110年 - 110 國立臺灣大學_碩士班招生考試_應用力學研究所甲、乙組:工程數學(G)#100871

科目：研究所、轉學考(插大)◆工程數學 | 年份：110年 | 選擇題數：0 | 申論題數：12

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所屬科目：研究所、轉學考(插大)◆工程數學

選擇題 (0)

申論題 (12)

(a). (3%). Find A.

(b). (3%). Show that S_n = Aⁿs₀.

(c). (8%). Find the eigenvalues and corresponding eigenvectors of A.

(d). (6%). Find r_n (in terms of a, c, and r_o).

(a). (5%). For what scalar c, A is not invertible?

(b). (5%). Assume A is invertible (i.e., c what calculated in (a)). Find the determinant of.

(A).(2%).=?

(b). (3%). Solve y'+y=0.

(c). (10%), Solve the initial value problem y"+ y' -2y = 0； y(0) = 4, y'(0) = -5.

(d). (15%). Solve the initial valuc problem

(a). (20%). Find a solution that satisfies the boundary conditions u(0, t) = 0 and u(1, t) = 0 for t ＞ 0, and the initial conditions u(x,0) = sin zx and u_t(x,0) = 0 for 0 ＜x＜1.

(b). (20%). Find a solution that satisfies the boundary conditions u(O,t) = 0 and u(1,t) = sinwt for t ＞ 0, and the initial conditions u(x,0) = 0 and u_t(x,0) = 0 for 0 ＜x＜1.