99年 - 99 淡江大學轉學考應用數學#55470

科目：研究所、轉學考(插大)-應用數學 | 年份：99年 | 選擇題數：0 | 申論題數：7

試卷資訊

所屬科目：研究所、轉學考(插大)-應用數學

選擇題 (0)

申論題 (7)

1. Show that

(10 points)

2. Write down the definition of Levi-Civita symbol ε_ijk and show that

(10 points)

3. Evaluate the area enclosed by a simply connected curve C : x^2/3 + y^2/3 = 4 in the x-y plane. (15 points)

4. Show that the sum of the square of the matrix elements is invariant under orthogonal similarity transformation. (15 points)

5. GivenA =

，and/(A) = A³ -2A² +5A-3, find f(A). (20 points)

Note: Evaluating each term in f (A) separately and then adding it up are not credited.

6. Solve the following 2nd-order ordinary differential equation. (15 points)

y" + 2y' + y = 4e^-x.

7. Evaluate

. (15 points)