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99年 - 99 淡江大學 轉學考 應用數學#55470
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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)
其他申論題
5. (a) Evaluate = ?
#208740
(b) Evaluate = ? for n = l,2, and 3 .
#208741
1. Show that approaches to (10 points)
#208742
2. Write down the definition of Levi-Civita symbol εijk and show that (10 points)
#208743
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
6. Solve the following 2nd-order ordinary differential equation. (15 points) y" + 2y' + y = 4e-x.
#208747
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
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