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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:

其他申論題

4. Use the Laplace transform to solve the problem and obtain y(t).

(a) Find the determinant of M and obtain the inverse matrix .

(b) Estimate the eigenvalues and eigenvectors of M.

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.

8. (a) The Fourier integral representation of f(x) is f(x)=cos wx+ b(w) sin wx]dx. Find a(w) and b(w).

(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)= cos wx + d(w) sin wx]dx. Find c(w) and d(w).

9. Solve the Dirichlet problem in polar coordinates: , 1≤r≤2, 0≤θ≤,wih u(r,0) =0, =0, u(1,θ) =0,u(2,θ)=10.

10.(a) Evaluate dz where C is the counterclockwise circle [z] = 4.

(b) Evaluate the integral dx by residue theorem.

1.我國的軍事危機以________________________為核心，配合________________________，成為國軍危機處理機制。

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