b.sc.mathematics sem.5 & 6 syllabus non cbcs final uni copy latest dt 23-03-2010

8/19/2019 B.sc.Mathematics Sem.5 & 6 Syllabus NON CBCS FINAL UNI COPY Latest Dt 23-03-2010

http://slidepdf.com/reader/full/bscmathematics-sem5-6-syllabus-non-cbcs-final-uni-copy-latest-dt-23-03-2010 1/22

SAURASHTRA UNIVERSITY, RAJKOT

B.Sc. Mathematics

New Syllabus

According To Semester System (Semester 5 & 6)

Effective from June !!"

SAURASHTRA UNIVERSITY

RAJKOT

of 22




• #$ Sc$ %ATE%AT'S SE%ESTE * +

• T,e ourse -esign of #$ Sc$ Sem$. + (%at,ematics)com/rising of 0a/er Number1 Name1 No$ of t,eory lectures /er

wee21 No$ of /ractical lectures /er wee2 1 total mar2s oft,e course and minimum number of lectures to com/lete t,ecourse is as follows *

SR.N

O.SUBJECT

NO. OF

THEORY

LECTURE

PER WEEK

NO. OF

PRACTICAL

LECTURE

PER WEEK

TOTAL

MARKS

MIN.

LECT.

1

0A0E.5!3

%at,ematical Analysis.3 & 4rou/T,eory

! 1"" "

#

0A0E.5! (A)(T,eory)0rogramming in & Numerical Analysis.3

! $% "

&

0A0E.5!

-iscrete %at,ematics

& om/le Analysis.3 ! 1"" "

'

0A0E.5! (#)(0ractical) 0rogramming in & Numerical Analysis.3

! & (&)* #% *"

%

0ro7ect 8or2 & +iva 1

+,i-ace

Lect. F/0

a 0/,2/3 # t/ %

st,-ets4

5ee6

The tit7e

/3 the

20/8ect

5/06 t/

9e

-eci-e-

!

1"

Lect.4+0/,2

• Evaluation of t,e /ro7ect wor2 will be done at t,e end oft,e sit, semester$

• Eac, 0a/er contains/ 5 lectures for student seminar1/ 5 lectures for e/ert tal2 and/ 5 lectures for student9s internal tests$

of 22




#$Sc$ %at,ematicsSE%ESTE . 5

%at,ematics 0a/er ; 5!3 %at,ematical Analysis and 4rou/ T,eory

SET'<N 3 = 5! %A>S? %at,ematical Analysis.3

@N'T 3*#% MARKSD

aD iemann 'ntegral*Pa0titi/s a- Riema s,ms U22e0 a- 7/5e0 R!ite0a7s R!

ite0a9i7it: The ite0a7 as 7imit S/me c7asses /3 ite0a97e

3,cti/s P0/2e0ties /3 ite0a97e 3,cti/ P0/2e0ties /3

ite0a97e 3,cti/s.

9D C/ti,it: >e0i;a9i7it: /3 the ite0a7 3,cti/s F,-ameta7

the/0em /3 ite0a7 ca7c,7,s Mea the/0em /3 ite0a7 ca7c,7,s.

@N'T * #% MARKSD

>e3iiti/ /3 a met0ic ce77s >e3iiti/ a- e@am27es /3 met0ic

s2ace eih9/0h//- 7imit 2/its ite0i/0 2/its O2e a-

c7/se- sets C7/s,0e a- ite0i/0 9/,-a0: 2/its.

C/ti,it: i met0ic s2ace sets S,9s2ace /3 met0ic s2ace

C/;e0ece a- c/m27eteess Ca,ch:s se?,ece c/m27eteess>ese sets Cat/0 sets include antor set is closed? but=<%'T* . cantor set is com/act and com/lete.D

SET'<N =5! %A>S?4rou/ T,eory

@N'T * #% MARKSD

aD >e3iiti/ /3 Bia0: O2e0ati/ P0/2e0ties /3 B.O. E@am27es

+0/,2 its P0/2e0ties E@am27es O3 +0/,2 S,90/,2 Its

P0/2e0ties C/sets Its P0/2e0ties La0aes the/0em.

9D Pe0m,tati/ T0as2/siti/ E;e O-- Pe0m,tati/ S:mmet0ic

+0/,2 I;e0se /3 Pe0m,tati/ A7te0ati;e +0/,2 Its Ui;e0sa7P0/2e0t:.

@N'T G #% MARKSD

aD C:c7ic +0/,2 C:c7ic S,90/,2 Its P0/2e0ties >e-,cti/ O3

La0aes The/0em. >e3iiti/ /3 Is/m/02hism E?,i;a7ece

Re7ati/.

9D Ca:7e: The/0em A,t/m/02hism P0/2e0ties /3 is/m/02hism N/0ma7

s,90/,2 a- ?,/tiet 0/,2.

0a/er Style*.3!! %A>S <@S

1 Attem2t a: 1# /,t /3 1% <Th0ee ?,esti/s /3 /e ma06 30/m

each ,it =33B3 %A>S?

# F0/m ,it 1 =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!

& F0/m ,it # =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!

' F0/m ,it & =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!

% F0/m ,it ' =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

of 22




<= Mathematica7 Aa7:sis 9: T. M. A2/st/7

<1"= Ra7 Aa7:sis 9: R. R. +/7-9e0 <Cha2e7 '%* $ 1".1=

<11= A c/,0se /3 Mathematica7 Aa7:s7s 9: Shatia0a:a S. Cha-

S/s.

<1#= Met0ic s2ace 9: E. T. Ca2s/

<1&= Met0ic s2ace P. K. Jai Ahma- Na0/0a P,97ishi H/,se

<1'= Rea7 Aa7:sis 9: Sha0ma a- asishtha K0isha P0a6asha Mee0,t!#.

