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研究所、轉學考(插大)◆工程數學
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109年 - 109 國立成功大學碩士班招生考試_電機工程學系、電機資訊學院、微電、奈米聯招:工程數學#103780
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5. Determine the inverse Laplace transform of the function
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其他申論題
2. Prove the integral as following (15%)
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(a) Find the eigenvalues (λ1 ≥ λ2 ≥ λ3) of the matrix (10%)
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(b) Obtain an orthogonal matrix P which givesPTAP=diag (λ1,λ2,λ3) (10%)
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4. Find the eigenvalues and eigenfunctions of the following problem. (20%) y"+λy=0；y'(0)=y'(L)=0
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6. Let vectorfield F=2yzi-4xzjtspk. Evaluate the value of the surface integral , where Σis the sphere of radius 5 about (-1,3,1) . (15%)
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For problem 1~10, each counts 10 points 1.
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2.
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3.
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4. Please prove the quotient rule: If f and g are differentiable at x and g(x)≠0, then the quotient f /g is differentiable at x and
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5.
#438958
. (15%) 
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. (15%)