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109年 - 109國立臺灣大學_碩士班招生考試_化學工程學研究所:工程數學(E)#106052
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3. (10%) Solve the differential equation, y"-ty'+y=1, y(0)=1, y'(0)=2
相關申論題
1. (10%) Given a position vector below, determine the velocity, speed, acceleration, the tangential and normal component of acceleration, the curvature, and the unit tangent vector, unit normal vector. F-3ti-2j-2k
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2. (10%) Find the Laplace transform of At)-[sin(t)-cos(t)]2
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4. (10%) Produce a matrix P that diagonalizes the matrix below:
#452422
5. (10%) Find the general solutions of
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6. (25%) Let u-u(x，y，t) be a function of the space (x.y) and the time t. S=S(s,f) is a function of x and t, and cl and co are constant. Determine whether the method of separation of variables is applicable to the following partial differential equations or not (each has 5 %). The rationale behind your answer needs be given; otherwise, it will not be credited.
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7. (25%) Let u=u(xy) be a function of x and y. (x), g(x), f1(y), and g1(y) are given; K and L are positive constant. Solve the problem:
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8. (10%) Find the inverse Fourier transform of the function
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7. (10%) Find the Fourier integral of f(x).
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6. (15%) Solve the PDE below.
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5. (15%) Solve the PDE below.
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相關試卷
110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:工程數學(E)#100594
110年 · #100594
109年 - 109國立臺灣大學_碩士班招生考試_化學工程學研究所:工程數學(E)#106052
109年 · #106052
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