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110年 - 國立新竹女中高二110上學期數學A第三次段考(期末考)#110230
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#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
(a). (10%) Find the values of the constants a,b, c for which F is conservative.
#471914
(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
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