b.sc.mathematics sem 5 & 6 syllabus cbcs dt 01 02 2013

8/19/2019 B.sc.Mathematics Sem 5 & 6 Syllabus CBCS Dt 01 02 2013

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SAURASHTRA UNIVERSITY, RAJKOT

SAURASHTRA UNIVERSITY

RAJKOT

MATHEMATICS

Syllabus of B.Sc. Semester-5 & 6

Accordin to C!oice Based Credit System

Effecti"e from #une $ %'%

(Updated on date:- 01-02-2013and updation ip!eented "#o June - 2013$

Updated on Date: - 01-02-2013 Page ' of %(




Syllabus of B.Sc. Semester-5



(Updated on date:- 01-02-2013

and updation ip!eented "#o June - 2013$

• )roram* B.Sc.

• Semester* 5

• Sub+ect* Mat!ematics

• Course codes* BSMT-5',A -T!eoryBSMT-5%,A -T!eory

BSMT-5,A -T!eory

BSMT-5',B - )ractical

BSMT-5%,B - )ractical

BSMT-5,B - )ractical

' )ro+ect

• Total Credit /f T!eSemester 5*

%0 Credit

Updated on Date: - 01-02-2013 Page % of %(




B. Sc. MATHEMATICS SEMESTE1* 2• T!e Course 3esin of B. Sc. Sem.- 2 ,Mat!ematics accordin to c!oice based

credit system ,CBCS com4risin of )a4er umber )a4er ame o. of t!eory

lectures 4er 7ee8 o. of 4ractical lectures 4er 7ee8 total mar8s of t!e eac! 4a4er

are as follo7s *

S1./

.S9B#ECT

/. /:

THE/1;

<ECT91E )E1

=EE>

/. /:

)1ACTICA<

<ECT91E

)E1 =EE>

T/TA<

MA1>S

Credit /f

Eac!

)a4er.

1

)A)E1 BSMT-5' ,A

,T!eory

Mat!ematical Analysis-' &

?rou4 T!eory

6 -

70(External)+

30 (Internal) =

100 Mar!

"

2

)A)E1 BSMT-5% ,A

,T!eory

)rorammin in C &

umerical Analysis-'

6 -

70(External)+

30 (Internal) =100 Mar!

"

3

)A)E1 BSMT-5 ,A

,T!eory

3iscrete Mat!ematics &

Com4le@ Analysis-'

6 -

70(External)+

30 (Internal) =

100 Mar!

"

"

)A)E1 BSMT-5' ,B

,)ractical

umerical Analysis $ I

- 6

3#(External)+

1#(Internal) =

#0 Mar!

3

#

)A)E1 BSMT-5% ,B

,)ractical)

)rorammin in C

lanuae

- 6

3#(External)+

1#(Internal) =

#0 Mar!

3

6

)A)E1 BSMT-5 ,B

,)ractical

)rorammin 7it!

SCI<AB

63#(External)+1#(Internal) =

#0 Mar!

3

7 )ro+ect =or8 & 2i"a

• 1 $%&dan'e e't%re for a

gro%p of 3 to # !t%dent! *

ee

• E,al%at&on of proe't &ll

.e &n /I !ee!ter

4e t&tle of t4e

proe't or to

.e de'&ded and

data &ll .e

'olle'ted &n t4&!

!ee!ter

3

Total credit of t!e semester 2 %0

Updated on Date: - 01-02-2013 Page of %(




Mar8s 3istribution /f Eac! )a4er

for

T!eory and )ractical , for SEMESTE1-2

• Total Mar8s of Eac! T!eory )a4er

E@ternal E@amination

% Mar8s ,MC testD

5 Mar8s ,3escri. ty4eF Total Mar8s.


Internal E@amination

' Mar8s Assinments D

' Mar8s 9IG test D

' Mar8s Internal e@am.

Total Mar8s

• Total Mar8s of Eac! )ractical

)a4er E@ternal E@amination

5 Mar8s


)a4erInternal E@amination

'5 Mar8s

Continuous internal assessment of4ractical 7or8

:ormat of uestion )a4er

• 4ere !4all .e one 5%e!t&on paper of F mar8s & %'

% !ours for ea'4 Mat4eat&'!

4eor Paper .

• 4ere !4all .e T=/ sections &n t4&! paper &e Section A and Section B

Section $ A

Section A &! of % Mar8s &t4 % MC tpe 5%e!t&on! (%lt&ple '4o&'e 5%e!t&on!) 'o,er&ng t4e

4ole !lla.%! &n e5%al e&g4tage

Section $ B

Section B is of 5 Mar8s &t4 t4e follo&ng tpe of 8 5%e!t&on! 'o,er&ng t4e 4ole

!lla.%! &n e5%al e&g4tage9 ea'4 of tent f&,e ar!

%e!t&on 1 and 2 &ll 'o,er %n&t 1 and 2 re!pe't&,el

uestion no. (;) ;n!er an t!ree out of si@ 6 Mar!(<) ;n!er an t!ree out of si@ Mar!

(>) ;n!er an t7o out of fi"e 10 Mar!

T/TA< %5 MA1>S

Updated on Date: - 01-02-2013 Page 0 of %(




-* )ro+ect =or8*-

• 4ere &ll .e a proe't on an top&' &n Mat4eat&'! prefera.l not 'o,ered &n t4e

!lla.%!

• 4e proe't &ll .e a!!&gned &n t4e tea! (gro%p!) of at lea!t one and at o!t f&,e

!t%dent!• 4ere &ll .e one le't%re per ee to g%&de and ot&,ate for ea'4 gro%p of !t%dent!

• op&' of t4e proe't a .e !ele'ted .a!ed on t4e follo&ng

1 Deand of at4eat&'! re5%&red to 'ater t4e need of &nd%!tr&e! and t4e !o'&et a! a4ole

2 ?e top&' not ta%g4t %p to f&nal !ee!ter

3 4e top&' a .e an exten!&on of top&' 'o,ered &n an of t4e top&'!*!%.e't ta%g4t %pto !&xt4 !ee!ter

" Inno,at&,e tea'4&ng et4odolog of Mat4eat&'! a al!o .e !ele'ted a! a top&' of

t4e proe't or

# /t%dent! a al!o 'on!tr%'t &nno,at&,e odel! .a!ed on at4eat&'al 'on'ept! e,en

t4o!e ta%g4t at !e'ondar or 4&g4er !e'ondar le,el6 E,er proe't or e,en odel %!t .e !%.&tted &t4 proper do'%entat&on a.o%t t4e

'on'ept and t4e odel

• 3urin t!e fift! semester students 7ill be

1 Introd%'ed and a!!&gned t&tle of t4e proe't92 ea! &ll .e fored for t4e !ae

3 Ea'4 gro%p &ll !t%d9 !ear'4 referen'e9 'olle't data and or-o%t deta&l! for t4e&r

top&' of proe't-or

• 3urin t!e si@t! semester

1 /t%dent! &ll f&nal&@e9 do'%ent9 !%.&t and get t4e proe't or 'ert&f&ed &n t4e&r

nae!

2 4e proe't or %!t .e !%.&tted . t4e !t%dent &n t4e fo%rteent4 ee of t4e !&xt4!ee!ter

3 8nl on t4e !%.&!!&on of proe't d&!!ertat&on t4e !t%dent &ll .e &!!%ed 4all t&'et for

t4e end !ee!ter t4eor and pra't&'al exa&nat&on" 4e d&!!ertat&on a .e tped or 4and-r&tten and .e l&&ted to "0 to 70 page! of ;"

!&@e

# Proe't or !4all .e e,al%ated . an external and one &nternal exa&ner 4&'4 &ll .e folloed . pre!entat&on of t4e or and ,&,a-,o'e

6 /t%dent! &ll .e re5%&red to %ndergo ,er&f&'at&on9 e,al%at&on and ,&,a of t4e proe't-

or t4e 4a,e done

7 >ert&f&ed do'%entat&on of t4e proe't-or done . ea'4 gro%p &! andator 4e'ert&f&ed do'%entat&on !4o%ld .e prod%'ed 4&le appear&ng for ,&,a and e,al%at&on

of proe't d%r&ng f&nal exa&nat&on of !&xt4 !ee!ter

• 4e proe't or &ll .e e,al%ated for 100 ar! of 4&'4 6 mar8s &ll .e allotted

for t4e dissertation and 0 for t!e 4resentation and "i"a-"oce

• T!e E"aluation of t!e 4ro+ect 7or8 7ill be done at t!e end of t!e si@t! semester. :or

t!e E"aluation of t!e 4ro+ect 7or8 t!ere s!all be t!ree !ours duration at t!e end of

t!e si@t! semester. T!ere s!all be batc! of '5 students for 4ro+ect and "i"a.

