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Welcome

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contents

Bessel function and its application

Bessel functions of rst kind

Solutions using bessels functions ofrst kind(problem)

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Applications of bessels

function Bessels euation arises %#en nding

seperable solutions to laplaceeuation and #elm#ot* euation insp#erical and cylindrical co+ordinates&

Bessels funtions are t#erefore

important for many problems of%a,e propagation and %a,epotentials&

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-or e'ample:

.ynamics of /oating bodies

0ngular resolution Heat conduction in cylindrical object

-reuency dependent friction in

circular pipelines& Bessels function also appear in signal

synt#esis (in fm or bessel lter)

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Bessels function

Bessel functions"rst dened by t#emat#ematician .aniel Bernoulli and t#engeneralised by -redric# Bessel"are t#e

canonical solutions y(') of bessels dierentialeuation

3y445'y45('3+n3)y 67 n7

%it# t#e general solution

96c;n( ')5c39n ') (

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Solutions using bessels

function of first kind 0 circular plate ofunit radius #as itsplane insulated &if

t#e initialtemperature if -(=)and if t#e rim is kept

at temperature *ero"nd t#e temperatureof t#e plate at anytime&

1 =

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gi,en :if t#e initial temperature if -(=)and if t#e rim is kept at temperature *erot#e temperature of t#e plate at any time&

(="t)?@&

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A

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Thank you