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研究所、轉學考(插大)-應用數學
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100年 - 100 淡江大學 轉學考 應用數學#55469
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(b) Evaluate
= ? for n = l,2, and 3 .
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【已刪除】(b)
#208737
4. (a) Expand the periodic function in a sine-cosine Fourier series
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(b) Qualitatively sketch a graph of the sum of three terms of the series. [Hint: Sketch each term separately on the same axes and add the terms graphically.]
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5. (a) Evaluate = ?
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1. Show that approaches to (10 points)
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2. Write down the definition of Levi-Civita symbol εijk and show that (10 points)
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3. Evaluate the area enclosed by a simply connected curve C : x2/3 + y2/3 = 4 in the x-y plane. (15 points)
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4. Show that the sum of the square of the matrix elements is invariant under orthogonal similarity transformation. (15 points)
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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.
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6. Solve the following 2nd-order ordinary differential equation. (15 points) y" + 2y' + y = 4e-x.
#208747
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= ? for n = l,2, and 3 .