Get premium membership and access revision papers, questions with answers as well as video lessons.

Sma2109:Applied Mathematics Question Paper

Sma2109:Applied Mathematics

Course:Bachelor Of Computer Science

Institution: Meru University Of Science And Technology question papers

Exam Year:2013

QUESTION ONE (30 MARKS)
a) Prove that ??-??(??) = -1 ??????(??), where n is a positive constant. (5 Marks) b) Solve the partial differential equation ??-?? ???? ?? = ??-?? ???? ?? = ??-?? ???? (6 Marks) c) Let ????(??) be the Lengendre polynomial of degree n. Show that for any function f(x), for which the nth derivative is continuous
dxxfx
n dxxPxf n n n n n ) ()1( !2 )1( )()( 1 1 2
1
1 ?? ?? ? ? ? (6 Marks) d) Expand the function
?? ?? =
0, - 1 < ?? < 0 1, 0 < ?? < 1
in terms of Legendre polynomials. (7 Marks) e) Show that
? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ??? ? ?
? ? ? ??
?
2
0
2
2
2
2
1
2
1
cossin ?
??
?
qp
qp
dqp
Where ?? = 2?? - 1 and ?? = 2?? - 1. (6 Marks)
QUESTION TWO (20 MARKS)
a) Show that x=0 is a regular point of the Bessel equation ??2 ??2?? ????2 + ?? ???? ???? + ??2?? = 0. Hence solve the equation. (15 Marks) b) Prove that ?????? ' = ?????? - ??????+1. (5 Marks)
2
QUESTION THREE (20 MARKS)
a) Find the Laplace transform of i. sin2??sin3?? (3 Marks) ii. sin3 2?? (4 Marks) b) If f(t) is of exponential order s and ?? ??(??) = ?? (??), prove that ?? ??'(??) = ???? ?? - ??(0). (6 Marks) c) Use Laplace transform method to solve ??2?? ????2 - 2 ???? ???? + ?? = ???? with ?? = 2,???? ???? = -1 at t=0. (7 Marks)
QUESTION FOUR (20 MARKS)
a) Find the Fourier series expansion for f(x) if
?? ?? =
-??, - ?? < ?? < 0 ??, 0 < ?? < ??
and deduce that ??2 8 = 1 12 + 1 32 + 1 52 + ?.
(10 Marks) b) Obtain the solution of the wave equation ??2?? ????2 = ??2 ??2?? ????2 using the method of separation of variables. (10 Marks)

Sma2109:Applied Mathematics Question Paper

More Question Papers

Popular Exams