<1%= Mathematica7 Aa7:sis 9: >0. +/:a7 a- +,2ta K0isha P0a6asha

Mee0,t!#.

of 22




0a/er Style*.

1 Attem2t a: % /,t /3 $

<ONE ?,esti/ /3 /e ma06 30/m each ,it= =3C3C3C3C3B5 %A>S?

# F0/m ,it 1 =3%A>S?Attem2t a:

T8< /,t /3

TEE =DCDB3?(a)1 (b)1 ()

& F0/m ,it # =3%A>S?Attem2t a: T8< /,t /3 TEE =DCDB3?(a)1 (b)1 ()

' F0/m ,it & =3%A>S?Attem2t a: T8< /,t /3 TEE =DCDB3?(a)1 (b)1 ()

% F0/m ,it ' =3%A>S?Attem2t a: T8< /,t /3 TEE =DCDB3?(a)1 (b)1 ()

* F0/m ,it % =3%A>S?Attem2t a: T8< /,t /3 TEE =DCDB3?

(a), (b), (C)

Tet #oo2 for %ATE%AT'S 0A0E.5!(A)*. (T,eory)0<4A%%'N4 'N is as follows*IHET @S 9 #y * Fas,vant >anet2er 5t, Edition1#0# 0ublications1 New -el,i$

ourse of SET'<N .3 0<4A%%'N4 'N (TE<F)

i$e$ @N'T 31 @N'T and @N'T are covered by following Sections,a/ters of

t,e boo2 KHET @S L

@nit 3G!

• ,a/ter 3 +etti Sta0te-

=<mit*. t,e section of Associativity of </erator?

• ,a/ter The -ecisi/ c/t0/7 St0,ct,0e Wh/7e cha2te0D

@nit G!

• ,a/ter The 7//2 c/t0/7 St0,ct,0e Wh/7e cha2te0D

F/0 the t/2ic /3 @ser -efined :unctionsL 0e3e0 t/the c,a/ter " /3 the 3/77/5i 9//6

K 0rogramming in ANS' L #y* . E #alagurusamy Thi0- E-iti/

Tata Mc+0a5 Hi77 P,97ishi C/m2a: Limite- Ne5 >e7hi.

• ,a/ter The case c/t0/7 St0,ct,0e

=<mit* . Switc, ;ase Statement and related sections?O7: The /t/ 6e:5/0- a- its ,sae.

@N'T *

•

,a/ter 5 *.=<mit*. T,e w,ole ,a/ter 5 ; namely K:unctions and 0ointersL of t,e boo2 KHET @S L ?

of 22




• ,a/ter 6*.>ata T:2es Re;isite-

=<mit*. Storage lasses li2e Automatic Storage lass egister Storage

lass1 Static Storage lass 1

Eternal Storage lass1 8,ic, to @se 8,enMetc$?

• ,a/ter D*.

The C P0e20/cess/0Feat,0es /3 C P0e20/cess/0 Mac0/ E@2asi/ Mac0/s 5ith A0,mets

Mac0/s ;e0s,s F,cti/s

=<%'T*. :ile 'nclusion onditional om/ilation1 Gif and Gelif

-irectives1 %iscellaneous -irectives1

Gundef -irective1 G/ragma -irective?

• A0TE *.

A00a:s. What a0e A00a:s A Sim27e P0/0am Usi A00a: M/0e / A00a:s

A00a: Iitia7iati/ B/,-s Chec6i Passi A00a: E7emets t/ a

F,cti/ T5/ >imesi/a7 A00a:s Iitia7ii a #!>imesi/a7 A00a:

=<%'T*.0ointers and Arrays1 0assing an Entire Array to a :unction1 T,e ealT,ing1 %emory %a/ of a .-imensional Array1 0ointers and .

-imensional Arrays10ointer to an Array10assing .- array to a:unction1 array of /ointers1 t,ree dimensional array1 summary$?Section*

The sc/2e /3 the s:77a9,s is 0/,h7: i-icate- as ,-e0G

N,me0ica7 meth/-s 9: >0. . N. e-am,0th: >0. N. Ch. S. N.

I:ea0 i6as P,97ishi h/,se.

Cha2. 1. <E@ce2t 1.'1.%1.111.1#= Cha2. ' <E@ce2t '.''.$= Cha2.

%. <E@ce2t %.1#= Cha2. *

Re3e0ece B//6sG <3/0 secti/ #=

<1= It0/-,cti/ t/ N,me0ica7 Aa7:sis <#- E-iti/= 9: C.E.F0/9e0

A--isi/ Was7e: 1$

<#= N,me0ica7 Mathematica7 Aa7:sis9: J. B.Sca03/0/,h O@3/0- IBH

P,97i.C/. P;t. Lt-. 1**

<&= N,me0ica7 meth/- P0/97ems S/7,ti/s 9: M. K. Jai S. R.

K.I:ea0 R. K. Jai Ne5 Ae Ite0ati/a7 P;t. Lt-.

1* nction1 Array of 0ointers1 T,ree -imensional Array1 Summary$?

of 22




#$Sc$ %at,ematics

SE%ESTE .5 %ATE%AT'S 0A0E.5!(#). (0AT'AH) 5 %A>S ?

0<4A%%'N4 'N and Numerical AnalysisSET'<N 3

UNIT 1G % MARKSD

P0. N/.<1= T/ 0e;e0se a ,m9e0 T/ 3i- s,m /3 the -iits

P0. N/.<#= T/ 3i- 20ime ,m9e0 9et5ee t5/ ,m9e0s T/ 3i- P0 a-

C0.

P0. N/.<&= T/ 20it A0mst0/ ,m9e0s T/ ee0ate a0ithmetic a-

e/met0ic 20/0essi/s.

P0. N/.<'= T/ 3i- c/m2/,- ite0est 3/0 i;e :ea0s T/ 3i- et

sa7a0: /3 the em27/:ee.

