| Course title | |||||
| 生体医用システム工学特別講義（微分方程式） [Special Lectures in Biomedical Engineering (Differential equation)] | |||||
| Course category | technology speciality courses | Requirement | Credit | 2 | |
| Department | Year | 1～4 | Semester | 4th | |
| Course type | 4th | Course code | 022272 | ||
| Instructor(s) | |||||
| 三沢 和彦 [MISAWA Kazuhiko] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
|
Differential equations, which appear in the first and second year courses of biomedical systems engineering, are taught and practiced with the aim of understanding their meaning and role in science and technology. By practicing the expression of various phenomena with differential equations, students will acquire basic skills that are useful for specialized courses and graduation research in biomedical systems engineering, rather than simply being motivated to solve problems using differential equations as tools. |
| Expected Learning |
|
(1) To be able to explain the meaning and role of differential equations in science and technology (2) To be able to express phenomena whose state depends on time using equations and to be able to explain the temporal changes of the phenomena (3) To be able to express phenomena whose state depends on time and coordinates using equations, and to be able to explain the temporal and spatial changes of the phenomena. |
| Course schedule |
|
Part I: What are differential equations? Explain why differential equations are so powerful for learning natural science and engineering technology Session 1: Friday, February 4, Period 3: Real-time hybrid Meaning and role of differential equations in science and technology Part 2: Fundamentals] One-variable ordinary differential equations Let's express phenomena whose state depends on one variable of time by equations and try to explain quantitatively how the phenomena change with time. Session 2: Friday, February 4, 4th Period: Real-time hybrid Let's try to explain the motion of the human body with equations of motion - vertical jump and walking motion Session 3: Monday, February 7, 3rd period: On-demand Differential Equations of Dynamical Phenomena Formulation and solution of differential equations of dynamical phenomena Session 4: Monday, February 7, 4th period: On-demand Differential equations of dynamical phenomena and second-order homogeneous constant coefficient linear differential equations Session 5: Tuesday, February 8, 3rd period: Real-time hybrid Explanation of cell membrane function with equations of electric circuits -Cell membrane potential Session 6: Feb. 8 (Tue) 4th period: Real-time hybrid Differential equations of electromagnetic phenomena Part 3: Solutions] Mathematical solution of ordinary differential equations in one variable Let's practice general solution methods of differential equations used frequently in natural sciences and engineering technology by type. Session 7: Wednesday, February 9, 3rd Period: Real-time hybrid Solving second-order homogeneous constant coefficient linear differential equations Session 8: Wednesday, February 9, Period 4: On-demand Differential equations of electromagnetic phenomena and second-order non-homogeneous constant coefficient linear differential equations Session 9: Feb. 10 (Thu.) 3rd period: Real-time hybrid Solving second-order non-homogeneous constant coefficient linear differential equations Part 4: Advanced] Partial differential equations in two variables Let's express phenomena whose state depends on two variables, time and position coordinates, by equations and try to explain the temporal and spatial changes of the phenomena quantitatively! Session 10: Thursday, February 10, Period 4: Real-time hybrids Let's try to explain sound waves propagating in the body by using wave equations. Session 11: Feb. 14 (Mon) 3rd period: Real-time hybrid Solving the wave equation and elasticity equation Session 12: Monday, February 14, Period 4: Real-time hybrid Solving the wave equation and its application to second-order linear differential equations Part 5: Development] Comprehensive Exercises Session 13: (Tue., Feb. 15, 3rd period): Real-time hybrids Check your level of understanding in Comprehensive Exercise 1 Session 14: (Tue., Feb. 15, 4th period): Real-time hybrids Comprehensive Exercise 2: Check your level of understanding |
| Prerequisites |
| None |
| Required Text(s) and Materials |
| Preparation and review materials will be available on Google Classroom. |
| References |
|
A Visual Guide to Physical Mathematics: Calculus and Ordinary Differential Equations in One Variable," Masahiro Maeno (Tokyo Book) Introduction to Physical Mathematics II: Differential Equations and Complex Functions," Chun Wa Wong (Maruzen) Physics for Biology and Medicine" Paul Davidovits (Kyoritsu Shuppan) Physics in Medical Diagnosis" T. A. Delchar (Chapman & Hall) Physics for Medical Sciences" Koichi Sato and Toshiyuki Fujishiro (Tokyo Kyogakusha) The Secret of Calculus Physics" Hitoshi Aoyama (Asakura Shoten) Differential Equations as Tools" (Blue Backs), Kyoichi Saito (Kodansha) Physics with Mathematics" Naoshi Takebe (Nippon Hyoronsha) A book that really understands derivatives," Masahiro Hosono (Shogakukan) Fundamentals of Medical Engineering" Kenjun Dohi (Tokyo Denki University Press) Differential Equations Anyone Can Understand," Sonoko Ishimura (Kodansha) Differential Equations for Easy Learning," Sonoko Ishimura (Kyoritsu Shuppan) |
| Assessment/Grading |
| Students will be given a confirmation test during each lecture, and will be given an assignment at the end of the lecture to evaluate the basic points. The examinations will be given during the general practice period in the third and fourth periods on February 15 and 16, respectively. |
| Message from instructor(s) |
| Course keywords |
| Office hours |
| Students can ask questions on Google Classroom at any time. |
| Remarks 1 |
|
This special lecture will not be offered in the academic year 2022; Basic Engineering Mathematics in the first semester of the first year and Applied Engineering Mathematics in the second semester of the first year will be newly offered. This syllabus is the content of the course offered in FY2021. |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 4/24/2022 12:53:41 PM |