Updated on Date: - 01-02-2013 of %(




B.Sc. Mat!ematics

SEMESTE1 - 5

Mat!ematics )A)E1 BSMT $ 5' ,A ,T!eory

Mat!ematical Analysis and ?rou4 T!eory

Mat!ematical Analysis-'9IT '* %5 MA1>S D ' MA1>S MC

AaB 1iemann Interal*

Part&t&on! and C&eann !%!9 Upper and loer C-&ntegral!9 C-&ntegra.&l&t9 4e

&ntegral a! l&&t9 /oe 'la!!e! of &ntegra.le f%n't&on! 9 Propert&e! of &ntegra.le

f%n't&on9 /tateent of 3arbou@s t!eorem (&t4o%t proof)

A.B >ont&n%&t9 Der&,a.&l&t of t4e &ntegral f%n't&on!9 %ndaental t4eore of

&ntegral 'al'%l%!9 Mean ,al%e t4eore of &ntegral 'al'%l%!

A'B Metric S4aces* Def&n&t&on and exaple! of etr&' !pa'e9

ne&g4.or4ood9 l&&t po&nt!9 &nter&or po&nt!9 8pen and 'lo!ed !et!9 >lo!%re9der&,ed !et and &nter&or9 .o%ndar po&nt! >ont&n%&t &n etr&' !pa'e9 Den!e !et!9

>antor !et! Ainclude Cantor set is closed but /MIT* - cantor set is com4act

and com4leteB

?rou4 T!eory

9IT %* %5 MA1>S D ' MA1>S MC

AaB Def&n&t&on of <&nar 8perat&on 9Propert&e! of <8 Exaple! 9 $ro%p &t!

Propert&e!9 Exaple! 8f $ro%p9 /%.gro%p It! Propert&e!9 >o!et! It!

Propert&e!9 agrangeF! t4eore

A.B Per%tat&on9 ran!po!&t&on9 E,en 8dd Per%tat&on9 /etr&' $ro%p9 In,er!eof Per%tat&on9 ;lternat&,e $ro%p It! Un&,er!al Propert

A'B >'l&' $ro%p >'l&' /%.gro%p It! Propert&e!9 Ded%'t&on 8f agrangeF!4eore Def&n&t&on of I!oorp4&!9 E5%&,alen'e Celat&on

AdB >ale 4eore9 ;%toorp4&!9 Propert&e! of &!oorp4&!9 ?oral !%.gro%p

and 5%ot&ent gro%p

Te@t Boo8 for MATHEMATICS )A)E1 BSMT - 5' 9nit $ % ?rou4 T!eory

Abstract Alebra

By * 3r. I. H. S!et!

)rentice Hall /f India

e7 3el!i.

Course of Mat!ematics )A)E1 BSMT $ 5' ?rou4 T!eory

&! 'o,ered . follo&ng >4apter!* /e't&on! of t4e a.o,e ent&oned .oo nael ;.!tra't

;lge.ra

C!a4ter 0: G "19 G "29 G "39 G ""9 G"# A8MI: Exaple "111B

C!a4ter 6:

• G 619 G 62A8MI: Exaple 627B9 G 639

• A /mit:- G 6"B9 G 6#

Updated on Date: - 01-02-2013 of %(




A/mit*- $eneral&@ed a!!o'&at&,e la9 4eore: 6#29 4eore: 6#3 B

G 669 G 67

C!a4ter F* G 719 G 729 G 73

C!a4ter (* G H19 G H29 G H3 A/mit*- 4eore: H22 B

C!a4ter J* G 19 G 29 G 3C!a4ter '* G 1019 G 102

C!a4ter ''

• /mit *- >4apter 11 >'l&' $ro%p!

• A4e 4ole '4apter &! to .e o&ttedB

C!a4ter '%*

• G 1239 G 12" A/mit*- G 12# B

ACea&n&ng !e't&on! of t4&! '4apter &ll .e 'o,ered &n 6t4 !ee!ter B

Ceferen'e!: -

(1) op&'! &n ;lge.ra9 1 ? er!te&n9 &lle Ea!tern td ?e+ Del4&

(2) ; text <oo of Modern ;.!tra't ;lge.ra9 . /4ant&naraan9 / >4and >o9 ?e+

Del4&

(3) %ndaental! of ;.!tra't ;lge.ra9 D / Mal&9 ? Mordo!on

and M J /en9 M'$ra+ &ll Internat&onal Ed&t&on - 1==7

(") Un&,er!&t ;lge.ra9 M / $opalar&!4na9 &le Ea!tern td

(#) ;.!tra't ;lge.ra9 < <4atta'4ara9 Kallo P%.l&'at&on!

(6) Modern ;lge.ra9 < Ja@& @a&%d&a /%r!&t9 L&a! P%.l&'at&on Del4&

(7) ext <oo: ;.!tra't ;lge.ra9 Dr 1 /4et49 ?&ra, Praa!4an9 ;4eda.ad

(H) Mat4eat&'al ;nal!&! (2nd ed&t&on) . / > Mal& ;rora9 ?e+ ;ge Inter P,t

(=) Mat4eat&'al ;nal!&!9 . M ;po!tol

(10) Ceal ;nal!&!9 . C C $old.erg (>4apel "9#969 79= 101)

(11) ; 'o%r!e of Mat4eat&'al ;nal!&!9 . /4ant&naraan9 / >4and /on!

(12) Metr&' !pa'e9 . E >ap!on

(13) Metr&' !pa'e9 P J a&n ;4ad9 ?arora P%.l&!4&ng o%!e

(1") Ceal ;nal!&! . /4ara and La!&!4t4a Jr&!4na Praa!4an9 Meer%t-2

(1#) Mat4eat&'al ;nal!&!9 . Dr $oal and $%pta9 Jr&!4na Praa!4an9 Meer%t-2

Updated on Date: - 01-02-2013 Page F of %(




B.Sc. Mat!ematics

SEMESTE1 -5

MATHEMATICS )A)E1 BSMT-5%,A- ,T!eory

)1/?1AMMI? I C and umerical Analysis

)1/?1AMMI? I C , THE/1;

9IT '* %5 MA1>S D ' MA1>S MC

AaB &!tor of >9 > '4ara'ter !et9 >on!tant!9 Lar&a.le!9 Jeord!9 pe De'larat&on9 pe

>on,er!&on9 &erar'4 of operator!9 pr&ntf !'anf f%n't&on!9 &f !tateent9 &f-el!e

!tateent!9 ?e!ted &f-el!e9 og&'al operator!9 >ond&t&onal operator!9

A.B 4&le loop9 for loop9 do 4&le loop9 .rea !tateent9 >ont&n%e !tateent goto !tateent9

Introd%'t&on to U!er Def&ned %n't&on!/mit*- s7itc! case statement )ointers and

1ecursion

A'B Data tpe! &n > Integer!: long and !4ort tpe!9 !&gned and %n!&gned '4ara'ter!9 /&gned

and %n!&gned float and do%.le!9 > pro'e!!or!9 ean&ng 9 8nl Ma'ro Expan!&on9 Ma'ro!&t4 ;rg%ent!9

/MIT*- :ile inclusion and "arious directi"es Conditional Com4ilation Kif and Kelif

3irecti"es Miscellaneous 3irecti"es Kundef 3irecti"e K4rama 3irecti"e

AdB ;rra!9 ean&ng: one d&en!&onal and to d&en!&onal9 onl &n&t&al&@at&on and %!e &n

!&ple progra! /MIT*- no 4ointers and no t!ree dimensional array Arrays and

functions.

