110年 - 110 國立中山大學_碩士暨碩士專班招生考試_海下所:工程數學#104424

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：11

試卷資訊

所屬科目：研究所、轉學考(插大)◆工程數學

選擇題 (0)

申論題 (11)

1. Evaluatefor any a ＞ 0. (5%)

(1) Let u1 = ＜3, 1＞, u2= ＜1, 1＞. Transform them into an orthonormal basis. (5%)

(2) Let u1 = ＜1, 1, 1＞, u2 = ＜1, 2, 2＞, u3 = ＜1, 1, 0＞ . Transform them into an orthonormal basis. (5%)

3.Let . Find a symmetric matrix B and a skew-symmetric matrix C, such that B+C=4. 1 0] (5%)

4.Solve +y=x, y(0)=3.(10%)

(1) Find L{sin(2t)}. (5%) (Write down the detailed process)

(2) Solve +3y= 13sin(2t), y(0)=6.(15%)

6.Please write down the Bessel's differential equation. (7%)

7. Find y when y"x² + (x² -81)y = -xy'.(10%)

8.Find the eigenfunction of the following equation: y"+ ky =0, y(0)-y(L)-0.(15%)

9. Find the Fourier series in complex form for the periodic function f(t) with period 2, .(18%)