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Four pages  Page one
University of the Witwatersrand
Advanced Techniques in Physics : 2002
Examination : June 2002

Instructions
 There are six questions in total, grouped into two sections.
The two sections must be answered in separate books.
 Section 1 comprises of questions 1, 2 and 3.
 Section 2 comprises of questions 4 and 5.
Section two also contains a take  home question. This will be question 6
which does not appear in this paper and will not be answered in the answer book.
You will receive question 6 on Wednesday 8:30 27 June. There will be
24 hours to answer question 6.
 Answer all questions, 1 to 5. Questions can be attempted in any order.
Start each new question on a new page.
Time: 
Questions 1 to 5 
2 hours 
(exam conditions) 



Total Marks (15) = 130 

Question 6 
One day 
(take home conditions) 



Total Marks (6) = 70 
Questions 13 not included.
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Four pages  Page three
PHYS400
PHYSICS HONOURS
June 2002 Advanced Techniques in Physics
 4.
 Consider the ordinary differential equation
where initial values are specified, and may
have either sign.
 (a)
 Discuss the condition (ill or otherwise) of an attempted
numerical integration of this O.D.E. by, for example, a
RungeKutta method.
(6)
 (b)
 Relate the above discussion to the condition of numerical
generation of special functions by recurrence relations.
As a specific example consider
recurrence relation for the cylindrical Bessel
functions
and are replaced by or
for the regular or
irregular solution respectively.
Demonstrate (using the recurrence relation)
why forward recurrence is stable for generation
of the but not for generation of the
unless .
(6)
 (c)
 Describe an alternative method for generation of the
when .
(3)
4/Page four...
Four pages  Page four
PHYS400
PHYSICS HONOURS
June 2002 Advanced Techniques in Physics


 5.
 In discussing computer representation of numbers and arithmetic we can
write :
The symbol represents any primary operation.
 a)
 Find the relative error in addition to first order and
show that if and differ in sign with
then there is a disasterous loss of accuracy.
(8)
 b)
 Show in addition that error propogation in summing truncated
series is minimised by adding terms in ascending order of
magnitude.
(7)
 6.
 To be a take home component on Friday 21 June.
(70)
Total Question 15 : [130 marks]
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