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

(a)

(b)

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(a) (7%) Find the Laplace transform for

(b) (8%) Given a second order differential equation y"-y = / with initial conditions J(0) = y(0)=I. please find the solution by using Laplace transform method.

3. (10%) F= [x. y. z] is a three-dimensional vector. Please calculate the value of a surface integral ∫∫s [ F● n] dA. where S is a surface defined as x³ + y² +z² =9 and n is the normal vector of S.

4. (10%) Solve the following ODE

5. (15%) Solve the PDE below.

6. (15%) Solve the PDE below.

7. (10%) Find the Fourier integral of f(x).

8. (10%) Find the inverse Fourier transform of the function

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

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