UNIT #G % MARKSD

P0. N/.<%= T/ s/7;e the ?,a-0atic e?,ati/ T/ 3i- ,m9e0 /3 /--

,m9e0 a- e;e ,m9e0s.

P0. N/.<*= T/ a-- a- m,7ti27: t5/ mat0ices.

P0. N/.<$= T/ s/7;e the e?,ati/ 9: Bisecti/ meth/- /0 N!R meth/-.

P0. N/.<= T/ ;e0i3: a st0iD ,m9e0 5hethe0 it is 2a7i-0/me /0 /t.

SET'<N UNIT &G % MARKSD

P0. N/.<= Fitti <1= a st0aiht 7ie a- <#= axe y =

P0. N/.<1"= Fitti <1= a 2a0a9/7a a- <#= bax y =

P0. N/.<11= +a,ss e7imiati/ /0 +a,ss J/0-a meth/- /0

=<%'T * T0ia,7a0isati/ meth/- a- C0/,ts meth/-.D

P0. N/.<1#= Jac/9is meth/- /0 +a,ss Sei-e7s meth/-

=<%'T* Re7a@ati/ meth/-D

UNIT 'G % MARKSD

P0. N/.<1&= Fiite -i33e0eces.

P0. N/.<1'= +0e/0:!Ne5t/s 3/05a0- /0 9ac65a0- ite02/7ati/ 3/0m,7a.

P0. N/.<1%= E00/0 i 2/7:/mia7 ite02/7ati/ E?,i-istace te0ms 5ith

/e /0 m/0e missi ;a7,es

UNIT %G % MARKSD

J/,0a7 a- i;a

N/tes G

• The0e sha77 9e th0ee 2e0i/-s /3 %% mi,tes 2e0 5ee6 2e0 9atch /3 1%

st,-ets 3/0 . SET'<N 3 and


st,-ets 3/0 . SET'<N

• Total S' lectures 2e0i/-s /3 %% mi,tes 2e0 5ee6 2e0 9atch /3 1%

st,-ets

3/0 %ATE%AT'S 0A0E.5!(#). (0AT'AH)

• 1% 20actica7 sh/,7- 9e -/e -,0i semeste0!%.

• At the time /3 e@amiati/ ca-i-ate sh/,7- 90i his4he0 /5

20actica7 8/,0a7 ce0ti3ie- a- sie- 9: H.O.>.

• The0e sha77 9e /e ?,esti/ 2a2e0 /3 #% ma06s a- & h/,0s 3/0

20actica7 e@amiati/

F/0mat /3 ,esti/ Pa2e0 3/0 P0actica7 E@amiati/

,esti/ /.1 As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. 1=G % Ma06s

,esti/ /.# As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. #=G % Ma06s

,esti/ /.& As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. &=G % Ma06s

,esti/ /.' As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. '=G % Ma06s

,esti/ /.% J/,0a7 a- i;aG % Ma06s

of 22




#$Sc$ %at,ematicsSE%ESTE .5

%at,ematics 0a/er ; 5! 3!! %A>S-'SETE %ATE%AT'S & <%0HE ANAHFS'S

SET'<N .3 =5! %A>S?-'SETE %ATE%AT'S

@N'T 3G =5 %A>S?Re7ati/s a- -i33e0et t:2es /3 0e7ati/s. Bia0: 0e7ati/s

E?,i;a7ece 0e7ati/s a- 2a0titi/s 2a0tia7 /0-e0 0e7ati/s

P/sets Hasse -ia0am Lattices as 2/sets P0/2e0ties /3 7attices

Lattices as a7e90aic s:stems S,9 7attices >i0ect 20/-,ct /3 t5/

7attices H/m/m/02hism /0-e0 is/m/02hism /3 t5/ 2/sets

Is/m/02hic 7attices C/m27ete 7attices >ist0i9,ti;e 7attices

C/m27emete- 7attices.

@N'T * =5 %A>S?B//7ea a7e90aG

>e3iiti/ E@am27es BA BA /3 7/ic /3 ci0c,it a- s5itches a-

statemets >i0ect 20/-,ct /3 t5/ BA h/m/m/02hism At/ms /3 BA

Ati at/ms St/es 0e20esetati/ the/0em The set A<@= /3 a77at/ms /3 BA a- its 20/2e0ties. Is/m/02hism /3 a 3iite /3 3iite

BA a- )),(( ⊆ A P B//7ea 3,cti/s 4 e@20essi/s Mite0ms

Ma@te0ms Re20esetati/ /3 a B. e@20essi/ as a s,m /3 20/-,ct

Ca/ica7 3/0m. Ka0a,h ma2. Miimiati/ /3 a B. e@20essi/ 9:

c,9e a00a: 0e20esetati/ a- 9: Ka0a,h ma2.

SET'<N = 5! %A>S ?<%0HE ANAHFS'S.3

@N'T * =5 %A>S? Analytic functions*F,cti/s /3 c/m27e@ ;a0ia97es 7imits The/0ems / 7imits

C/ti,it: a- -i33e0etia9i7it: /3 c/m27e@ 3,cti/s ha0m/ic

3,cti/s Eti0e 3,cti/s a- aa7:tic 3,cti/s Ca,ch: Riemac/-iti/s i Ca0tesia a- 2/7a0 3/0m.

@N'T * =5 %A>S?>e3iite ite0a7 c/t/,0s 7ie ite0a7s Ca,ch:!+/,0sat

the/0em(wit,out /roof)1 Ca,ch:s ite0a7 3/0m,7a Hihe0 /0-e0

-e0i;ati;e /3 aa7:tic 3,cti/ M/0e0as the/0em Ca,ch:s

ie?,a7it: a- Li/,;i77es the/0em F,-ameta7 the/0em /3

a7e90a Ma@im,m m/-,7,s the/0em.