9ME1ICA< AA<;SIS-'

9IT %* %5 MA1>S D ' MA1>S MC

a Simultaneous linear alebraic eLuation*D&re't et4od!: $a%!! el&&nat&on et4od9 $a%!! ordan et4od9 Met4od of

fa'tor&@at&on ( U De'opo!&t&on)9 >ro%tF! et4od Iterat&,e et4od!: a'o.&F! et4od9$a%!! /e&dalF! et4od

b Em4irical la7s and cur"e fittin.

4e l&near la9 a! red%'&.le to l&near la!9 Pr&n'&ple of lea!t !5%are9 &tt&ng a !tra&g4t

l&ne9 a para.ola and exponent&al '%r,e and t4e '%r,e bax y =

c :inite differences

&n&te d&fferen'e!(forard 9 .a'ard and 'entral)9

D&fferen'e! of polno&al!9 a'tor&al polno&al9 Ce'&pro'al a'tor&al polno&al 9Polno&al fa'tor&al notat&on9 Error propagat&on &n d&fferen'e ta.le9 8t4er d&fferen'e

operator!(/4&ft9 a,erag&ng9 d&fferent&al and %n&t ) and relat&on .eteen t4e

d Inter4olation 7it! eLual inter"als*

$regor- ?eton forard &nterpolat&on for%la9 $regor- ?eton .a'ard

&nterpolat&on for%la9 E5%&d&!tan'e ter! &t4 one or ore &!!&ng ,al%e!9

Te@t Boo8 for MATHEMATICS )A)E1 BSMT-5%,A ,T!eory

)1/?1AMMI? I C is as follo7s*

<ET 9S CN By * ;as!"ant >anet8er 5t! Edition

B)B )ublications e7 3el!i.

Updated on Date: - 01-02-2013 Page ( of %(




Course of )1/?1AMMI? I C ,THE/1;

i.e. 9IT ' is co"ered by follo7in Sections O C!a4ters of t!e boo8 P<ET 9S CQ

9nit ':-

• C!a4ter '

$ett&ng /tarted

/mit*- t!e section of Associati"ity of /4eratorC!a4ter %

4e de'&!&on 'ontrol /tr%'t%re A4ole '4apterB

• C!a4ter

4e loop 'ontrol /tr%'t%re A4ole '4apterB

or t4e top&' of N9ser 3efined :unctionsQ refer to

any ot!er standard boo8

• C!a4ter 0

4e 'a!e 'ontrol /tr%'t%re

/mit* - S7itc! $Case Statement and related sections

8nl 4e goto eord and &t! %!age

• C!a4ter 5 *-

/mit*- T!e 7!ole C!a4ter 5 $ namely P:unctions and )ointersQ of t!e boo8 P<ET

9S CQ

• C!a4ter 6*-

Data pe! Ce,&!&ted/mit*- Storae Classes li8e Automatic Storae Class 1eister Storae Class StaticStorae Class E@ternal Storae Class =!ic! to 9se =!enRetc.

• C!a4ter F*-4e > Prepro'e!!or eat%re! of > Prepro'e!!or9 Ma'ro Expan!&on9 Ma'ro! &t4 ;rg%ent!9 Ma'ro! ,er!%!

%n't&on! /MIT*- :ile Inclusion Conditional Com4ilation Kif and Kelif 3irecti"esMiscellaneous 3irecti"esKundef 3irecti"e K4rama 3irecti"e

• CHA)TE1 (*-;rra! 4at are ;rra!9 ; /&ple Progra U!&ng ;rra9 More on ;rra!9 ;rraIn&t&al&@at&on9 <o%nd! >4e'&ng9 Pa!!&ng ;rra Eleent! to a %n't&on9 oD&en!&onal ;rra!9 In&t&al&@&ng a 2-D&en!&onal ;rra

/MIT*-)ointers and Arrays )assin an Entire Array to a :unction T!e 1eal

T!in Memory Ma4 of a %-3imensional Array )ointers and %-3imensional

Arrays )ointer to an Array )assin %-3 array to a :unction array of

4ointers t!ree dimensional array summary.4e !'ope of t4e !lla.%! of 95IT % &! ro%g4l &nd&'ated a! %nder:

S5umerical met!odsS . Dr L ? 2edamurt!y Dr ? >4 / ? Iengar9 L&a!P%.l&!4&ng 4o%!e

>4ap 1 (Ex'ept 1"91#91119112)9 >4ap " (Ex'ept ""9"7)9 >4ap # (Ex'ept #12)9

>4ap 6

1eference Boo8s* ,for 9nit %-

(1) Introd%'t&on to ?%er&'al ;nal!&! (2nd Ed&t&on) . >Ero.erg ;dd&!&on a!le9

1=7=

(2) ?%er&'al Mat4eat&'al ;nal!&!9 . </'arforo%g49 8xford I< P%.l&>oP,t td9 1=66

(3) ?%er&'al et4od9 Pro.le! /ol%t&on!9 . M J a&n9 / C JIengar9 C Ja&n9 ?e+ ;ge Internat&onal P,t td9 1==6.

Updated on Date: - 01-02-2013 Page J of %(




B.Sc. Mat!ematics

SEMESTE1 -5

MATHEMATICS )A)E1 BSMT-5 ,A- ,T!eory

3ISC1ETE MATHEMATICS & C/M)<E AA<;SIS

3ISC1ETE MATHEMATICS

9IT '* %5 MA1>S D ' MA1>S MC

AaB 1elations and d&fferent tpe! of relat&on! <&nar relat&on!9 E5%&,alen'e relat&on! and

part&t&on!9 part&al order relat&on!9 Po!et!9 a!!e d&agra9 att&'e! a! po!et!9 Propert&e! of

latt&'e!9 att&'e! a! alge.ra&' !!te!9 /%. latt&'e!9 D&re't prod%'t of to latt&'e!9

ooorp4&!9 order &!oorp4&! of to po!et!9 I!oorp4&' latt&'e!9 >opletelatt&'e!9 D&!tr&.%t&,e latt&'e!9 >opleented latt&'e!

A.B Boolean alebra*

Def&n&t&on9 Exaple! <;9 D&re't prod%'t of to <;9 4ooorp4&!9 ;to! of <;9 ;nt&

ato!9 /toneF! repre!entat&on t4eore9 4e !et ;(x) of all ato! of <; and &t! propert&e!I!oorp4&! of a f&n&te of f&n&te <; and ))9(( ⊆ A P 9 <oolean f%n't&on! * expre!!&on!9

M&nter!9 Maxter!9 Cepre!entat&on of a < expre!!&on a! a !% of prod%'t >anon&'al

for Jarna%g4 ap M&n&&@at&on of a < expre!!&on . '%.e arra repre!entat&on and . Jarna%g4 ap

C/M)<E AA<;SIS-I

9IT %* %5 MA1>S D ' MA1>S MC

a Analytic functions*

%n't&on! of 'oplex ,ar&a.le!9 l&&t!9 4eore! on l&&t!9 >ont&n%&t and

d&fferent&a.&l&t9 of 'oplex f%n't&on!9 4aron&' f%n't&on!9 Ent&re f%n't&on! and analt&'f%n't&on!9 >a%'4 C&eann 'ond&t&on! &n >arte!&an and polar for

A.B Def&n&te &ntegral 'onto%r!9 l&ne &ntegral! >a%'4-$o%r!at t4eore,7it!out 4roof

>a%'4F! &ntegral for%la9 &g4er order der&,at&,e of analt&' f%n't&on9 MoreraF!

t4eore9 >a%'4F! &ne5%al&t and &o%,&lleF! t4eore9 %ndaental t4eore of alge.ra9Max&% od%l%! t4eore

Te@t Boo8 of Mat!ematics )A)E1 BSMT 5 ,A 9IT %

C/M)<E AA<;SIS-'

P Com4le@ 2ariables and A44licationsQ:ift! Edition

1ul 2. C!urc!ill and #ames =ard Bro7n.

