阿摩線上測驗
登入
首頁
>
研究所、轉學考(插大)◆工程數學
>
110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:工程數學(A)#104946
>
Problem 6. Use Laplace transform to solve the following differential equation:
其他申論題
(a) the first-order ODE:
#445030
(b) the second-order ODE:
#445031
(a)
#445032
(b)f(x)= {1,-1≤x≤1, 0,x＜-1;x＞1
#445033
(a) Assume that Re{f(z)} = x3 -3xy2. Find the imaginary part Im{f(z)} so that f(z) is analytic for all x .
#445035
(b) Assume that u(x, y) = x3 +3xy2. Show that it is impossible to find a real-valued function v(x, y) such that f(z) = u(x,y) + iu(x,y) is differentiable with respect to z for all z .
#445036
(a) Calculate f'(0) and f"(0).
#445037
(b) Find the Taylor series expansion of f(z) about the point z = 0; that is, find the coefficients such that in a certain neighborhood of x = 0.
#445038
(c) Continuing from part (b), what is the region of convergence?
#445039
(d) Let C denote the path along the y axis from -∞ to oo. Calculate f(z)dz; i.e., evaluate the following integral:
#445040
阿摩線上測驗
登入
阿摩線上測驗
登入