ENGI 3424
Final Examination 2013 Fall
Page 1 of 2
1.
By any valid method, find the complete solution to the initial value problem
dy
y ( 0)
,
= e7 x = 1
+ 7y
dx
2.
The response x(t) of a mass-spring system that is subjected to a sudden hammer
blow at the
ENGI 3424 Engineering Mathematics
Problem Set 8 Solutions
(Sections 4.5 - 4.8 Gradient Vector, Maxima & Minima)
1.
A scalar field V ( x, y, z ) in 3 is defined by
x2 + y 2
V ( x, y , z ) =
1+ z2
(a) Evaluate the gradient vector V at the point P (3, 4, 0)
ENGI 3424 Engineering Mathematics
Problem Set 9 Solutions
(Sections 5.01 5.06 Sequences, Series, Tests for Convergence)
1.
Write down the next two terms and the general term an of the sequence
1 3 7 15
cfw_ an = , , , ,
2 4 8 16
Determine whether or no
ENGI 3424 Engineering Mathematics
Problem Set 7 Solutions
(Sections 4.1 - 4.4 Partial Derivatives, Differentials, Jacobians)
1.
2u
2u
Find
and
for the function u ( x, y, z , t ) defined by
x2
z t
u 2 = x2 + y 2 + z 2 t 2
Differentiate implicitly:
u 2
ENGI 3424 Engineering Mathematics
Problem Set 4 Solutions
(Sections 2.2 - 2.4 Second order linear ordinary differential equations)
Determine the general or complete solution, as appropriate, without using Laplace transforms.
Note: If a complete solution i
ENGI 3424 Engineering Mathematics
Problem Set 6 Solutions
(Chapter 3 Laplace transforms)
1.
Find the Laplace transform F (s) for the function
f ( t ) = t 4e 2t
cfw_
The first shift theorem is L cfw_ f ( t ) = F ( s ) L f ( t ) e at
and L cfw_ t n =
n!
s
ENGI 3424 Engineering Mathematics
Problem Set 5 Solutions
(Chapter 3 Laplace transforms applied to linear ODEs; complex numbers)
Where possible, use Laplace transforms to determine the general or complete solution, as
appropriate. Questions 1-13 are ident
ENGI 3424 Engineering Mathematics
Problem Set 2 Solutions
(Chapter 1 all sections)
1.
Find the complete solution of the initial value problem
dy
4x
y ( 0)
,
= 2 x e= 1
+ 4y
dx
dy
2x e
+ 4 y =4 x is linear.
dx
R
P
P dx = 4 dx =
h=
R dx
e= e
h
4x
eh =
ENGI 3424 Engineering Mathematics
Problem Set 3 Solutions
(Section 2.1 Second order homogeneous linear ordinary differential equations)
Determine the general or complete solution, as appropriate, without using Laplace transforms.
Note: If a complete solut
ENGI 3424 Engineering Mathematics
Problem Set 1 Solutions
(Sections 1.1 and 1.2)
1.
Find the general solution of the ordinary differential equation
dy
y
+ x = 0
dx
dy
). However, it is separable.
dx
y2
x2
=
+ C
2
2
This ODE is not linear (due to the prod
ENGI 3424 Engineering Mathematics
2011 Fall
Final Examination Questions
1.
By any valid method, find the complete solution to the initial value problem
d2y
dy
+ 2
= 4 e 2 x ,
y ( 0 ) = y ( 0 ) = 0
2
dx
dx
[14]
2.
Find the general solution of the ordinary
2010 Fall
ENGI 3424 Final Examination Questions
Page 1 of 2
1.
By any valid method, find the complete solution of the ordinary differential equation [12]
d2y
dy
+ 8
+ 15 y = x ,
6
y ( 0 ) = ( 0 ) =
2 e5
1, y
2
dx
dx
2.
A metal bar in a bucket of ice water
ENGI 3424 Engineering Mathematics
2012 Fall
Final Examination Questions
1. (a) Use the RK4 (Runge-Kutta) method with a single step (h = 0.2) to estimate
the value of y at x = 0.2 given that y(0) = 1 and that y is the solution of
the ordinary differential
ENGI 3424 Engineering Mathematics
Problem Set 10 Solutions
(Sections 5.07 5.11 Power Series, Fourier Series, Series Solutions of ODEs)
1.
Find the radius R and interval I of convergence for the power series
f ( x) =
( 2x 6)
n
n =1
lim
n
( 2x 6)
lim
=
un+1