Engineering Mathematics 2
Assignment 9
1. State the Divergence Theorem. Evaluate both sides of the Divergence Theorem for the vector
field =
over a volume V which is the interior of the unit cube, i.e. the cube whose
vertices are (0,0,0, (1,0,0), (0,1,0),
Engineering Mathematics 2
Assignment 10
1. Verify the conclusion of Greens Theorem (Curl integral) by evaluation of both sides of
Greens Theorem for the field = + . Take the domains of integration in each case to be
the disk R: +
and its bounding circle
Engineering Mathematics 2
Assignment 8
1. Calculate
.d
where
=4
(a) C:
=
(b) C:
=
2. If
=
3 +2
+ +
0 1
+ +
+
over each of the following curves from (0, 0, 0) to (1, 1, 1)
0 1
, evaluate
. d
where S is the rectangular box formed by the six planes
= 0, =
Engineering Mathematics 2
Assignment 11
1. Evaluate
.d
where, is the circle
+
= 4, = 3 orientated counterclockwise as seen by a person
standing at the origin, and with respect to right-handed Cartesian coordinates.
Here,
=
+
Use Stokes Theorem to evaluate
Engineering Mathematics 2
Assignment 12
1. A 2 - periodic function ( ) can be represented in Fourier-series form
( )=
(
+
cos
+
sin
)
Show that the coefficients are given by Eulers formulae
=
=
=
1
1
1
2
( )d
( ) cos
d
( ) sin
d
n =1, 2,3,
2. Consider
Nazarbayev University, School of Engineering, Eng Maths 2
Engineering Mathematics 2
Assignment 1
Learning Outcomes: This assignment will give you practice in
double and triple integrals
curves and surfaces
vectors including scalar and vector products
grad
Nazarbayev University, School of Engineering, Eng Maths 2
Engineering Mathematics 2
Assignment 2
Learning Outcomes: This assignment will give you practice in
investigating the equations of cross-sections for a function of 3 variables
parameterizing a spac
Nazarbayev University, School of Engineering, Eng Maths 2
Engineering Mathematics 2
Assignment 4
Learning Outcomes: This assignment will give you practice in
Div, Grad and Curl
Taylor Series for more than one variable
1. (a) Find the gradient of the scala
CENG1001 Transport Processes I Deadlines: Qu 1 & 2 : Qu 3 & 4: Friday 18th December 2009 Friday 15th January 2010
Coursework
1.
2009, Q6 Heat is conducted through a large flat wall of uniform thickness, which is made of material whose thermal conductivity