1 Attem2t a: 1# /,t /3 1%

<Th0ee ?,esti/s /3 /e ma06 30/m each ,it= =33B3 %A>S?

# F0/m ,it 1 =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

& F0/m ,it # =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

' F0/m ,it & =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

% F0/m ,it ' =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

of 22




Tet #oo2 of %at,ematics 0a/er 5! SET'<N .<%0HE ANAHFS'S.3

K om/le +ariables and A//licationsL:ift, Edition1ul +$ ,urc,ill and James 8ard #rown$

%c 4raw ill 0ublis,ing om/any$

,a/ter

• Secti/s t/ #1.

,a/ter

• Secti/s &" t/ &%.

• Secti/s &* t/ &$.

Lemma a- Ca,ch:!+/,0sat the/0em <i secti/s= &* wit,out /roof)1

• Secti/s & t/ '&.

eferences* (for section 3 and )

<1= C/m27e@ ;a0ia97es a- a227icati/s 9: R. . Ch,0chi77 a- J. Q

B0/5

<#= The/0: /3 3,cti/s /3 a C/m27e@ ;a0ia97es 9: Shatia0a:a Cha-

C/.

<&= C/m27e@ ;a0ia97es It0/-,cti/ a- a227icati/s 9: Ma06 A97/5it

a- A. S. F/6as Cam90i-e Ui;e0sit: P0ess.

<'= +0a2h the/0: 5ith a227icati/ t/ eiee0i a- c/m2,te0sciece.9: Na0sih >e/. 1&P0etice Ha77 /3 I-ia P;t. Lt-.

<%= F/,-ati/ /3 >isc0ete Mathematics K. >. J/shi Ne5 Ae

Ite0ati/a7 Lt-. P,97ishe0s.

<*= A 3i0st 7//6 at +0a2h the/0: 9: C7a06.

<$= >isc0ete Mathematica7 St0,ct,0es 5ith a227icati/s t/ c/m2,te0

sciece

9: T0em97e: 1.P. a- Ma/ha0 R.

<= E7emets /3 >isc0ete Mathematics <#- e-iti/= 9: L. Li, Me.

+0a5Hi77 Ite0ati/a7 e-iti/ C/m2,te0 Sciece se0ies 1*.

<= >isc0ete Mathematics B: atsa i6as P,97icati/s.

<1"= It0/-,cti/ +0a2h The/0: B: R. J. Wi77s/s

<11= >isc0ete Mathematics St0,ct,0e B:. >,0ai Na0/0a P,9.

of 22




#$ Sc$ %ATE%AT'S SE%ESTE * +'

• T,e ourse -esign of #$ Sc$ Sem$. +' (%at,ematics)com/rising of 0a/er Number1 Name1 No$ of t,eory lectures /er wee21 No of /ractical lectures /er wee2 1 total mar2s of t,e /a/er and minimum number of lectures to com/lete t,e course

is as follows *

SR.

NO.SUBJECT

NO. OF

THEORY

LECTURE PER

WEEK

NO. OF

PRACTICAL

LECTURE

PER WEEK

TOTAL

MARKS

MIN.

LECT.

10A0E.6!3

4ra/, T,eory &om/le Analysis.

! 1"" "

#

0A0E.6! Analysis. & Abstract Algebra.

! 1"" "

&

0A0E.6! (A)(T,eory)

</timiOation & Numerical Analysis.

! $% "

'

0A0E.6! (#)(0ractical)</timiOation & Numerical Analysis.

! & (& #% *"

%

0ro7ect 8or2 & +iva1 +,i-ace

Lect. F/0 a

0/,2 /3 #

t/ %

st,-ets45e

e6

The

P0/8ect

W/06 t/

9e

s,9mitte-

at the

e- /3this sem.

1""3!

Hect$4rou/

• Eac, 0a/er contains/ 5 lectures for student seminar1/ 5 lectures for e/ert tal2 and/ 5 lectures for student9s internal tests$

• Total mar2s of /ro7ect and viva will be 3!!$

• T,e Evaluation of t,e /ro7ect wor2 will be done at t,e end of t,e sit,semester$:or t,e Evaluation of t,e /ro7ect wor2 t,ere s,all be t,ree,ours duretion at t,e end of t,e sit, semester$T,ere s,all be batc, of35 students for /ro7ect and viva$

of 22





%at,ematics 0a/er ; 6!3 3!! %A>S4ra/, t,eory and <%0HE ANAHFS'S

SET'<N 3 = 5! %A>S ?

4ra/, t,eory@N'T 3* =5 %A>S?

4ra/, t,eoryGBasic -e3iiti/s a- sim27e e@am27es >i0ecte- U-i0ecte- m,7ti!

0a2h mi@e- 0a2h. Ici-ece 0e7ati/ a- -e0ee /3 the 0a2h. Em2t:

c/m27ete 0e,7a0 0a2hs. S,9 0a2h c/ecte- a- -isc/ecte- 0a2hs.

Wa76 a- ,i7ate0a7 c/m2/ets E,7e0 0a2hs Uic,0sa7 0a2h O2e0ati/

/3 0a2h ci0c,it t0ee. Hami7t/ia 2ath a- c:c7es t0ee Bia0: a-

S2ai t0ees. 1 is/m/02hism #! is/m/02hism

@N'T * =5 %A>S?ut.set1 connectivity and se/arability=<%'T*.3.isomor/,ism1 .isomor/,ism? 27ae0 0a2hs a- thei0 -i33e0et 0e20esetati/ >,a7 /3 a 27ae0

0a2h E,7e0s 3/0m,7a K,0at/5s6is 3i0st a- sec/- /!27ae0 0a2h

;ect/0 s2ace ass/ciate- 5ith a 0a2h Ci0c,it s,9s2ace a- c,t sets

s,9s2ace O0th//a7 s2ace.

e0te@ c/7/0i Ch0/matic ,m9e0 I-e@ ,m9e0 a- 2a0titi/ C:c7ic

0a2h a- -em:e7iati/ /3 c:c7ic 0a2hs Mat0i@ 0e20esetati/ /3 a

0a2h A-8acec: mat0i@ Ici-ece mat0i@ Path mat0i@

=<%'T *. ircuit matri1 :undamental circuit matri and cut set matri1elation s,i/ of t,ese matrices?an2 of t,e ad7acency matri.