Mc ?ra7 Hill )ublis!in Com4any.

C!a4ter %

• /e't&on! to 21

C!a4ter 0

• /e't&on! 30 to 3#

• /e't&on! 36 to 37

Aea and >a%'4-$o%r!at t4eore (&n !e't&on!) 36 7it!out 4roof• /e't&on! 3 to "3





1eferences*

(1) >oplex ,ar&a.le! and appl&'at&on!9 . C L >4%r'4&ll and O <ro+n

(2) 4eor of f%n't&on! of a >oplex ,ar&a.le!9 . /4ant&naraan9 >4and >o

(3) >oplex ,ar&a.le!9 Introd%'t&on and appl&'at&on!9 . Mar ;.lo+&t@ and ; / oa!9

>a.r&dge Un&,er!&t Pre!!

(") $rap4 t4eor +&t4 appl&'at&on to eng&neer&ng and 'op%ter !'&en'e . ?ar!&ng4

Deo 1==39Prent&'e all of Ind&a P,t td

(#) o%ndat&on of D&!'rete Mat4eat&'!9 J D o!4&9 ?e+ ;ge Internat&onal td

P%.l&!4er!

(6) ; f&r!t loo at $rap4 t4eor9 . >lar

(7) D&!'rete Mat4eat&'al /tr%'t%re! +&t4 appl&'at&on! to 'op%ter !'&en'e9

. re.le 1P and Mano4ar C

(H) Eleent! of D&!'rete Mat4eat&'! (2nd ed&t&on) . &%9 Me

$ra+&ll9 Internat&onal ed&t&on9 >op%ter /'&en'e !er&e!9 1=H6

(=) D&!'rete Mat4eat&'!9 < Lat!a9 L&a! P%.l&'at&on!

(10) Introd%'t&on $rap4 4eor9 < C &ll!on!

(11) D&!'rete Mat4eat&'! /tr%'t%re9 < D%grag&9 ?arora P%.

Updated on Date: - 01-02-2013 Page '' of %(




B.Sc. Mat!ematics

SEMESTE1 - 5

Mat!ematics )A)E1 BSMT $ 5' ,B ,)ractical

umerical Analysis $ I

• Total Mar8s*- 5 Mar8s ,E@ternal D '5 Mar8s ,Internal 5 Mar8s O !ours

Pr ?o(1) &tt&ng (1) a !tra&g4t l&ne and (2) axe y =

Pr ?o(2) &tt&ng (1) a para.ola and (2)bax y =

Pr ?o(3) $a%!! el&&nat&onPr ?o(") $a%!! ordan et4od

/MIT * r&ang%lar&!at&on et4od and >ro%tF! et4odB

Pr ?o(#) a'o.&F! et4od

Pr ?o(6) $a%!! /e&delF! et4od

/MIT* Celaxat&on et4odBPr ?o(7) &n&te d&fferen'e!

Pr ?o(H) $regor-?etonF! forard &nterpolat&on for%la

Pr ?o() $regor-?etonF! .a'ard &nterpolat&on for%laPr ?o(10) E5%&d&!tan'e ter! &t4 one or ore &!!&ng ,al%e!

otes :

• 4ere !4all .e SI per&od! of ' !our per ee per .at'4 of '5 !t%dent!

• ' pra't&'al !4o%ld .e done d%r&ng !ee!ter-#.

• ;t t4e t&e of exa&nat&on 'and&date %!t .r&ng 4&!*4er on pra't&'al o%rnal d%l

'ert&f&ed and !&gned . H./.3.

• 4ere !4all .e one 5%e!t&on paper of 5 Mar8s and Hours for pra't&'al exa&nat&on

• 4ere !4all .e '5 mar8s for Internal Pra't&'al Exa&nat&on

(&e >ont&n%o%! &nternal a!!e!!ent of perforan'e of ea'4 !t%dent d%r&ng t4e pra't&'al

or)

:ormat of uestion )a4er for )ractical E@amination

%e!t&on 1 ;n!er an CEE o%t of ILE A ++= 27 Mar!

%e!t&on 2 o%rnal and L&,a: A H Mar!

%e!t&on 3: Internal Pra't&'al Exa&nat&on A 1# Mar!

T/TA< 5 Mar8s

Updated on Date: - 01-02-2013 Page '% of %(




B.Sc. Mat!ematics

SEMESTE1 - 5

Mat!ematics )A)E1 BSMT $ 5% ,B ,)ractical

)rorammin in C lanuae

• Total Mar8s*- 5 Mar8s ,E@ternalD '5 Mar8s ,Internal 5 Mar8s O !ours

Pr ?o(1) o r&te a progra to re,er!e a n%.er9

Pr ?o(2) o r&te a progra to f&nd !% of t4e d&g&t!9Pr ?o(3) o r&te a progra to f&nd pr&e n%.er .eteen to n%.er!9

Pr ?o(") o r&te a progra to f&nd nPr and n>r

Pr ?o(#) o r&te a progra to pr&nt ;r!trong n%.er!9Pr ?o(6) o r&te a progra to generate ar&t4et&' and geoetr&' progre!!&on!

Pr ?o(7) o r&te a progra to f&nd 'opo%nd &ntere!t for g&,en ear!9

Pr ?o(H) o r&te a progra to f&nd net !alar of t4e eploeePr ?o() o r&te a progra to !ol,e t4e 5%adrat&' e5%at&on9

Pr ?o(10) o r&te a progra to f&nd n%.er of odd n%.er and e,en n%.er!

Pr ?o(11) o r&te a progra to add and %lt&pl to atr&'e!Pr ?o(12) o r&te a progra to !ol,e t4e e5%at&on . <&!e't&on et4od or

Pr ?o(13) o r&te a progra to !ol,e t4e e5%at&on . ?-C et4od

Pr ?o(1") o r&te a progra to ,er&f a n%.er 4et4er &t &! pal&ndroe or not

otes :








or)

:ormat of uestion )a4er for )ractical E@amination%e!t&on 1 ;n!er an CEE o%t of ILE A ++= 27 Mar!



T/TA< 5 Mar8s





B.Sc. Mat!ematics

SEMESTE1 - 5

Mat!ematics )A)E1 BSMT $ 5 ,B ,)ractical

)rorammin 7it! SCI<AB

• Total Mar8s*- 5 Mar8s ,E@ternalD '5 Mar8s ,Internal 5 Mar8s O !ours

Pr ?o(1) o f&nd t4e &n,er!e of a atr&x %!&ng ?A9SS-E<IMIATI/ et4od

Pr ?o(2) o f&nd &n,er!e of g&,en atr&x %!&ng ?A9SS-#/13A et4od

Pr ?o(3) o f&nd Eien "alues and Eien "ectors of g&,en atr&x

Pr ?o(") o f&nd &n,er!e of g&,en atr&x %!&ng CA;<E;-HAMI<T/ t4eorePr ?o(#) o !ol,e g&,en !!te of !&%ltaneo%! l&near alge.ra&' e5%at&on! %!&ng

?A9SS-#/13A et4od

Pr ?o(6) o !ol,e g&,en !!te of !&%ltaneo%! l&near alge.ra&' e5%at&on! %!&ng

?A9SS-#AC/BI et4od

Pr ?o(7) o !ol,e g&,en !!te of !&%ltaneo%! l&near alge.ra&' e5%at&on! %!&ng?A9SS-SEI3A<NS et4odPr ?o(H) o dra grap4! of Cycloid

Pr ?o() o dra grap4! of Catenaries

Pr ?o(10) o dra grap4! of s4iral r e@4,-t!etaO'.

otes :








or)





T/TA< 5 Mar8s

Updated on Date: - 01-02-2013 Page '0 of %(




Syllabus of B.Sc. Semester-6



(Updated on date:- 01-02-2013

and updation ip!eented "#o June - 2013$

• )roram* B.Sc.

