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研究所、轉學考(插大)-應用數學
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99年 - 99 淡江大學 轉學考 應用數學#55470
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6. Solve the following 2nd-order ordinary differential equation. (15 points)
y" + 2y' + y = 4e
-x
.
其他申論題
2. Write down the definition of Levi-Civita symbol εijk and show that (10 points)
#208743
3. Evaluate the area enclosed by a simply connected curve C : x2/3 + y2/3 = 4 in the x-y plane. (15 points)
#208744
4. Show that the sum of the square of the matrix elements is invariant under orthogonal similarity transformation. (15 points)
#208745
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.
#208746
7. Evaluate . (15 points)
#208748
3. Prove or disprove: If (mod 4), where a and b are integers, then (mod 4). (12 pts)
#208749
4. Find the smallest equivalence relation on {1,2,3} that contains (1,2). (12 pts) Justify your answer.
#208750
5. How many nonnegative integer solutions are there to the equation x1 x2 + x3 + x4 = 21 such that (12 pts) Show enough work to get full credits.
#208751
6. Apply Dijkstra’s Algorithm to find a shortest path from a to f. Indicate what is your shortest path and the total weight of the path. You must show every step in order to get full credits. (14 pts)
#208752
7. Use mathematical induction to prove that 3 divides n3+2n whenever n is a nonnegative integer. (15 pts) (3整除n3+2n, n為非負整數）（必須以歸納證明的方法證得）
#208753
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