SET'<N = 5! %A>S ?<%0HE ANAHFS'S.

@N'T * =5 %A>S?0ower series*

>e3iiti/ /3 c/m27e@ se?,ece C/m27e@ se0ies a- 2/5e0 se0iesE@2asi/ /3 a c/m27e@ 3,cti/ i Ta:7/0s se0ies a- La,0ets se0ies.

%a//ing and onformal ma//ing*E7emeta0: 3,cti/s ma22i 9: e7emeta0: 3,cti/s M/9i/,s ma22i

7iea0 3,cti/

Bi7iea0 ma22i wB(aOCb)(cOCd) 2 z w =

z w

1= )exp( z w =

=<%'T* z w sin= 1 z w cos= 1 z w cosh= 1 z w sinh=

Transformations1 onformal ma//ings and t,eir eam/les$?

@N'T * =5 %A>S?

esidues and /oles*>e3iiti/ /3 a si,7a0 2/it Is/7ate- si,7a0 2/its e0/s /3

c/m27e@ 3,cti/s P/7es a- 0esi-,es /3 c/m27e@ 3,cti/ Ca,ch:s

0esi-,es the/0em E;a7,ati/ /3 im20/2e0 0ea7 ite0a7s 9: 0esi-,e

the/0em a- e;/7,ti/ /3 -e3iite ite0a7 /3 t0i//met0ic 3,cti/s 9:

0esi-,e the/0em.

of 22




.* 0a/er Style*.3!! %A>S <@S

P$ 3 Attem2t a: 1# /,t /3 1%

<Th0ee ?,esti/s /3 /e ma06 30/m each ,it= =33B3 %A>S?

P$ F0/m ,it 1 =%A>S?<a= Attem2t a:

T8< /,t /3

TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

P$ F0/m ,it # =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

P$ F0/m ,it & =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!?

P$ 5 F0/m ,it ' =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?

<9= Attem2t a: T8< out of TEE =5C5B3!?

Tet boo2 for %at,ematics 0a/er ; 6!3SET'<N 3 4ra/, t,eory

4ra/, t,eory wit, a//lication to engineering and com/uter science#y* . Narsing, -eo10rentice all of 'ndia 0rivate Himited1 New -el,i$

,a/ter* 3

• 1.1 1.& 1.' 1.%

• =<%'T * . Q 3$ and Q 3$6?,a/ter*

• #.1 #.# #.& #.' #.% #.* #.$ #. #.• =<%'T* . Q$3!D

,a/ter*

• &.1 &.# &.& &.% &.* &.$ &.

• =<%'T* . Q $1 Q $"1 Q $3!?,a/ter*

• '.1 '.# '.& '.' '.%

• =<%'T* . Q $61 Q $D1 Q $ ?,a/ter* 5

• %.# %.& %.' %.% %.*

• =<%'T* . Q 5$31 Q 5$D1 Q 5$1 Q 5$"?,a/ter* 6

• *.1 *.% *.$ *.

• <%'T* . Q 6$1 Q 6$1 Q 6$1 Q 6$?,a/ter* D

• $.1 $. $.

• <%'T* . Q D$1 Q D$1 Q D$1 Q D$51 Q D$61 Q D$D?,a/ter*

• .1 .# .%

• <%'T* . Q $1 Q $1 Q $6,a/ter* "

• .1 .11

• <%'T* . Q "$ to Q "$3!?

of 22




Tet #oo2 of %at,ematics 0a/er 6!3SET'<N .<%0HE ANAHFS'S.

Kom/le +ariables and A//licationsL:ift, Edition1uel +$ ,urc,ill and James 8ard #rown$

%c 4raw ; ill 0ublis,ing om/any

,a/ter 5

• Secti/s '' '% '* '$ ' Omit Secti/sG !' %" %1D

,a/ter 6

• Secti/s %& t/ % *" <%'T*! Secti/s %D,a/ter D

• Secti/s *' *% ** *$ * $"

<%'T Secti/s* ! *& $1 $#D<%'T* . ,a/ter D

eferences*

<1= C/m27e@ ;a0ia97es a- a227icati/s 9: R. . Ch,0chi77 a- J. QB0/5

<#= The/0: /3 3,cti/s /3 a C/m27e@ ;a0ia97es 9: Shatia0a:a Cha-

C/.

<&= C/m27e@ ;a0ia97es It0/-,cti/ a- a227icati/s 9: Ma06 A97/5it

a- A. S. F/6as Cam90i-e Ui;e0sit: P0ess.

<'= +0a2h the/0: 5ith a227icati/ t/ eiee0i a- c/m2,te0

sciece.9: Na0sih >e/. 1&P0etice Ha77 /3 I-ia P;t. Lt-.

<%= F/,-ati/ /3 >isc0ete Mathematics K. >. J/shi Ne5 Ae

Ite0ati/a7 Lt-. P,97ishe0s.

<*= A 3i0st 7//6 at +0a2h the/0: 9: C7a06.

<$= >isc0ete Mathematica7 St0,ct,0es 5ith a227icati/s t/ c/m2,te0

sciece

9: T0em97e: 1.P. a- Ma/ha0 R.

<= E7emets /3 >isc0ete Mathematics <#- e-iti/= 9: L. Li, Me.

+0a5Hi77 Ite0ati/a7 e-iti/ C/m2,te0 Sciece se0ies 1*.

