Kingdom of Saudi Arabia
Ministry of Education
قسم الرياضيات
Islamic University of Madinah
Faculty of Science
Department of Mathematics
Assignment
Methods of Applied Mathematics (Math 3031, Math 3431)
Last date of submission (May 13, 2025)
Q.1
0, 0 t 3
Evaluate L F ( t ) for F ( t ) =
2, t 3
Q.2
s 2 + 6s + 9
Evaluate L−1
.
( s − 1)( s − 2 )( s + 4 )
Q.3
Using Laplace transform, solve the initial value problem y − 6 y + 9 y = t 2e3t subject to
the conditions y ( 0 ) = 2, y ( 0 ) = 17
Q.4
Show that the set 1, cos x, cos 2 x, cos 3x,...... is orthogonal on the interval − , .
Q.5
Using Laplace transform, solve the boundary value problem
2u 2u
=
; 0 x 1, t 0
x 2 t 2
subject to the conditions:
u ( 0, t ) = 0, u (1, t ) = 0, t 0; u ( x, 0 ) = 0,
Q.6
u
= sin x, 0 x 1.
t t =0
Using Gauss-Jordan elimination method to solve the following system of linear
equations:
x1 + 3x2 − 2 x3 = −7,
4 x1 + x2 + 3x3 = 5,
2 x1 − 5 x2 + 7 x3 = 19.
Q.7
Using Cramer’s method, solve the following system of linear equations:
3x1 + 2 x2 + x3 = 7,
x1 − x2 + 3x3 = 3,
5 x1 + 4 x2 − 2 x3 = 1.
0
