109年 - 109國立臺灣大學_碩士班招生考試_化學工程學研究所:工程數學(E)#106052

1. (10%) Given a position vector below, determine the velocity, speed, acceleration, the tangential and normal component of acceleration, the curvature, and the unit tangent vector, unit normal vector.
F-3ti-2j-2k

2. (10%) Find the Laplace transform of At)-[sin(t)-cos(t)]²

3. (10%) Solve the differential equation, y"-ty'+y=1, y(0)=1, y'(0)=2

4. (10%) Produce a matrix P that diagonalizes the matrix below:

5. (10%) Find the general solutions of

6. (25%) Let u-u(x，y，t) be a function of the space (x.y) and the time t. S=S(s,f) is a function of x and t, and cl and co are constant. Determine whether the method of separation of variables is applicable to the following partial differential equations or not (each has 5 %). The rationale behind your answer needs be given; otherwise, it will not be credited.

7. (25%) Let u=u(xy) be a function of x and y. (x), g(x), f₁(y), and g₁(y) are given; K and L are positive constant. Solve the problem:

109年 - 109國立臺灣大學_碩士班招生考試_化學工程學研究所:工程數學(E)#106052

試卷資訊

選擇題 (0)

申論題 (7)