Page 1 of 2
FDM1033 VECTOR CALCULUS (May 2015 Semester)
This is an individual assignment worth 10% of your assessment in
this course. You must answer all the
questions. Each question/part carries equal mark. Do not use
computer to make your drawing, only
hand sketching is allowed.
Deadline: Please submit to FASD office by 10th July 2015
(Friday) before 5pm.
Note: You must provide your name, student ID and the course of
study, i.e., Petroleum Engineering,
Mechanical Engineering, etc. You can submit your answer script
to FASD office, Building 20.
Instruction:
Rule 1: For 3-dimensional space, you must use the standard
direction for the axes. Example:
Rule 2: Transparent object behind another transparent object if
object A is located behind object B,
object A is drawn in dashed line and object B is drawn in solid
line. Example:
y
But not
x
z
y
z
x
Page 2 of 2
QUESTION 1
In each of the following part, sketch the surface in
3-dimensional space represented by the following
equations. Unless otherwise stated, the domain for the graph
should be the whole 3-dimensional space.
a) xy in the first octant only
b) 242 zyx in the first octant only
c) 12 zy
d) 422 zx
e) 22 zxy
f) 22 yxz
QUESTION 2
In each of the following part, sketch and highlight the region R
in 2-dimensional space.
a) 2,82|),( 31 yxxyxR b) xeyxyxR 2),3ln()2ln(|),( c) 5,4|),(
411 xyyxR
x
d) 43
4,21|),( rrR
e) 20,12sin0|),( rrR
f) 23
,cossin|),( rrR
QUESTION 3
In each of the following part, sketch the solid S bounded by the
surfaces in 3-dimensional space.
a) 0,2,|),,( 2 zzyxyzyxS
b) 0,,1|),,( 22222 zyxzzyxzyxS c) 4,|),,( 2 zrzzrS d)
1,,4|),,(
232 zrzzrS
e) 20,,1|),,(43
4S
f) 23
2,0,2,1|),,( S