• Semester* 6

• Sub+ect* Mat!ematics

• Course codes* BSMT-6',A -T!eoryBSMT-6%,A -T!eory

BSMT-6,A -T!eory

BSMT-6',B - )ractical

BSMT-6%,B - )ractical

BSMT-6,B - )ractical

' )ro+ect

• Total Credit /f T!eSemester

%0 Credit





B. Sc. MATHEMATICS SEMESTE1 * 2I• T!e Course 3esin of B. Sc. Sem.- 2I ,Mat!ematics accordin to c!oice based

credit system ,CBCS com4risin of )a4er umber ame o. of t!eory lectures

4er 7ee8 o. of 4ractical lectures 4er 7ee8 total mar8s of t!e course are as

follo7s *

/C?8

/U<E>

?8 8

E8CK

E>UCE PEC

EEJ

?8 8

PC;>I>;

E>UCE

PEC EEJ

8;

M;CJ/

>red&t 8f

Ea'4

Paper

1

)A)E1 BSMT-6' ,A

,T!eory

?ra4! T!eory & Com4le@

Analysis-%

6 -70(External)+30 (Internal) =

100 Mar!

"

2

)A)E1 BSMT-6% ,A

,T!eory

Analysis-% & Abstract

Alebra-%

6 -

70(External)+

30 (Internal) =

100 Mar!

"

3

)A)E1 BSMT-6 ,A

(4eor)

/4timiUation & umerical

Analysis-II

6 -

70(External)+

30 (Internal) =

100 Mar!

"

")A)E1 BSMT-6' ,B

,)ractical

Introduction to SA?E

- 6

3#(External)+

1#(Internal) =#0 Mar!

3

#

)A)E1 BSMT-6% ,B

,)ractical)

umerical Analysis-II- 6

3#(External)+

1#(Internal) =

#0 Mar!

3

6)A)E1 BSMT-6 ,B

,)ractical

/4timiUation

- 63#(External)+1#(Internal) =

#0 Mar!

3

7

)ro+ect =or8 & 2i"a1 $%&dan'e e't

or a gro%p of 2to # !t%dent! *

ee

Proe't or to

.e f&nal&@edand 'ert&f&ed

and e,al%ated

6Mar8s

,3issertation D

0 Mar8s, 2i"a =

' Mar8s

3

Total credit of t!e semester fi"e %0





Mar8s 3istribution /f Eac! )a4er

for

T!eory and )ractical , for SEMESTE1-2I

• Total Mar8s of Eac! T!eory )a4erE@ternal E@amination

% Mar8s ,MC testD5 Mar8s ,3escri. ty4e

F Total Mar8s.


Internal E@amination

' Mar8s Assinments D

' Mar8s 9IG test D

' Internal e@am.

Total Mar8s


)a4er E@ternal E@amination

5 Mar8s

• Total Mar8s of Eac! )ractical)a4er Internal E@amination

'5 Mar8sContinuous internal assessment of

4ractical 7or8

:ormat of uestion )a4er

• 4ere !4all .e one 5%e!t&on paper of F mar8s %'

% !ours for ea'4 Mat4eat&'!

T!eory )a4er.

• 4ere !4all .e T=/ !e't&on! &n t4&! paper &e Section A and Section B

Section $ A

Section A is of % Mar8s &t4 % MC tpe 5%e!t&on! (%lt&ple '4o&'e 5%e!t&on!) 'o,er&ng t4e

4ole !lla.%! &n e5%al e&g4tage

Section $ B

Section B &! of 5 Mar8s &t4 t4e follo&ng tpe of T=/ 5%e!t&on! 'o,er&ng t4e 4ole

!lla.%! &n e5%al e&g4tage9 ea'4 of tent f&,e ar!

uestion ' and % &ll 'o,er %n&t 1 and 2 re!pe't&,el

uestion no. (;) ;n!er an t!ree out of si@ 6 Mar!(<) ;n!er an t!ree out of si@ Mar!

(>) ;n!er an t7o out of fi"e 10 Mar!

T/TA< %5 MA1>S

Updated on Date: - 01-02-2013 Page 'F of %(




B.Sc. Mat!ematics

SEMESTE1 - 6

MATHEMATICS )A)E1 BSMT $ 6' ,A ,T!eory

?1A)H THE/1; and C/M)<E AA<;SIS

?1A)H THE/1;

9IT '* %5 MA1>S D ' MA1>S MC

a ?ra4! t!eory:

<a!&' def&n&t&on! and !&ple exaple!9 D&re'ted9 Und&re'ted9 %lt&-grap49 &xed grap4

In'&den'e relat&on and degree of t4e grap4 Ept9 'oplete9 reg%lar grap4! /%. grap49'onne'ted and d&!'onne'ted grap4!

al and %n&lateral 'oponent!9 E%ler grap4!9 Un&'%r!al grap49 8perat&on of grap4

'&r'%&t tree a&lton&an pat4 and ''le!9 tree9 <&nar and /pann&ng tree!

b Cut-set connecti"ity and se4arability

/MIT*-'-isomor4!ism %-isomor4!ism planner grap4! and t4e&r d&fferent repre!entat&on9 D%al of a planner grap49 E%lerF!

for%la9 J%rato!&F! f&r!t and !e'ond non-planner grap49 ,e'tor !pa'e a!!o'&ated &t4 a

grap49 >&r'%&t !%.!pa'e and '%t !et! !%.!pa'e9 8rt4ogonal !pa'eLertex 'olor&ng9 >4roat&' n%.er9 Index n%.er and part&t&on9 >'l&' grap4 and

deel&@at&on of ''l&' grap4!9 Matr&x repre!entat&on of a grap49 ;da'en' atr&x9

In'&den'e atr&x9 Pat4 atr&x9

/MIT *- Circuit matri@ :undamental circuit matri@ and cut set matri@ 1elation

s!i4 of t!ese matrices

1an8 of t!e ad+acency matri@

C/M)<E AA<;SIS-%

9IT %* %5 MA1>S D ' MA1>S MC

a Ma44in and Conformal ma44in*

Eleentar f%n't&on!9 app&ng . eleentar f%n't&on!9 Mo.&o%! app&ng9 l&near

f%n't&on

<&l&near app&ng 7,aUDbO,cUDd9 2 z w = 9

z w

1= 9 )exp( z w = 9

/MIT* z w !&n= z w 'o!= z w 'o!4= z w !&n4=

Transformations Conformal ma44ins and t!eir e@am4les.

b )o7er series*Def&n&t&on of 'oplex !e5%en'e9 >oplex !er&e! and poer !er&e! Expan!&on of a

'oplex f%n't&on &n alorF! !er&e! and a%rentF! !er&e!

c 1esidues and 4oles*

Def&n&t&on of a !&ng%lar po&nt9 I!olated !&ng%lar po&nt!9 ero! of 'oplex f%n't&on!9 Pole!and re!&d%e! of 'oplex f%n't&on9 >a%'4F! re!&d%eF! t4eore9 E,al%at&on of &proper

real &ntegral! . re!&d%e t4eore and e,ol%t&on of def&n&te &ntegral of tr&gonoetr&'

f%n't&on! . re!&d%e t4eore

Updated on Date: - 01-02-2013 Page '( of %(




Te@t boo8 for Mat!ematics )A)E1 BSMT $ 6'

?ra4! t!eory

?ra4! t!eory 7it! a44lication to enineerin and com4uter science

By* - arsin! 3eo

)rentice Hall of India )ri"ate <imited e7 3el!i.

