108年 - 108 國立嘉義大學_碩士班招生考試試題_生物機電工程學系：工程數學#146471

科目：研究所、轉學考(插大)◆工程數學 | 年份：108年 | 選擇題數：0 | 申論題數：12

試卷資訊

所屬科目：研究所、轉學考(插大)◆工程數學

選擇題 (0)

申論題 (12)

(a)\( (x^3 - y)dx + (y^3 - x)dy = 0 \) (10%)

(b) \( y''+3y'+2y=2e^{-x} \) (15%)

(a) L{cos 2t}= ? (10%)

(b) \( L\{e^{3t} \cos 2t\} = ? \) (5%)

(c) \( L\{3^t \sin 2t\} = ? \) (5%)

(d)\( L\{e^{3t} t \sin 2t\} = ? \) (5%)

(a) Formulate the system as an Ordinary Differential Equation. (5%)

(b) Specify the initial conditions. (10%)

(c) Find the solution of this system. (10%)

(a) Find the surface elevations at point A(2,2). (5%)

(b) Determine the magnitude of the slope at point A. (10%)

(c) Determine the unit normal vector to the land surface at point A. (10%) (10%)