110年 - 110 國立中山大學_碩士暨碩士專班招生考試_部分碩士班:工程數學#104438

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

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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 (11)

(a) Solve x² y"-xy-3y= x²by undetermined coefficients and variation of parameters respectively. (10%)

(b) y"+4y=g(x), y(0)=1,y'(0)=2 (10%)

[Hint]: Solve this problem on two intervals, and then find a solution so that y and y' are continuous at x=π/2.

(a) Evaluate the net outflow rate of V across a sphere x+ y +2'=4 (10%)

(b) What is the outflow rate across the upper hemi-sphere x² + y² +z²=4 、 z ＞0 and the lower hemi-sphere x²+y²+z²=4 、z＜0,respectively. (10%)

(a)(6%)

(o) (7%)

(C) (7%)

(a) Find the Fourier integral representation of the function f(t). (10%)

(b) Evaluate dw (5%)

5.(Partial Differential Equation】(15%)

Solve the following PDE using the Method of Separation of Variables.

=0,0＜x＜a, 0＜y＜b boundary conditions:

6. (Complex Analysis】 (10%)
Evaluate the integral