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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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4. Use the Laplace transform to solve the following ODE (10 分)
y(0)=0, y'(0)=-1
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#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
3. Find out the particular solution of the ODE (10分) y"+4y=-12 sin2x, y(0)= 1.8, y'(0)=5.0
#451879
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
10. Find the trigonometric polynomial F(x) of the form:for which the square error with respect to the given f(x) = x2 on the interval -π ＜x ＜ π is minimum. Compute the minimum value for N = 1, 2, ..., 5. (10 分)
#451886
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