1. Coddington, E.A., An Introduction to Ordinary Differential Equations, Dover Publications, 1961. (Highly recommended for advanced students.)
2. Tenenbaum, M & Pollard, H., Ordinary Differential Equations, Dover Publications, 1963. (Highly recommended for 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) | | | You are expected to revise the lecture notes, read the textbook, and solve assignment problems outside lecture hours. You cannot learn physics and mathematics by only attending lectures. The exams will consist of questions covering both lecture notes and assignments. |
| | 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.
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 at most times during the day to answer questions via Teams chat. |
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