C!a4ter* '

• G 119 G 139 G 1"9 G 1#

• /MIT * - V '.% and V '.6

C!a4ter* %

• G 219 G 229 G 239 G 2"9 G 2#9 G 269 G 279 G 2H9 G2

• /MIT* - V%.'B

C!a4ter*

• G 319 G 329 G 339 G 3#9 G 369 G 379 G 3H

• /MIT* - V .0 V .J V .'

C!a4ter* 0• G "19 G "29 G "39 G ""9 G "#9

• /MIT* - V 0.6 V 0.F V 0.(

C!a4ter* 5

• G #29 G #39 G #"9 G ##9 G #6

• /MIT* - V 5.' V 5.F V 5.( V 5.J

C!a4ter* 6

• G 619 G 6#9 G 679 G 6

• A/MIT* - V 6.% V 6. V 6.0 V 6.(

C!a4ter* F

•

G 719 G 7H9 G 7• A/MIT* - V F.% V F. V F.0 V F.5 V F.6 V F.F

C!a4ter* (

• G H19 G H29 G H#

• A/MIT* - V (. V (.0 V (.6

C!a4ter* J

• G 19 G 11

• A/MIT* - V J.% to V J.'

Updated on Date: - 01-02-2013 Page 'J of %(




Te@t Boo8 of Mat!ematics )A)E1 BSMT 6'

C/M)<E AA<;SIS-%

PCom4le@ 2ariables and A44licationsQ

:ift! Edition

1uel 2. C!urc!ill and #ames =ard Bro7n.

Mc ?ra7 $ Hill )ublis!in Com4any

C!a4ter 5

• /e't&on! ""9 "#9 "69 "79 "H A8&t /e't&on!: -"9 #09 #1B9

C!a4ter 6

• /e't&on! #3 to #H9 60 A/MIT*- /e't&on! #B

C!a4ter F

• /e't&on! 6"9 6#9 669 679 6H9 70

A/MIT /e't&on!* - 639 719 72B

A/MIT* - C!a4ter (B

1eferences*

(1) >oplex ,ar&a.le! and appl&'at&on!9 . C L >4%r'4&ll and O <ro+n

(2) 4eor of f%n't&on! of a >oplex ,ar&a.le!9 . /4ant&naraan9 >4and >o

(3) >oplex ,ar&a.le!9 Introd%'t&on and appl&'at&on!9 . Mar ;.lo+&t@ and ; / oa!9

>a.r&dge Un&,er!&t Pre!!

(") $rap4 t4eor +&t4 appl&'at&on to eng&neer&ng and 'op%ter !'&en'e. ?ar!&ng4 Deo

1==39Prent&'e all of Ind&a P,t td

(#) o%ndat&on of D&!'rete Mat4eat&'!9 J D o!4&9 ?e+ ;ge Internat&onal td

P%.l&!4er!

(6) ; f&r!t loo at $rap4 t4eor9 . >lar

(7) D&!'rete Mat4eat&'al /tr%'t%re! +&t4 appl&'at&on! to 'op%ter !'&en'e9

. re.le 1P and Mano4ar C

(H) Eleent! of D&!'rete Mat4eat&'! (2nd ed&t&on) . &%9 Me

$ra+&ll9 Internat&onal ed&t&on9 >op%ter /'&en'e !er&e!9 1=H6

(=) D&!'rete Mat4eat&'!9 < Lat!a9 L&a! P%.l&'at&on!

(10) Introd%'t&on $rap4 4eor9 < C &ll!on!

(11) D&!'rete Mat4eat&'! /tr%'t%re9 < D%grag&9 ?





B.Sc. Mat!ematics

SEMESTE1 - 6

MATHEMATICS )A)E1 BSMT $ 6% ,A ,T!eory

AA<;SIS and ABST1ACT A<?EB1A

AA<;SIS-%

9IT '* %5 MA1>S D ' MA1>S MC

AaB >o,er9 8pen 'o,er9 &n&te !%. 'o,er9 >opa't !et9 Propert&e! of 'opa't !et!

Connected sets Se4arated sets BolUano-=eirstrass t!eorem Countable set.

A.B oeoorp4&! of to etr&'!9 /e5%ent&al 'opa'tne!!9 totall .o%nded!pa'e

A'B <a4lace Transforms

Def&n&t&on of apla'e ran!for!9 apla'e ran!for! of eleentar %n't&onIn,er!e apla'e ran!for!9 apla'e ran!for! of Der&,at&,e and Integral!9

apla'e ran!for! D&fferent&at&on and &ntegrat&on of apla'e ran!for!9

>on,ol%t&on t4eore /mit* - A44lication to 3ifferential ELuations.

ABST1ACT A<?EB1A-%

9IT %* %5 MA1>S D ' MA1>S MC

AaB ooorp4&! of gro%p!9 Jernel of 4ooorp4&!9 &r!t f%ndaental t4eore

of 4ooorp4&! of gro%p! C&ng and &t! propert&e!9 /%.r&ng9 /MIT*- Boolean

rin Euclidean rin

A.B &eld9 ero d&,&!or9 Integral doa&n9 >4ara'ter&!t&'! of r&ng9 >an'ellat&on la9

Ideal!9 Pr&n'&pal &deal9 9Polno&al r&ng9 /MIT*- uotient rin. Ma@imal

ideal Polno&al9 Degree of polno&al9 a'tor and rea&nder t4eore of

polno&al9 Prod%'t9 !% and d&,&!&on of polno&al!A'B Ced%'&.le and &rred%'&.le polno&al!9 a'tor&@at&on of polno&al!( %n&5%e

a'tor&@at&on t4eore ,7it!out 4roof /MIT*- EisensteinNs criterionBD&,&!&on algor&t4 t4eore of polno&al

AdB $>D of polno&al!9 %atern&on /MIT*- 1in !omomor4!ism Euler and

:ermatNs t!eorem

Te@t boo8 for Mat!ematics )A)E1 BSMT $ 6%

AA<;SIS-%

:or <a4lace Transforms

Ad"anced Mat!ematics for )!armacyN By* - Ma!a+an )ublis!in House A!medabad

C!a4ter* - 'F <a4lace Transforms

G 1719 G 1729 G 1739 G 17"9 G 17#9 G 176

/MIT *- A44lication to 3ifferential ELuations

Updated on Date: - 01-02-2013 Page %' of %(




Te@t Boo8 for MATHEMATICS )A)E1 BSMT-6%,A

PAbstract AlebraQ By* 3r. I. H. S!et! )rentice Hall /f India e7 3el!i.

Course of Mat!ematics )A)E1 BSMT $ 6% ,Abstract Alebra-% are 'o,ered . follo&ng>4apter!* /e't&on! of t4e a.o,e ent&oned .oo ;.!tra't ;lge.ra

C!a4ter '%: G 1219 G 1229 G 126

C!a4ter ': G 1319 G 1329 G 1339 G 13"

C!a4ter '0* G 1"19 G 1"29 G 1"39 G 1""

C!a4ter '5* G 1#19 G 1#29 G 1#" /MIT*- V '5.

C!a4ter '(* G 1H19 G 1H29 G 1H39G 1H" A/mit* T!eorem* '(.0.(

i. e. %n&5%e a'tor&@at&on t4eore ,7it!out 4roofB9

G 1H#/MIT* - V '(.6 - EisensteinNs criterion G 1H7

1eferences :

(1) op&'! &n ;lge.ra9 I ? er!te&n9 &lle Ea!tern td ?e+ Del4&

(2) ; text <oo of Modern ;.!tra't ;lge.ra9 . /4ant&naraan9 / >4and >o9 ?e+

Del4&

(3) %ndaental! of ;.!tra't ;lge.ra9 D / Mal&9 ? Mordo!on

and M J /en9 M'$ra+ &ll Internat&onal Ed&t&on - 1==7

(") Un&,er!&t ;lge.ra9 M / $opalar&!4na9 &le Ea!tern td

(#) ;.!tra't ;lge.ra9 < <4atta'4ara9 Kallo P%.l&'at&on!

