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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 4. Solve the ODEs:
(a) the first-order ODE:
其他申論題
(ii) find the projection matrix such that , and;
#445026
(ii) find the eignevalues and eigenvectors of .
#445027
(i) Is Tr(AX)≥ 0 true?
#445028
(ii) Is it true that if Tr(AX) = 0, then AX = 0 (zero matrix)? Prove or disprove your answer.
#445029
(b) the second-order ODE:
#445031
(a)
#445032
(b)f(x)= {1,-1≤x≤1, 0,x＜-1;x＞1
#445033
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
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