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104年 - 104 國立中山大學_碩士班招生考試_電機系(甲組、丁組、己組)：工程數學甲#110231
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題組內容
Problem 2 (25%) Let F = (y
2
+ axz + yz)i +(x
2
+ bcy +xz)j +(x
2
+ cyz+ wy)k.
(a). (10%) Find the values of the constants a,b, c for which F is conservative.
其他申論題
沒有 【段考】高二數學上學期 權限，請先開通．
#471910
沒有 【段考】高二數學上學期 權限，請先開通．
#471911
(a) (10%) Define the thermal energyu(t,x)da. Show that under the above assumptions, T(t)is constant in time; i.e., f(x)dr, for all t≥0.
#471912
(b) (10%) Let f(x) = cos(πx). Find the solution u.
#471913
(b). (15%) For the values found in (a), ind a surface S with the following property: the path integral F ㆍ dr is equal to O for any two points P, Q (connected by any curve C) on the surface S.
#471915
(a) Suppose ItaA is nonsingular, thus, for any nonzero scalar a, Ωa := is a well-definedmatrix. Then we know from knowledge of eigensystem of a square matrix that, corresponding to any. What is the mathematical relation betweenλ and μ?(3%)
#471916
(b) If Ω1 , that is , is an orthogonal matrix, then what mathematical relation between A and ATcan be derived? (5%)
#471917
(c) If Ωa. is an idempotent matrix, then what are all possible values of det A ? (5%)
#471918
(a) Write out the set,where N(●)and R(●) indicate the null space and the range of a matrix, respectively. (5%)
#471919
(b) Consider the inner product space V =, where ＜A,B) :=tr(ATB) for A and B in . Describe Sh as the span of a set of orthonormal vectors in . (7%)
#471920
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