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.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction of ordinary differential equation - as a tool to understand phenomena | can explain the necessity of learning mathematics in engineering and identify basic terminologies |
Class 2 | First-order ordinary differential equation (1) | Can solve some examples of fundamental first-order ordinary differential equation |
Class 3 | First-order ordinary differential equation (2) | Can solve some examples of fundamental first-order ordinary differential equation |
Class 4 | First-order ordinary differential equation (3) | Can solve some examples of fundamental first-order ordinary differential equation |
Class 5 | Second-order homogeneous linear ordinary differential equation | Can solve some examples of second-order homogeneous linear ordinary differential equations |
Class 6 | Second-order homogeneous linear ordinary differential equation | Visualize various phenomena expressed by second-order homogeneous linear ordinary differential equations and obtain the theoretical solutions. |
Class 7 | Second-order homogeneous linear ordinary differential equation | Visualize the theoretical solutions of second-order homogeneous linear ordinary differential equation using PC and obtain the theoretical solutions. |
Class 8 | Review and midterm examination | Review the former half of this class and evaluate the achievement by mid-term examination |
Class 9 | Second-order inhomogeneous linear ordinary differential equation | Can solve some examples of second-order inhomogeneous linear ordinary differential equations |
Class 10 | Second-order inhomogeneous linear ordinary differential equation | Can solve some examples of second-order inhomogeneous linear ordinary differential equations |
Class 11 | Second-order inhomogeneous linear ordinary differential equation | Can solve some examples of second-order inhomogeneous linear ordinary differential equations |
Class 12 | Numerical solution of ordinary differential equation - Euler method | Can numerically solve some examples of ordinary differential equations by Euler method. |
Class 13 | Numerical solution of ordinary differential equation - Runge-Kutta method | Can numerically solve some examples of ordinary differential equations by Runge-Kutta method. |
Class 14 | Numerical solution of ordinary differential equation - multivariable / n-th order system | Can numerically solve some examples of ordinary differential equations of multivariable and n-th order system. |
Class 15 | Nonlinear ordinary differential equation and Chaos | Can obtain the numerical solutions of nonlinear ordinary differential equation using PC and visualize the Chaos phenomena. |
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mid-term examination (45%)
term-end examination (45%)
mini-examinations (10%)
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tnakamur[at]tse.ens.titech.ac.jp
Appointment by e-mail is required.