Download PHE-05 (2003)

PHE-05
ASSIGNMENT BOOKLET
Bachelor's Degree Programme
MATHEMATICAL METHODS IN PHYSICS-II
School of Sciences
Indira Gandhi National Open University
Maidan Garhi,
New Delhi-110068
2003
Dear Student,
We hope you are familiar with the system of evaluation to be followed for the Bachelor’s Degree Programme. At
this stage you may probably like to re-read the section on assignments in the Programme Guide for Elective
Courses that we sent you after your enrolment. A weightage of 30 per cent, as you are aware, has been earmarked
for continuous evaluation which would consist of one tutor-marked assignment for this course.
Instructions for Formating Your Assignments
Before attempting the assignment please read the following instructions carefully.
1) On top of the first page of your TMA answer sheet, please write the details exactly in the following format:
ENROLMENT NO.:……………………………………………
NAME :……………………………………………
ADDRESS :……………………………………………
……………………………………………
……………………………………………
COURSE CODE:
…………………………….
COURSE TITLE :
…………………………….
ASSIGNMENT NO. ………………………….…
STUDY CENTRE:
………………………..…..
DATE :………….……………………….………...
PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION AND TO
AVOID DELAY.
2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.
3) Leave 4 cm margin on the left, top and bottom of your answer sheet.
4) Your answers should be precise.
5) While solving problems, clearly indicate the question number along with the part being solved. Be precise.
Write units at each step of your calculations as done in the text because marks will be deducted for such
mistakes. Take care of significant digits in your work. Recheck your work before submitting it.
6) This assignment will remain valid for one year. However, you are advised to submit it within 8 weeks of
receiving this booklet to accomplish its purpose as a teaching-tool.
Answer sheets received after the due date shall not be accepted.
We strongly feel that you should retain a copy of your assignment response to avoid any unforeseen situation and
append, if possible, a photocopy of this booklet with your response.
We wish you good luck.
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Tutor Marked Assignment
Mathematical Methods in Physics-II
Course Code: PHE-05
Assignment Code: PHE-05/TMA-1/2003
Max. Marks: 100
Note: The marks for each question are indicated against it. Symbols have their usual meanings.
1. Classify and solve the following differential equations.
a)
y + y tan x = sin 2x
b)
x2 y  1.5 xy  1.5 y = 0 (Hint: Put y = xm).
(25)
2. Obtain the series solution of the equation
x(x  1) y + (3x  1) y + y = 0.
(10)
3. Solve the following equations:
(a)
y  y  2y = 10 cos x
(5)
(b)
y  2y + y = ex + x
(5)
4. Obtain the electric current in an RC circuit to which a sinusoidal signal E = E0 sin t is applied. It is given
that at t = 0, the current and the charge in the circuit are both zero.
(10)
5. Solve the following equation for u up to the first three non-vanishing terms:


d 
du 
1 x 2
 u  x 2 u  0

dx 
dx 
This equation represents the hydrogen molecular ion with  and  being constants.
(10)
6. Classify and separate the following PDEs into ODEs:
a)
 2u
t 2
 c2
 2u
x 2
 A sin t
where A is constant.
b)
 2u
t 2
 c2
 4u
x 4
(5)
0
(5)
7. Obtain all partial derivatives up to the second order of the following functions:
a)
f = k sin x sin 2y
(5)
b)
f = xy (a2  x2) (b2  y2)
(5)
3
8. Solve the equation
u ( x, t )
 2 u ( x, t )
 c2
t
x 2
given that u (x, 0) = sin 0.1 x
u (0, t) = 0 = u (L, t) for all t.
(10)
9. Obtain the Fourier series of the following functions:
(a)
f ( x)  x 3
(  x  )
(b)

 2k t
f (t )  
2k (1  t )

0t
1
2
(25)
1
 t 1
2
10. A vibrating string of length  has both its ends fixed. Obtain its deflection u(x, t) corresponding to zero initial
velocity and initial deflection: k(sin x  sin 2x), where k is a constant. Take c2 = 1.
(10)
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