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110年 - 110 國立清華大學碩士班考試入學試題_工程與系統科學系/乙組:工程數學#105230
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2. Solve the system of differential equations for x(t) and y(t).
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16.1995年時任美國國防大學的李必奇教授將資訊作戰區分為哪七大類？
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(b)
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3. Find the scries solution of the following differential equation about x = 0.You have to express the solution in the form of y(x) = C1y1(x)+ C2y2(x). To save time,you can only show the first five terms of yi(x) and y2(x).
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4. Use the Laplace transform to solve the problem and obtain y(t).
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(a) Find the determinant of M and obtain the inverse matrix .
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(b) Estimate the eigenvalues and eigenvectors of M.
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7. (a) Apply the divergence theorem to evaluate , (Fㆍn)dS where and S is the surface of the region bounded by the cylinder: r ≤ 5, 0≤θ ≤2π, 0≤ z≤ 4.
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(b) . Find ▽ X F. Evaluate , Fㆍdr where C is a counterclockwise circle x2 + y2 = 9 on the xy plane. [Formula] Divergence and curl in cylindrical coordinates:
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