研究所、轉學考(插大)◆工程數學題庫 下載題庫

110 年 - 110 國立臺灣大學_碩士班招生考試_ 工程科學及海洋工程學研究所丙組:工程數學(L)#100704 

選擇:0題,非選:8題 我要補題 回報試卷錯誤

1. (25%) Show that the equation is exact, and obtain its general solution. Also, find the particular solution corresponding to the given initial condition as well.

2. (20%) Determine the equation of the phase trajectories for the given systen, and sketch several representative trajectories. Use arrows to indicate the direction of movement along those trajectories.

【題組】(a) x'=y,y'=-x

3.【題組】(b) x'=xy, y'=-x

3. (25%) Determine whether the following set is LI (Linear independence) or LD (Linear Dependence). If it is LD, then give a linear relation among the vectors.

【題組】 (a) (1,3,2,0),(4,1,-2,-2),(0,2,0,3),(4,7,1,2)

5.【題組】(b) (2,0,1.-1,0),(1,2.0.3.D),(4,-4.3.-9,-2)


4. (20%) It is known that the nxn tridiagonal matrix

61270fea68032.jpghas eigenvalues 6127101c4fe06.jpg
for j=1,2,... ..,n. (A is called tridiagonal because all elements are zero except for those on the main diagonal and the two adjacent diagonals.)
Verify Bquation (1) by calculating the eigenvalues for n = 1 and n = 2.

5. (10%)

【題組】 (a) Is it possible for a matrix to have no eigenvalues? Explain.

8.【題組】(b) A given eigenvalue can have more than one LI eigenvector. Can a given eigenvector correspond to more than one eigenvalue? Explain.



4. 投擲一枚公正的硬幣,前三次已經出現的結果是反面、反面、正面,以此推測第四次的情況,請問 以下四個人的推論,正確的選項為何? (A) 高高:...

50 x


110 年 - 110 國立臺灣大學_碩士班招生考試_ 工程科學及海洋工程學研究所丙組:工程數學(L)#100704-阿摩線上測驗

110 年 - 110 國立臺灣大學_碩士班招生考試_工程科學及海洋工程學研究所丙組:工程數學(L)#100704