<= >isc0ete Mathematics B: atsa i6as P,97icati/s.

<1"= It0/-,cti/ +0a2h The/0: B: R. J. Wi77s/s

<11= >isc0ete Mathematics St0,ct,0e B:. >,0ai N

of 22




B.Sc. Mathematics

SE%ESTE .6 %at,ematics 0a/er ; 6! 3!! %A>S ANAHFS'S and Abstract Algebra

SET'<N 3 =5! %A>S?

ANAHFS'S.@N'T 3* =5 %A>S?

aD C/;e0 O2e c/;e0 Fiite s,9 c/;e0 C/m2act set P0/2e0ties /3

c/m2act sets onnected sets1 Se/arated sets1 #olOano.8eirstrasst,eorem1 ountable set$

9D C/ti,it: a- ,i3/0m c/ti,it: is/met0: a- h/me/m/02hism /3

t5/ met0ics E?,i;a7et met0ics C/m2actess Se?,etia7

c/m2actess t/ta77: 9/,-e- s2ace

@N'T * =5 %A>S?Ha/lace Transforms>e3iiti/ /3 La27ace T0as3/0ms La27ace T0as3/0ms /3 e7emeta0:

F,cti/ I;e0se La27ace T0as3/0ms La27ace T0as3/0ms /3

>e0i;ati;e a- Ite0a7s La27ace T0as3/0ms >i33e0etiati/ a-

ite0ati/ /3 La27ace T0as3/0ms C/;/7,ti/ the/0em. =<mit* . A//lication to -ifferential ERuations$?

SET'<N =5! %A>S? Abstract Algebra.

@N'T * =5 %A>S?H/m/m/02hism Ke0e7 /3 h/m/m/02hism F,-ameta7 the/0em /3

h/m/m/02hism. Ri a- its 20/2e0ties S,90i =<%'T*. #ooleanring1 Euclidean ring?Fie7- e0/ -i;is/0 Ite0a7 -/mai Cha0acte0istics /3 0i

Cace77ati/ 7a5 I-ea7s P0ici2a7 i-ea7 P/7:/mia7 0i

=<%'T*. Puotient ring$ %aimal ideal? P/7:/mia7 >e0ee /3

2/7:/mia7 Fact/0 a- 0emai-e0 the/0em /3 2/7:/mia7 P0/-,ct

s,m a- -i;isi/ /3 2/7:/mia7s.

@N'T * =5 %A>S?aD Re-,ci97e a- i00e-,ci97e 2/7:/mia7s Fact/0iati/ /3

2/7:/mia7s< ,i?,e Fact/0iati/ the/0em (wit,out /roof)1 =<%'T*.Eisenstein9s criterionD >i;isi/ a7/0ithm the/0em /3 2/7:/mia7

9D +.C.>. /3 2/7:/mia7s ,ate0i/ =<%'T*. ing ,omomor/,ism1 Eulerand :ermat9s t,eorem?


P$ 3 Attem2t a: 1# /,t /3 1% <Th0ee ?,esti/s /3 /e ma06 30/m

each ,it= =33B3 %A>S?P$ F0/m ,it 1 =%A>S?

<a= Attem2t a: T8< /,t /3 TEE =6C6B3?

<9= Attem2t a: T8< out of TEE =5C5B3!P$ F0/m ,it # =%A>S?

<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!

P$ F0/m ,it & =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!

P$ 5 F0/m ,it ' =%A>S?<a= Attem2t a: T8< /,t /3 TEE =6C6B3?<9= Attem2t a: T8< out of TEE =5C5B3!

Tet boo2 for %at,ematics 0a/er ; 6!SET'<N 3

of 22




ANAHFS'S.

:or unit

IAdvanced %at,ematics for 0,armacy9 #y* . %a,a7an 0ublis,ing ouse1 A,medabad

,a/ter* . 3D Ha/lace Transforms 1$.1 1$.# 1$.& 1$.' 1$.% 1$.* =<%'T *. A//lication to -ifferential ERuations?

Tet #oo2 for %ATE%AT'S 0A0E.6!SET'<N

Abstract Algebra.

KAbstract AlgebraL #y* -r$ '$ $ S,et,1 0rentice all <f 'ndia1 New -el,i$

ourse of %at,ematics 0a/er ; 6! =SET'<N .? Abstract Algebra. ( i$e$ @N'T1 & @N'T ) a0e c/;e0e- 9: 3/77/5i Cha2te0s4 Secti/s /3 the a9/;e

meti/e- 9//6 A9st0act A7e90a

,a/ter 3G 1#.1 1#.# 1#.*

,a/ter 3G 1&.1 1&.# 1&.& 1&.'

,a/ter 3* 1'.1 1'.# 1'.& 1'.'

,a/ter 35* 1%.1 1%.# 1%.' =<%'T*. Q 35$?,a/ter 3* 1.1 1.# 1.&

1.' <mit* T,eorem* 3$$i$ e$ ,i?,e Fact/0iati/ the/0em (wit,out /roof)D 1.%=<%'T* . Q 3$6 . Eisenstein9s criterion ? 1.$.

Re3e0eces G<3/0 secti/ 1 a- #=

<1= T/2ics i A7e90a 1. N. He0stei Wi77e: Easte0 Lt-. Ne5 >e7hi

<#= A te@t B//6 /3 M/-e0 A9st0actA7e90a 9: Shatia0a:a S. Cha-

C/. Ne5 >e7hi.

<&= F,-ameta7s /3 A9st0act A7e90a >. S. Ma7i6 J. N. M/0-/s/

a- M. K. Se Mc+0a5 Hi77 Ite0ati/a7 E-iti/ ! 1$

<'= Ui;e0sit: A7e90a M. S. +/2a7a60isha Wi7e: Easte0 Lt-.

