103年 - 103 國立嘉義大學_碩士班(甲組)招生考試試題_土木與水資源工程學系：工程數學#146090

1. Find the solution by separating variables method. (20%) \[ \frac{\partial u}{\partial x} = \frac{\partial u}{\partial y} \] B.C.: \( u(0, y) = 2e^{-4y} \)

2. \( z^2 + z + 1 - i = 0 \), find the solution. (20%)

(a) Calculate the determinant for A (5 %)

(b) Calculate A⁵ -A =? (10 %)

(c) Calculate A^T +A =? (5 %)

(a) y+xy′=0 (5%)

(b) y′′ + y = t , y(0) = 1 , y′(0) =0 (using Laplace transform method) (15%)

(a) Calculate the Laplace Transform of f(t) (10%)

(b) Calculate the Fourier Transform of f(t) (10%)
Hint: The Heaviside function H(t) and shifted Heaviside function