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研究所、轉學考(插大)◆工程數學
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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
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題組內容
Problem 5. Find the Fourier series of f(x).
(b)f(x)= {1,-1≤x≤1, 0,x＜-1;x＞1
其他申論題
(ii) Is it true that if Tr(AX) = 0, then AX = 0 (zero matrix)? Prove or disprove your answer.
#445029
(a) the first-order ODE:
#445030
(b) the second-order ODE:
#445031
(a)
#445032
Problem 6. Use Laplace transform to solve the following differential equation:
#445034
(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
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