(6) Modern ;lgera9 < Ja@& @a&%d&a /%r!&t9 L&a! P%.l&'at&on Del4&

(7) ext <oo: ;.!tra't ;lge.ra9 Dr 1 /4et49 ?&ra, Praa!4an9 ;4eda.ad

(H) Mat4eat&'al ;nal!&! (2nd ed&t&on) . / > Mal& ;rora9 ?e+ ;ge Inter P,t

(=) Mat4eat&'al ;nal!&!9 . M ;po!tol

(10) Ceal ;nal!&!9 . C C $old.erg (>4apel "9#969 79= 101)

(11) ; 'o%r!e of Mat4eat&'al ;nal!&!9 . /4ant&naraan9 / >4and /on!

(12) Metr&' !pa'e9 . E >ap!on

(13) Metr&' !pa'e9 P J a&n ;4ad9 ?arora P%.l&!4&ng o%!e

(1") Ceal ;nal!&! . /4ara and La!&!4t4a Jr&!4na Praa!4an9 Meer%t-2

(1#) Mat4eat&'al ;nal!&!9 . Dr $oal and $%pta9 Jr&!4na Praa!4an9 Meer%t-2

Updated on Date: - 01-02-2013 Page %% of %(




B.Sc. Mat!ematics

SEMESTE1 - 6

MATHEMATICS )A)E1 BSMT $ 6 ,A ,T!eory

/)TIMIGATI/ and 9ME1ICA< AA<;SIS

/)TIMIGATI/

9IT '* %5 MA1>S D ' MA1>S MC

AaB 4e l&near progra&ng pro.le!9 or%lat&on of PP9 Matr&x for of t4e PP9general for9 >anon&'al for 9 /tandard for of t4e PP9 $rap4&'al et4od to

!ol,e PP9 /oe def&n&t&on! and .a!&' propert&e! of 'on,ex !et! 'on,ex f%n't&on!

and 'on'a,e f%n't&on <a!&' def&n&t&on! to %!e /&plex et4od9 /&plex et4od9

<&g-M et4od (Penalt et4od)9 o p4a!e et4od to !ol,e PP( &t4o%talternat&,e !ol%t&on and %n.o%nded !ol%t&on)

A.B Pr&n'&ple of d%al&t &n PP9 Pr&al PP and et4od to f&nd &t! d%al PP (/&ple pro.le! of a.o,e art&'le!) 4e tran!portat&on pro.le!: Mat4eat&'al and

atr&x for of P In&t&al !ol%t&on of P . ?>M9 >M and L;M9 8pt&%

!ol%t&on of P . Mod& et4od ( %-, et4od ) (ex'ept degenerate !ol%t&on)9<alan'ed and %n.alan'ed P(/&ple pro.le )9 ;!!&gnent pro.le:

Mat4eat&'al and atr&x for of ;P9 %ngar&an et4od to !ol,e et4od(!&ple

et4od)

9ME1ICA< AA<;SIS -%

9IT %* %5 MA1>S D ' MA1>S MC

AaB Central difference inter4olation formulae*$a%!!F! forard9 $a%!!F! .a'ard9 /terl&ngF!9 <e!!elF! and apla'e- E,erettF!

&nterpolat&on for%laeA.B Inter4olation 7it! uneLual inter"als:

D&,&ded d&fferen'e!9 Propert&e! of d&,&ded d&fferen'e9 Celat&on .eteen d&,&ded

d&fferen'e! and forard d&fferen'e9 ?etonF! d&,&ded d&fferen'e for%la9agrangeF! &nterpolat&on for%la9 In,er!e &nterpolat&on9 agrangeF! &n,er!e

&nterpolat&on for%la9

A'B umerical 3ifferentiation:

?%er&'al D&fferent&at&on9 Der&,at&,e! %!&ng $regor-?etonF! forardd&fferen'e for%la9 Der&,at&,e! %!&ng $regor-?etonF! .a'ard d&fferen'e

for%la9 Der&,at&,e %!&ng /terl&ngF! for%laAdB umerical Interation:

?%er&'al Integrat&on9 $eneral 5%adrat%re for%la9 rape@o&dal r%le9 /&p!on Q!

1*3 r%le9 /&p!onF! 3*H r%le

AeB umerical solution of ordinary differential eLuations

/ol%t&on . alorF! !er&e! et4od9 alorF! !er&e! et4od for !&%ltaneo%! f&r!t

order d&fferent&al e5%at&on!9 P&'ardF! et4od9 P&'ardF! et4od for !&%ltaneo%!

f&r!t order d&fferent&al e5%at&on!9 E%lerF! et4od9 Ipro,ed E%lerF! et4od9

Mod&f&ed E%lerF! et4odAfB C%ngeF! et4od9 C%nge-J%tta et4od!9 &g4er order C%nge-J%tta et4od!9

C%nge-J%tta et4od! for !&%ltaneo%! f&r!t order d&fferent&al e5%at&on!9 C-J

et4od! for !&%ltaneo%! f&r!t order d&fferent&al e5%at&on!9 Pred&'tor->onne'tor et4od!9 M&lneF! et4od





Te@t Boo8 for Mat!ematics )A)E1 BSMT $ 6,A ,T!eory

/)TIMIGATI/

/4eration 1esearc! T!eory and A44licationsN

#. >. S!arma Second EditionMACMI<<A I3IA <T3

Course of Mat!ematics )A)E1 BSMT $ 6,A /)TIMIGATI/

&! 'o,ered . follo&ng >4apter!* /e't&on! of t4e a.o,e ent&oned .oo

C!a4ter %*-

• G 26 A8nlB

C!a4ter *-

• G 319 G 329 G 33 /mit*- V .0

C!a4ter 0

• G "19 G "29 G "39 G "" /mit*- V 0.5 and V 0.6

C!a4ter 5

• G #19 G #29 G #3 /mit*- V 5.0 V 5.5

C!a4ter J

• G 1 to G # G 6

• /nly V J.6.' 9nbalanced Su44ly and 3emand

• /mit* - V J.6.% V J.6. V J.6.0R etc in V J.6

• /mit* - V J.F V J.(

C!a4ter ' G 101 to G 103

• A44endi@ A ;10 and ;12

• /mit* - V '.0 to V '.6

• /mit* - t!e rest

4e !'ope of t4e !lla.%! of 95IT $ % &! ro%g4l &nd&'ated a! %nder:

R?%er&'al et4od!R . Dr L Leda%rt4 Dr ? >4 / ? Iengar9 L&a!P%.l&!4&ng 4o%!e

>4ap7 (Ex'ept 7797H)9 >4ap H (Ex'ept HH)9 >4ap = (Ex'ept =#9 =13)9 >4ap 11

(Ex'ept 1119 11291139 1169 11=9 11179 1120)

1eference Boo8s*

(1) Introd%'t&on to ?%er&'al ;nal!&! (2nd Ed&t&on) . >Ero.erg ;dd&!&on a!le91=7=

(2) ?%er&'al Mat4eat&'al ;nal!&!9 . </'arforo%g49 8xford I< P%.l&>o

P,t td9 1=66

(3) ?%er&'al et4od9 Pro.le! /ol%t&on!9 . M J a&n9 / C JIengar9 C J

a&n9 ?e+ ;ge Internat&onal P,t td9 1==6

Updated on Date: - 01-02-2013 Page %0 of %(




B.Sc. Mat!ematics

SEMESTE1 -6

MATHEMATICS )A)E1 BSMT $ 6',B ,)1ACTICA<

Introduction to SA?E)r no* ,' Introduction to Sae*

&e Introd%'t&on to ,ar&a.le!9 'on!tant!9 data tpe!9 !oe &n.%&lt (l&.rar ) 'on!tant!

f%n't&on! 94o to enter a atr&x9 4o to enter a ,e'tor9 operator!9 4o to get 4elp et'

)r no* ,% /4erations on e@4ressions*

(a) /ol,e(f(x)==g(x)9x)

(.) /ol,e(Af(x9)==09g(x9)==0B9x9)

(') &nd a root of f(x) &n t4e g&,en &nter,al Aa9 .B !%'4 t4at f(x) 0 (approx&ate root)

(d) Finding sum and product of the given series from 1 to n terms.(using

sum() and prod() functions)

)r no* , Calculus *

(a) &nd l&&t of a g&,en f%n't&on(.) &nd left and r&g4t 4and !&de l&&t! of a g&,en f%n't&on

(') &nd der&,at&,e of a g&,en f%n't&on(d) &nd&ng ax&a and &n&a of a g&,en f%n't&on f(x) &n t4e g&,en &nter,al (a9 .)

