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MMP701S - MATHEMATICAL METHODS IN PHYSICS - 2ND Opp - JULY 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF NATURAL AND APPLIED SCIENCES
QUALIFICATION : BACHELOR OF SCIENCE
QUALIFICATION CODE: 07BOSC
COURSE CODE: MMP701S
SESSION: JULY 2022
DURATION: 3 HOURS
LEVEL: 7
COURSE NAME:
IN PHYSICS
PAPER: THEORY
MATHEMATICAL METHODS
MARKS: 100
EXAMINER(S)
SUPPLEMENTARY/SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
Prof Dipti R Sahu
MODERATOR: __| Prof. S.C. Ray
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
Non-programmable Calculators
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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Question 1
[25]
LJ
Newton’s law of cooling states that the rate of cooling of a body is directly proportional
to the temperature difference between the body and the surroundings
1.1.1 Formulate the differential equation and determine the temperature of the body
(10)
at any time, t.
1.1.2 A body at a temperature of 80°C cools to 60°C in 30min in a room
(5)
temperature environment of 300C. Find the temperature of the body after
16 min.
12 Solve the equation
xd +y(x+1) = 9x;y(1) = 15
(5)
1.3
Solve the initial value problem ty’ + 3y = 0, y (1) = 2, assuming t > 0
(5)
Question 2
[25]
2.1
A series circuit consists of a resistor with R = 40 , an inductor with L= 1H, a capacitor with
C=16x 10*F are connected with E(t) =100 cos10t. The circuit initial charge and current are
both zero.
2.1.1 Find the charge and current at time (t) in the circuit using the differential
(15)
equation of the above circuit
2.1.2 | Write down the steady state solution of the equation.
(5)
2.2 Solvey”+4y =e
Question 3
3.1
1 -l
IfA=
3
1
12
0 1]
andB=|2
3
1 |. find AB
1
3.2
Solve the system of equations using Gauss-Jordan elimination method
2x-3y =-21
3x- 2y=1
8x-5y = -49
3.3
Find the eigenvalues and eigenvectors of the 3 x 3 matrix
2 -1
Q
{=} -1l
2 —]1
(10)
[25]
(5)
(10)
(10)
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Question 4
[25]
4.1
Find the first three Laguerre polynomials from the Rodrigues formula
(5)
l
7”
L,() = —noe d:x” (x"e™ )
4.2 Determine the inner product of the following functions in [0, 1]
(10)
(a) f(x) = 8x,
(b) g(x) =x°- 1.
(c) Also find ||f|| and ||g]].
1
0
0
4.3.
Gi.ven the i: ndependent set of vectors: V, = l; ; v= 1; ; V;= 0; and
(10)
I
1
l
the corresponding orthonormal set
I
—3
0
e =2!t1P|; 7?) t2e3) 11 )7. %6-03372})-? 1
1
1
l
express the vector
3
B= ; as a superposition of (i) V (ii) ande