The purpose of this course is to obtain basic knowledge of mathematics for solving various problems related to engineering and science from an interdisciplinary view point. Focusing on ordinary differential equations, the instructor lectures on basic skills for both theoretical and/or numerical solutions.
By the end of this course, students will be able to:
(1) Judge which ordinary equations should be used to express the phenomena of interest.
(2) Solve the problem using theoretical and numerical methods.
(3) Understand the implications of solutions and interpret the phenomena physically.
ordinary differential equations: theoretical solution: numerical solution: interdisciplinary view point: physical interpretation
✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Lectures mainly consist of classroom teaching with mini-tests. After the end of each chapter, students will do a PC exercise and visualize the solution thereby deepening their physical insight into the phenomena of interest.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction of ordinary differential equations - as a tool to understand phenomena | Understand the necessity of learning mathematics in engineering and identify basic terminologies |
Class 2 | First-order ordinary differential equation | Understand various phenomena expressed by first-order ordinary differential equations and obtain theoretical solutions |
Class 3 | First-order ordinary differential equation (PC exercise) | Visualize the theoretical solutions of first-order ordinary differential equations using PC and deeply understand the corresponding phenomena |
Class 4 | Second-order homogeneous linear ordinary differential equation | Understand various phenomena expressed by second-order homogeneous linear ordinary differential equations and obtain the theoretical solutions |
Class 5 | Second-order homogeneous linear ordinary differential equation (PC exercise) | Visualize the theoretical solutions of second-order homogeneous linear ordinary differential equation using PC and deeply understand the corresponding phenomena |
Class 6 | Second-order inhomogeneous linear ordinary differential equation | Understand various phenomena expressed by second-order inhomogeneous linear ordinary differential equations and obtain the theoretical solutions |
Class 7 | Second-order inhomogeneous linear ordinary differential equation (PC exercise) | Visualize the theoretical solutions of second-order inhomogeneous linear ordinary differential equation using PC and deeply understand the corresponding phenomena |
Class 8 | Numerical solution of ordinary differential equation - Euler method | Understand the Euler method to solve ordinary differential equations |
Class 9 | Numerical solution of ordinary differential equation - Runge-Kutta method | Understand the Runge-Kutta method to solve ordinary differential equations |
Class 10 | Numerical solution of ordinary differential equation (PC exercise) | Visualize the numerical solutions of linear ordinary differential equation using PC and deeply understand the corresponding phenomena |
Class 11 | Nonlinear ordinary differential equation and Chaos (Nonlinear spring system) | Understand the features of Chaos phenomena expressed by nonlinear ordinary differential equations - Nonlinear spring system |
Class 12 | Nonlinear ordinary differential equation and Chaos (Food chain and Ecosystem) | Understand the features of Chaos phenomena expressed by nonlinear ordinary differential equations - Food chain and Ecosystem |
Class 13 | Nonlinear ordinary differential equation and Chaos (PC exercise) | Visualize the numerical solutions of nonlinear ordinary differential equation using PC and deeply understand the corresponding Chaos phenomena |
Class 14 | The Butterfly Effect (PC exercise) | Visualize the Lorenz Attractor (Chaos phenomena) |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Ordinary Differential Equations and Physical Phenomena: A Short Introduction with Python, Kanda Manabu trans. Varquez Alvin CG, Asakura Publishing
(purchase through University Coop, Amazon, Rakuten, or the publisher's website)
Supplementary Textbook:
Advanced Engineering Mathematics by Erwin Kreyszig.
About Python:
https://docs.python.org/3/ for python.
Online exercises:
Python exercises will be done through Google Colab.
mid-term examination (45%)
term-end examination (45%)
mini-examinations or homeworks (10%)
Nothing
All communications will be conducted through T2Schola or Slack.
Private meetings (online) may be scheduled through T2Schola.
Students may also contact the instructor by e-mail.