This course will address several mathematical methods that can be applied to solve various governing equations in fundamental sciences or engineering applications. We will put special emphasis on both the physical meaning and the mathematical significance of each topic. The students should strengthen their capability of understanding and solving a real problem in the fields of engineering and science.

We will talk about 1st and 2nd ordinary differential equations (ODE). Then we will learn the series method and Laplace transformation in detail as they are two powerful methods in practice. The second half of the term will focus on the concept of vector space and its calculation. We will finish the term with the fundamentals of linear algebra.