الفهرس 
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Abstract
The thesis contains four chapters. In chapter I a c’ear summary of the well known methods of numerical io- t~rration such as the trapezoidal and Simpson rules is Given and an approximate upper bound of thr; error in these two methods is derived. Also the method of quadrature fro~ a table of values and the Gauss tWG-pdint and three point integration formulae are giver: in ~ clear and sys-
Chapter 11 eives a new method of exp3.nding a defi-nite integral as
rals of the form a series. Asymptotic formulae b . ( )
1(0<.) = J f(p) F(p)e-c”p-c
a for integ- dp are c:iven• Using these results,expansions for integrals such 0.: oc cc sin xp
~ J J
as J f(p) sin xp dp, f(p) cos xn dp, f(p) dp,
t’
0 0 0 p
~ ex: 0,:: _x2p2
J J f(p)J1 (xp)dp ( .•. ’ ( ,
f(p) J (xu)dp, ar,d .’ p) e dp
o . j
0 0 0
cculd be obtained, which are very useful in solving boun-
dary value problems by the method of integral transforms
and in the evaluation of many difficult integrals which
appear in math~matical physics.
Chapter 111 also gives a new method for the evalua¬tion of indefinite integrals involving Legendre,aermite,