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研究所、轉學考(插大)◆工程數學
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110年 - 110 國立清華大學碩士班考試入學試題_聯合招生:工程數學#105258
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題組內容
6.
(a) Let f(x,y) = asin(xy) +x
2
+4y
2
(1 -y). For what values of a will f have a local minimum at (0,0)? (5%)
其他申論題
3. Find the series solution of the following differential equation about x = 0. (10%) 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 y1(x) and y2(x).
#446423
4. Use the Laplace transform to solve the problem and obtain y(t). (5%)
#446424
(a) Find the determinant of M and obtain the inverse matrix .(3%+4%)
#446425
(b) Estimate the eigenvalues and eigenvectors of M.(4%+4%)
#446426
(b) Let (a≥0). Find I'(a). It is evident that I(0) = 0. Solve I(a). (5%)
#446428
(a) Apply the divergence theorem to evaluate and S is the surface of the region bounded by the cylinder: r≤5, 0≤ θ ≤ 2π, 0≤ Z≤ 4. (5%)
#446429
(b) Let F =Fㆍdr where C is a counterclockwise circle x2 + y2 = 9 on the xy plane. (5%) [Formula] Divergence and curl in cylindrical coordinates:
#446430
(a)Let A0 ＞0. The Fourier integral representation of b(ω) sin wx]dx. Find a(ω) and b(ω). (5%)
#446431
(b) Consider an infinite beam problem Elu"" + ku = f(x) with the loading f(x) given in (a). The deflection u can be solved and written as u(x)= d(ω) sin wxJdx. Find c(ω) and d(ω). (5%)
#446432
9. Solve the Dirichlet problem in polar coordinates:,u(1,θ)=0,u(2,θ)=10. (10%)
#446433
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