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研究所、轉學考(插大)◆工程數學
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110年 - 110 國立中山大學碩士暨碩士專班招生考試_部分碩士班:工程數學#105935
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3. Find out the particular solution of the ODE (10分)
y"+4y=-12 sin2x, y(0)= 1.8, y'(0)=5.0
其他申論題
2. 郁離子曰善戰者省敵不善戰者益敵省敵者昌益敵者亡夫欲取人之國則彼國之人皆我 敵也故善省敵者不使人我敵湯武之所以無敵者以我之敵敵敵也惟天下至仁為能以我之 敵敵敵是故敵不敵而天下服。 《郁離子‧省敵》
#451875
三、作文：40% 題目：論現今中文系學生的社會責任【文言白話不拘，請勿以詩歌或歌詞的形式寫作。請將內容寫於答案卷上】 【考生不可於文中書寫個人姓名或任何足以識別身分之文字或符號】
#451876
1. Find the general solutions of y1 and y2 (10 分) y'1=-y1-y2+8t+5y'2=-4y1+2y2+-15t-2
#451877
2. The tank in Fig. 1 contains 80 Ib of salt dissolved in 500 gal of water. The inflow per minute is 20 Ib of salt dissolved in 20 gal of water. The outflow is 20 gal/min of the uniform mixture. Find the time when the salt content y(t) in the tank reaches 95% of its limiting value (as t → ∞). (10分)
#451878
4. Use the Laplace transform to solve the following ODE (10 分) y(0)=0, y'(0)=-1
#451880
5. Use the Laplace transform to solve the following ODE (10 分) y" +2y'+5y = 25t-1000(t-π),y(0)=-2,y'(0)=5
#451881
6. LetFind the resultant matrices of the following expressions or give reasons why they are undefined. Each calculation result should be given in a step-by-step way. (a) BTA；(b) (3A -2B)T (e)aBaT；(d)3AT-2BT (10分)
#451882
7.Find the det(A) = ?, det(A x B)=?, and =?.
#451883
8.f = , plot the curve. Hin. Through the quadratic form, transform it to principal axes, and express [x1 x2] in terms of the new coordinate vector [y1 y2]. Please try specifying each dimension of your plotted conic section. (10 分)
#451884
9. Find the complex Fourier Series of f(x)=ex if-p＜x ＜pandf(x+2p)=T(x).(10分)
#451885
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