The purpose of this class is to obtain basic knowledge of mathematics to solve various problems related to engineering and science from an interdisciplinary view point. Focusing on ordinary differential equations, basic skills for both theoretical and/or numerical solutions are lectured.
By the end of this class, students will be able to:
(1) Judge which ordinary equations should be used to express the phenomena of interest.
(2) Solve the problem by using theoretical and numerical methods.
(3) Understand the implication 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 |
The course mainly provides classroom lectures with mini-examination. At the end of each chapter, students will do PC exercises and visualize the solutions thereby deepen the physical insight of the phenomena of interest.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction of ordinary differential equation - 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 | 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 | Review and midterm examination | Review the former half of this class and evaluate the achievement by mid-term examination |
Class 9 | Numerical solution of ordinary differential equation - Euler method | Understand the Euler method to solve ordinary differential equations |
Class 10 | Numerical solution of ordinary differential equation - Runge-Kutta method | Understand theRunge-Kutta method to solve ordinary differential equations |
Class 11 | 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 12 | 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 13 | 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 14 | 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 15 | Review and Q&A | Review and Q&A |
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mid-term examination (45%)
term-end examination (45%)
mini-examinations (10%)
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