110873574 bsc maths subjects

7/24/2019 110873574 Bsc Maths Subjects

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Please click on a link below to access the Syllabus of the course.

BSc Mathematics - Semester I

Paper I - Algebra and Trigonometry I

Allied I - or B.Sc. Mathematics

BSc Mathematics - Semester II

Paper II - !alculus and !oordinate "eometry of # $imensions

Allied I - or B.Sc. Mathematics

BSc Mathematics - Semester III

Paper III - Algebra and Trigonometry II

Paper I% - !alculus and $ifferential "eometry

Paper % - $ifferential &'uations and (aplace Transforms

Paper %I - !oordinate "eometry of ) $imensions and Probability

Allied - Mathematics for Statistics I

BSc Mathematics - Semester I%

Paper %II - %ector !alculus ourier Series and ourier Transforms

Paper %III - Statics

Allied - Mathematics for Statistics II

BSc Mathematics - Semester %

Paper I* - Algebraic Structures I

Paper * - +eal Analysis I

Paper *I - $ynamics

Semester %I - Paper *III - Algebraic Structures

Semester %I - Paper *I% - +eal Analysis II

Semester %I - Paper *% - !omple, Analysis

Application riented Subect I - "raph Theory I
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te-courses/bachelor-of-science/Mathematics/Paper-XI-Dynamics.asphttp://www.indiastudycenter.com/Other/Syllabus/maduniv/under-graduate-courses/bachelor-of-science/Mathematics/Paper-XIII-Algebraic-Structures.asphttp://www.indiastudycenter.com/Other/Syllabus/maduniv/under-graduate-courses/bachelor-of-science/Mathematics/Paper-XIV-Real-Analysis-II.asphttp://www.indiastudycenter.com/Other/Syllabus/maduniv/under-graduate-courses/bachelor-of-science/Mathematics/Paper-XV-Complex-Analysis.asphttp://www.indiastudycenter.com/Other/Syllabus/maduniv/under-graduate-courses/bachelor-of-science/Mathematics/AOS-Graph-Theory-I.asp


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Application riented Subect I - $iscrete Mathematics

Application riented Subect I - Special unctions I

BSc Mathematics - Semester %I

Application riented Subect II - &lementary /umber Theory

Application riented Subect II - Special unctions II
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0/I%&+SIT1 MA$+ASB.Sc. $&"+&& !0+S& I/ MAT2&MATI!SS&M&ST&+ S1ST&M 3IT2 !+&$ITS4&ffecti5e from the Academic 1ear #66)-#6678

S1((AB0S

Semester I - Paper I - Algebra and Trigonometry I

$uration of &,amination9 ) hrsMa,imum Marks9 :66!redits9 7

Algebra 9-

Theory of &'uations9 Polynomial e'uations; Imaginary and irrational roots; Symmetric

functions of roots in terms of coefficients; Sum of rthpowers of roots; +eciprocal e'uations;Transformations of e'uations.

$escartes< rule of signs9 Appro,imate solutions of roots of polynomials by /ewton-+aphsonmethod - 2omernight 42M publications - :??78

). Pure Mathematics 9 2ardy

7. Trigonometry 9 P. $uraipandian

@. Plane Trigonometry part # 9 S. (. (oney= 4Macmillan and !o. (ondon8

. Algebra= Analytical "eometry 4#$8 and Trigonometry9 $r. S. Sudha 4&merald Publishers8.


4/21

Semester I - Allied I - or B.Sc. Mathematics


!alculus of finite differences and /umerical Analysis - Paper I 4:)@ hrs8

Solutions of algebraic and Transcendental e'uations= Bisection method= Iteration method=+egula falsi method= /ewton-+aphson method.

Solution of simultaneous linear e'uations9

"uass - elimination method= "uass - ordan method= "auss - Siedel method= !routonark publishing.

7. !alculus of finite differences and /umerical Analysis by Sa,ena= S.!hand D !o.


5/21

Semester II - Paper II - !alculus and !oordinate "eometry of # $imensions


$ifferential !alculus 9-

nthderi5ati5e; (eibnitC. Manicka5achagam Pillai and others 4S. %iswanathanPublications8

#. Analytical "eometry of # dimensions9 P. $uraipandian

). !oordinate "eometry9 $r. P. Balasubramanian and others 4Mc"raw 2ill publishers8

7. !alculus9 S. /arayanan and others 4S. %iswanathan Publications8

@. Integral !alculus9 Shanti /arayanan 4S. !hand and !o.8

. Integral !alculus and $ifferential &'uations9 $ipak !hatteri 4TATA Mc"raw 2illpublishing company8

E. !alculus9 $r. S. Sudha 4&merald Publishers8.

Semester II - Allied I - or B.Sc. Mathematics


6/21


!alculus of finite differences and /umerical Analysis - Paper II 4:)@ hrs.8

/umerical differentiation9

$eri5ati5es using /ewtonrishna prakastanMandir= Meerut.

#. /umerical methods in Science and &ngineering by M.>.5enkataraman= /ational publishinghouse= !hennai.

). /umerical Analysis by B.$. "upta= >onark publishing.

