96年 - 96 淡江大學轉學考應用數學#55961

科目：研究所、轉學考(插大)-應用數學 | 年份：96年 | 選擇題數：0 | 申論題數：8

試卷資訊

所屬科目：研究所、轉學考(插大)-應用數學

選擇題 (0)

申論題 (8)

1 Show that the area A enclosed by a simply connected curve C : x^2/3 + y^2/3 = 4 in the x-y plane is 24π. (15 points)

2. A matrix is both Hermitian and Unitary. Show that its eigenvalues are ±1, (15 points)

【已刪除】3. Find (he Laplace transformation of the square wave with period of a defined by

(15 points)

【已刪除】4. Suppose that/(jc) = jc',/2is a self-reciprocal under Fourier cosine transform, apply the given result and evaluate the Fresnel integral

(15 points)

【已刪除】5’ Given

=π ln 2, show that

(15 points)

6, Given/(jc) = (x + 1)²,-1≤x≤1) expand f(x) in terms of Legendre polynomials. (10 points)

【已刪除】7. (a) Write down ftinction form of Legendre polynomials

(5 points)

【已刪除】(b) Using

(10 points)