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 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
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 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 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
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
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 1
Learning Outcomes: This assignment will give you practice in
double and triple integrals
curves and surfaces
vectors including scalar and vector products
grad
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