課程名稱︰工程數學一
課程性質︰化工系必修
課程教師︰李克強
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2018年1月12日
考試時限（分鐘）：120分鐘
試題 :
(1) (25%)Find each of the power series solutions of the following ODE:
y''+y'+(1/(1-x))y=0 │x│<1
Write the first two non-zero terms for each of the series of solutions.
(2) (25%)Find the solution of the following Bessel equation:
x^2y''+xy'+(x^2-1)y=0, x∈[0,1]
BC:y(0) is finite and y(1)=1
(3) (25%)Find the eigenvalues and corresponding eigenfunctions of the
following S-L problem:
y''+λy=0 x∈[0,1]
BC:y'(0)=0 and y(1)=0
Note:λ>0 here
(4) (25%)Use finite difference (FD) method to solve the following ODE
with only one interior point, i.e. N=1, located at x=0.5:
y''+siny=1, x∈[0,1]
BC:y(0)=1 and y'(1)=0
(A)Write down the corresponding finite difference equation in
terms of y1=y(0.5)
(B)Solve the equation numerically with the Newton-Raphson iteration
scheme and find out the value of y(0.5)