Multivariable Calculus (MATS3101)
BSc, Chemistry - CHMS
Semester: Resit
Level: 300
Year: 2018
REPUBLIC OF CAMEROON THE UNIVERSITY OF BAMENDA
School/Faculty:SCIENCE Department:_CHEMISTRY Lecturer(s): Chi Walter Ndifon___
Course Code: _MATS3102____Course Title: MULTIVARIABLE CALCULUS RESIT
Date: _06-09-2018_______Halls: __ ________TIME: 2 HOUR (10:00-12:00)
Answers all questions each carry equal marks
QUESTION 1
Define the following terms
(i)
Dense set
(ii)
Nowhere dense set
(iii)
Neighborhood,
(iv)
Closure of a set
(v)
Cauchy sequence
(vi)
Complete set
(vii)
Interior of a set
(viii) Normed linear space
Question 2
(a) Define Vector space and list its examples, list all the axioms of a vector space
(b) Define linear combination and hence express the polynomial V=3t
2
+ 5t-5 as a linear combination
of the polynomial P
1
=
t
2
+2t +1, P
2
=
2t
2
+5t+4, P
3
=t
2
+3t+6
(c) Define linear dependent and hence show that the vectors (3,0,-3),(-1,1,2),(4,2,-2) and (2,1,1) are
linearly dependent over R
QUESTION 3
(a) Define Euclidean space and hence show that x
2
+y
2
+y
2
+4x- 6y+2z+6=0 is the equation of the
sphere. Describe its integration with the plane at Z= 1.
(b) Discuss greens theorem
Question 4
(a)
Define greens theorem, line integral and hence evaluate
−
+
−
,
,
along the straight
(0,1 to 1,2)
(b)
The straight lines (0,1), (1,1)
Verify that green theorem exist whereby C is a closed curve of the region bounded by y=x
2
,y
2
=x at
∮
2 −
+
−
(c)
Evaluate the following triple integrals
(i)
∭
− + dxdydz where
D = 1≤ X ≤2, 2≤y≤ 3, 1≤ Z ≤2.
(ii)
∭
+ − dxdydz where
D = 1≤ X ≤2, 2≤y≤ 3, 1≤ Z ≤2
GOOD LUCK
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