(e) &nd part&al der&,at&,e of a g&,en .&-,ar&ate f%n't&on

(f) &nd &ndef&n&te &ntegral of a g&,en f%n't&on(g) &nd def&n&te &ntegral of a g&,en f%n't&on

(4) &nd n%er&'al &ntegral of a g&,en f%n't&on

(&) &nd alor !er&e! expan!&on of a g&,en f%n't&on f(x) a.o%t x=a %pto degree n

)r no* ,0 %3 ?ra4!ics *

(a) Dra a l&ne pa!!&ng t4ro%g4 t4e g&,en po&nt!

(.) Dra a polgon 4a,&ng t4e g&,en po&nt! a! &t! ,ert&'e!(') Dra a '&r'le &t4 t4e g&,en po&nt a! 'enter and &t4 t4e g&,en rad&%!

(d) Plott&ng t4e grap4 of a g&,en f%n't&on f(x)

(e) Dra t4e grap4 of t4e f%n't&on (g&,en &n paraetr&' for)

(f) Dra&ng grap4 of t4e f%n't&on( &n polar for)(g) Dra&ng 'o.&ne grap4!

(4) U!&ng opt&on! &n plott&ng of 2D grap4!

)r no* ,5 3 ?ra4!ics *

(a) Dra&ng a l&ne &n t4ree d&en!&on

(.) Dra a !p4ere &t4 t4e g&,en po&nt a! 'enter and &t4 t4e g&,en rad&%!

(') Dra&ng Platon&' !ol&d! ( tetra4edron9'%.e9o'ta4edron9dode'a4edron9&'o!a4edron!)(d) Dra t4e grap4 of g&,en f%n't&on f(x9) &n 3D

(e) Dra t4e grap4 of g&,en f%n't&on f(x9) &n 3D(paraetr&' for)

(f) U!&ng opt&on! &n plott&ng of 3D grap4!

)r no* ,6 Sim4lification and e@4ansion of a i"en symbolic function.

)r no* ,F:indin 4artial fractions of a i"en function f,@.

)r no* ,(<inear Alebra*

(a) Enter&ng x n atr&x and f&nd&ng &t! deter&nant

(.) &nd&ng tran!po!e9 ado&nt and 'on%gate of a g&,en atr&x

(') o deter&ne 4et4er t4e entered atr&x &! !5%are9 @ero9 &dent&t9 !'alar9 !etr&'9&n,ert&.le 9 n&lpotent9 &depotent or not





(d) Enter&ng a !5%are atr&x and f&nd&ng &t! &n,er!e &f ex&!t!

(e) &nd&ng ran9 n%ll&t no of ro!9 no of 'ol%n!9 tra'e9 tran!po!e of a g&,en atr&x(f) &nd&ng E'4elon for of t4e entered atr&x

(g) &nd&ng '4ara'ter&!t&' polno&al9 e&gen ,al%e! and e&gen ,e'tor! of t4e entered

atr&x

(4) Perfor&ng ro operat&on! on t4e entered atr&x

)r no* ,J umber T!eory*

(a) Deter&ne t4e entered n%.er &! a pr&e or not

(.) &nd t4e next pr&e 9pre,&o%! pr&e next pro.a.le pr&e to t4e entered n%.er(') &nd&ng pr&e! p !%'4 t4at S p T n (%!&ng pr&erange(9n))

(d) &nd&ng pr&e poer! ( %!&ng pr&epoer!(9n)

(e) &nd&ng 'ont&n%ed fra't&on! of x

)r no* ,' ?rou4 T!eory and ?ra4! T!eory*

(a) Per%tat&on gro%p9 /etr&' gro%p and ;lternat&ng gro%p of n !.ol!(.) ;.el&an gro%p9 Matr&x gro%p! ($=$eneral &near gro%p and /=/pe'&al &near

gro%p)9 noral !%.gro%p!(') Dra&ng grap4! &t4 g&,en ,ert&'e! and edge!(d) >4roat&' polno&al of grap4 $

(e) e!t&ng planar&t of grap4

(f) &nd&ng /4orte!t Pat4 &n a grap4 $

otes :


• ' pra't&'al !4o%ld .e done d%r&ng !ee!ter-6.




• 4ere !4all .e '5 mar8s for Internal Pra't&'al Exa&nat&on (&e >ont&n%o%! &nternal

a!!e!!ent of perforan'e of ea'4 !t%dent d%r&ng t4e pra't&'al or)



%e!t&on 2 o%rnal and L&,a: A H Mar!%e!t&on 3: Internal Pra't&'al Exa&nat&on A 1# Mar!

T/TA< 5 Mar8s





B.Sc. Mat!ematics

SEMESTE1 -6

MATHEMATICS )A)E1 BSMT $ 6%,B ,)1ACTICA<

9ME1ICA< AA<;SIS $ II

Pr ?o(1) $a%!! forard &nterpolat&on for%laPr ?o(2) $a%!! .a'ard &nterpolat&on for%laPr ?o(3) /terl&ngF! or <e!!elF! for%la

Pr ?o(") apla'e-E,erettF! for%la

Pr ?o(#) Interpolat&on &t4 %ne5%al &nter,al!

Pr ?o(6) ?%er&'al d&fferent&at&onPr ?o(7) ?%er&'al &ntegrat&on

Pr ?o(H) alorF! or P&'ardF!

Pr ?o() E%lerF! et4odPr ?o(10) C%ngeF! et4od

Pr ?o(11) C%nge-J%ttaF! et4od

Pr ?o(12) M&lneF! et4od

o%rnal and ,&,a

otes :








or)





T/TA< 5 Mar8s

Updated on Date: - 01-02-2013 Page %F of %(




B.Sc. Mat!ematics

SEMESTE1 -6

MATHEMATICS )A)E1 BSMT $ 6,B ,)1ACTICA<

/)TIMIGATI/

Pr ?o(1) /ol,e t4e g&,en PP %!&ng $rap4&'al et4odPr ?o(2) /ol,e t4e g&,en PP %!&ng /&plex et4od

Pr ?o(3) /ol,e t4e g&,en PP %!&ng <I$ -M et4od

Pr ?o(") /ol,e t4e g&,en PP %!&ng 8-P;/E et4od

Pr ?o(#) 8.ta&n DU; of t4e g&,en Pr&al PPVPr ?o(6) &nd t4e &n&t&al !ol%t&on of g&,en tran!portat&on pro.le %!&ng ?>M et4od

Pr ?o(7) &nd t4e opt&% !ol%t&on of g&,en tran!portat&on pro.le %!&ng >M et4od

Pr ?o(H) &nd t4e opt&% !ol%t&on of g&,en tran!portat&on pro.le %!&ng L;M et4odPr ?o() &nd t4e opt&% !ol%t&on of g&,en tran!portat&on pro.le %!&ng M8DI et4od

Pr ?o(10) &nd t4e opt&% !ol%t&on of g&,en a!!&gnent pro.le

o%rnal and ,&,a

otes :








or)





T/TA< 5 Mar8s

b.sc.mathematics sem 5 & 6 syllabus cbcs dt 01 02 2013

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