<%= A9st0act A7e90a B: Bhattacha0:a Ya77/ P,97icati/s.

<*= M/-e0 A7e0a B: Kai ami,-ia S,0sit i6as P,97icati/.

>e7hi.

<$= Te@t B//6G A9st0act A7e90a >0. 1. H. Sheth i0a; P0a6asha

Ahme-a9a-.

<= Mathematica7 Aa7:sis <#- e-iti/= 9: S. C. Ma7i6 A0/0a Ne5 Ae

Ite0. P;t.

<= Mathematica7 Aa7:sis 9: T. M. A2/st/7

<1"= Rea7 Aa7:sis 9: R. R. +/7-9e0 <Cha2e7 '%* $ 1".1=

<11= A c/,0se /3 Mathematica7 Aa7:s7s 9: Shatia0a:a S. Cha-

of 22




S/s.

<1#= Met0ic s2ace 9: E. T. Ca2s/

<1&= Met0ic s2ace P. K. Jai Ahma- Na0/0a P,97ishi H/,se

<1'= Rea7 Aa7:sis 9: Sha0ma a- asishtha K0isha P0a6asha Mee0,t!#.

<1%= Mathematica7 Aa7:sis 9: >0. +/:a7 a- +,2ta K0isha P0a6asha

Mee0,t!#.

of 22





%at,ematics 0a/er ; 6!(A) D5 %A>S<0T'%'AT'<N and N@%E'AH ANAHFS'S

SET'<N 3 = ! %A>S ?<0T'%'AT'<N

@N'T 3* =35 %A>S?The 7iea0 20/0ammi 20/97ems F/0m,7ati/ /3 LPP Mat0i@ 3/0m /3 the

LPP ee0a7 3/0m Ca/ica7 3/0m Sta-a0- 3/0m /3 the LPP +0a2hica7

meth/- t/ s/7;e LPP S/me -e3iiti/s a- 9asic 20/2e0ties /3 c/;e@

sets c/;e@ 3,cti/s a- c/ca;e 3,cti/. Basic -e3iiti/s t/ ,se

Sim27e@ meth/- Sim27e@ meth/- Bi!M meth/- <Pea7t: meth/-= T5/ 2hase

meth/- t/ s/7;e LPP< 5ith/,t a7te0ati;e s/7,ti/ a- ,9/,-e-

s/7,ti/=

@N'T * =35 %A>S?P0ici27e /3 -,a7it: i LPP P0ima7 LPP a- meth/- t/ 3i- its -,a7 LPP

<Sim27e 20/97ems /3 a9/;e a0tic7es=. The t0as2/0tati/ 20/97emsG

Mathematica7 a- mat0i@ 3/0m /3 TP. Iitia7 s/7,ti/ /3 TP 9: NWCM LCM

a- AM O2tim,m s/7,ti/ /3 TP 9: M/-i meth/- < ,!; meth/- = <e@ce2t-eee0ate s/7,ti/= Ba7ace- a- ,9a7ace- TP<Sim27e 20/97em =

Assimet 20/97emG Mathematica7 a- mat0i@ 3/0m /3 AP H,a0ia

meth/- t/ s/7;e meth/-<sim27e meth/-=.

SET'<N = 5 %A>S ? N@%E'AH ANAHFS'S .

@N'T * =35 %A>S?aD entral difference inter/olation formulae* % Ma06sD

+a,sss 3/05a0- +a,sss 9ac65a0- Ste07is Besse7s a-

La27ace! E;e0etts ite02/7ati/ 3/0m,7ae.

9D Ite02/7ati/ 5ith ,e?,a7 ite0;a7sG 1" ma06sD

>i;i-e- -i33e0eces P0/2e0ties /3 -i;i-e- -i33e0ece Re7ati/9et5ee -i;i-e- -i33e0eces a- 3/05a0- -i33e0ece Ne5t/s

-i;i-e- -i33e0ece 3/0m,7a La0aes ite02/7ati/ 3/0m,7a

I;e0se ite02/7ati/ La0aes i;e0se ite02/7ati/ 3/0m,7a

@N'T * =35 %A>S?aD Numerical -ifferentiation G % Ma06sD

N,me0ica7 >i33e0etiati/ >e0i;ati;es ,si +0e/0:!Ne5t/s

3/05a0- -i33e0ece 3/0m,7a >e0i;ati;es ,si +0e/0:!Ne5t/s

9ac65a0- -i33e0ece 3/0m,7a >e0i;ati;e ,si Ste07is 3/0m,7a.

9D N,me0ica7 Ite0ati/G

1" Ma06sD

N,me0ica7 Ite0ati/ +ee0a7 ?,a-0at,0e 3/0m,7a T0a2e/i-a7

0,7e Sim2s/ s 14& 0,7e Sim2s/s &4 0,7e We--7es 0,7e a-

e00/0s i ?,a-0at,0e 3/0m,7ae

@N'T 5* N@%E'AH S<H@T'<N <: <-'NAF -'::EENT'AH EP@AT'<NS=35 %A>S?

aD S/7,ti/ 9: Ta:7/0s se0ies meth/- Ta:7/0s se0ies meth/- 3/0

sim,7tae/,s 3i0st /0-e0 -i33e0etia7 e?,ati/s Pica0-s meth/-

Pica0-s meth/- 3/0 sim,7tae/,s 3i0st /0-e0 -i33e0etia7

e?,ati/s E,7e0s meth/- Im20/;e- E,7e0s meth/- M/-i3ie-

E,7e0s meth/-. 1" ma06sD

9D R,es meth/- R,e!K,tta meth/-s Hihe0 /0-e0 R,e!K,tta

meth/-s R,e!K,tta meth/-s 3/0 sim,7tae/,s 3i0st /0-e0

-i33e0etia7 e?,ati/s R!K meth/-s 3/0 sim,7tae/,s 3i0st /0-e0

-i33e0etia7 e?,ati/s P0e-ict/0!C/ect/0 meth/-s Mi7es

meth/-. %Ma06sD

of 22




Tet #oo2 for %at,ematics 0a/er ; 6!(A) SET'<N .3<0T'%'AT'<N SET'<N 3

</eration esearc, T,eory and A//lications91J$ >$ S,arma1 Second Edition1

%A%'HHAN 'N-'A HT-

ourse of %at,ematics 0a/er ; 6!(#) =SET'<N .3? <0T'%'AT'<N( i$e$ @N'T 31 & @N'T ) a0e c/;e0e- 9: 3/77/5i Cha2te0s4 Secti/s /3 the

a9/;e meti/e- 9//6

,a/ter *.

• #.* O7:D

,a/ter *.

• &.1 &.# &.& =<mit*. Q $?

,a/ter

• '.1 '.# '.& '.' =<mit*. Q $5 and Q $6?

,a/ter 5

• %.1 %.# %.& =<mit*. Q 5$1 Q 5$5 ?

,a/ter "

• .1 t/ .% .*

• =<nly Q "$6$3 @nbalanced Su//ly and -emand?

• =<mit* . Q "$6$1 Q "$6$1 Q "$6$M etc in Q "$6?

• =<mit* . Q "$D1 Q "$?

,a/ter 3! 1".1 t/ 1".&

• A//endi A A.1" a- A.1#

• =<mit* . Q 3!$ to Q 3!$6?

• =<mit* . t,e rest?

SET'<N

The sc/2e /3 the s:77a9,s is 0/,h7: i-icate- as ,-e0G

N,me0ica7 meth/-s 9: >0. . . e-am,0th: >0. N. Ch. S. N. I:ea0

i6as P,97ishi h/,se.

Cha2.$ <E@ce2t $.$$.= Cha2. . <E@ce2t .= Cha2. . <E@ce2t .%

.1&= Cha2. 11. <E@ce2t 11.1 11.#11.& 11.* 11. 11.1$ 11.#"=

Re3e0ece B//6s <3/0 secti/ #=

<1= It0/-,cti/ t/ N,me0ica7 Aa7:sis <#- E-iti/= 9: C.E.F0/9e0

A--isi/ Was7e: 1$

<#= N,me0ica7 Mathematica7 Aa7:sis9: J. B.Sca03/0/,h O@3/0- IBH

P,97i.C/. P;t. Lt-. 1**

<&= N,me0ica7 meth/- P0/97ems S/7,ti/s 9: M. K. Jai S. R.

K.I:ea0 R. K. Jai Ne5 Ae Ite0ati/a7 P;t. Lt-. 1*

of 22





%at,ematics 0a/er ; 6!(#) 0AT'AH . 5 %A>S<0T'%'AT'<N and N@%E'AH ANAHFS'S

SET'<N 3@N'T 3* =5 %A>S?

P0.N/.<1= S/7;e the 3/77/5i LPP ,si 0a2hica7 meth/-.

P0.N/.<#= S/7;e the 3/77/5i LPP ,si Sim27e@ meth/-.

P0.N/.<&= S/7;e the 3/77/5i LPP ,si 9i !M meth/-.

P0.N/.<'= S/7;e the 3/77/5i LPP ,si t5/ 2hase meth/-.

@N'T * =5 %A>S?P0.N/.<%= O9tai -,a7 /3 the 3/77/5i P0ima7 LPP

P0.N/.<*= Fi- the /2tim,m s/7,ti/ /3 3/77/5i t0as2/0tati/

20/97em.

P0.N/.<$= Fi- the /2tim,m s/7,ti/ /3 3/77/5i assimet

20/97em.

SET'<N @N'T * =5 %A>S?

P0.N/.<= +a,ss 3/05a0- a- 9ac65a0- ite02/7ati/ 3/0m,7a.P0.N/.<= Ste07is /0 Besse7s /0 La27ace!E;e0etts 3/0m,7a

P0.N/.<1"= Ite02/7ati/ 5ith ,e?,a7 ite0;a7s.

P0.N/.<11= N,me0ica7 -i33e0etiati/.

@N'T * =5 %A>S?P0.N/.<1#= N,me0ica7 ite0ati/.

P0.N/.<1&= Ta:7/0s /0 Pica0-s

P0.N/.<1'= E,7e0s meth/-.

P0.N/.<1%= R,es /0 R,e!K,ttas /0 Mi7es meth/-

@N'T 5* =5 %A>S?J/,0a7 a- ;i;a.

N/tes G


st,-ets 3/0 . SET'<N 3 and


st,-ets 3/0 . SET'<N

• Total S' lectures 2e0i/-s /3 %% mi,tes 2e0 5ee6 2e0 9atch /3 1%

st,-ets

3/0 %ATE%AT'S 0A0E.6!(#). (0AT'AH)

• 1% 20actica7 sh/,7- 9e -/e -,0i semeste0!*.

• At the time /3 e@amiati/ ca-i-ate sh/,7- 90i his4he0 /5

20actica7 8/,0a7 ce0ti3ie- a- sie- 9: H.O.>.

• The0e sha77 9e /e ?,esti/ 2a2e0 /3 #% ma06s a- & h/,0s 3/0

20actica7 e@amiati/

:ormat of Puestion 0a/er for 0ractical Eamination

• ,esti/ /.1 As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. 1=G % Ma06s

• ,esti/ /.# As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. #=G % Ma06s

• ,esti/ /.& As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. &=G % Ma06s

• ,esti/ /.' As5e0 a: t5/ /,t /3 th0ee <F0/m Uit /. '=G % Ma06s

• ,esti/ /.% J/,0a7 a- i;aG % Ma06s

b.sc.mathematics sem.5 & 6 syllabus non cbcs final uni copy latest dt 23-03-2010

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