7. !alculus of finite differences and /umerical Analysis by Sa,ena= !hand D !o.

Semester III - Paper III - Algebra and Trigonometry II


7/21


Matrices 9-

Symmetric; Skew Symmetric; 2ermitian; Skew 2ermitian; rthogonal and 0nitary Matrices;+ank of a matri,; !onsistency and solutions of (inear &'uations; !ayley 2amilton Theorem;&igen 5alues; &igen %ectors; Similar matrices; $iagonaliCation of a matri,.

"roup Theory and number theory 9-

&'ui5alence relations; "roups; subgroups - cyclic groups and properties of cyclic groups -simple problems; (agrange


8/21

!ur5ature; radius of cur5ature in !artesian coordinates; polar coordinates; e'uation of astraight line= circle and conic; radius of cur5ature in polar coordinates; p-r e'uations; e5olutes;en5elopes;

Asymptotes 9

Methods 4without proof8 of finding asymptotes of rational algebraic cur5es with special cases.

Beta and "amma functions= properties and simple problems.

$ouble Integrals; change of order of integration; triple integrals; applications to area= surfacearea and 5olume.

+eference books 9-

:. !alculus 9 S. /arayanan and others 4S. %iswanathan publishers8

#. Integral !alculus and differential e'uations 9 $ipak !hatteree 4TATA Mc"raw 2illPublishing company ltd.8

Semester III - Paper % - $ifferential &'uations and (aplace Transforms

$uration of &,amination9 ) hrsMa,imum Marks9 :66

!redits9 7

irst order but of higher degree e'uations - sol5able for p= sol5able for ,= sol5able for y=!lairaut


9/21

+eference Books 9-

:. &ngineering Mathematics %olume )9 M. >. %enkataraman 4/ational Publishing !o.8

#. &ngineering Mathematics %olume )9 P. >andasamy and others 4S. !hand and !o.8

). Integral !alculus and differential e'uations 9 $ipak !hatteree 4TATA Mc"raw 2illPublishing company ltd.8

7. Ad5anced &ngineering mathematics9 &rwin >reysCig 4ohn 3iley and sons /ew 1ork :???8

@. !alculus9 /arayanan and others 4S. %iswanathan publishers8

. $ifferential &'uations D Integral Transforms9 $r. S. Sudha 4&merald Publishers8.

Semester III - Paper %I - !oordinate "eometry of ) $imensions and Probability


Planes and lines; reduction to symmetric form of a line gi5en by a pair of planes; conditions for# lines to be coplanar and the e'uation of the plane containing the lines; length and e'uation ofthe shortest distance between # skew lines; image of a point and a line w. r. t. a plane= bisector

planes.

Sphere 9-

&'uations of a sphere; general e'uation; section of a sphere by a plane; tangent plane; radicalplane; coa,ial system of spheres; orthogonal spheres.

Probability 9-

Probability space; total probability; multiplication law on probability; conditional probability;independent e5ents; Baye


10/21

7. Ad5anced &ngineering Mathematics 9 Stanley "rossman and 3illiam +. $e5it 42arper and+ow publisher8

@. undamentals of mathematical statistics9 S. !. "upta and %. >. >apoor 4Sultan !hand andsons8

. Mathematical Statistics and Probability by $r. P. +. %ittal 4Margham Publishers8

Semester III - Allied - Mathematics for Statistics I


Sets= perations on sets - real 5alued functions - countability - real numbers bounds= supremumand infimum - se'uence of real numbers - limit inferior and limit superior and limits of realse'uences - limit theorems - summability of con5ergence and di5ergence of series with non-negati5e terms - alternating series - conditional and absolute con5ergence - rearrangement ofseries - test for absolute con5ergence - summation by parts.

!ontinuity and deri5ati5e - the deri5ati5e of a real function - mean 5alue theorems Taylor


11/21

gradient= di5ergence= curl= directional deri5ati5e= unit normal to a surface.

%ector integration9

line surface and 5olume integrals; theorems of "auss= Stokes and "reen 4without proof8 -

simple problems.

ourier Series9

&,pansions of periodic function of period #N e,pansion of e5en and odd functions9 half rangeseries.

ourier transforms9

Infinite ourier transform 4!omple, form= no deri5ation8; sine and cosine transforms; simpleproperties of ourier Transforms; !on5olution theorem; Parse5al. %enkataraman 4/ational Publishing !o.8

#. &ngineering Mathematics %olume )9 P. >andasamy and others 4S. !hand and !o.8

). %ector Analysis9 Murray Spiegel 4Schaum Publishing company= /ew 1ork8

7. %ector Analysis9 P. $uraipandian and (a,mi $uraipanciian 4&merald Publishers8

Semester I% - Paper %III - Statics


orces9

Types of forces= Magnitude and direction of the resultant of the forces acting on a particle=(ami


12/21

+eference Books9

:. Mechanics-P.duraipandian and others= S.chand D !o.

#. Statics->.5iswanatha naik and M.S.>asi= &merald publishers.

). Statics-S./arayanan and others= S.chand and co.

7. Statics-A.%.$harmapadam= S.%iswanathan and co.

emester I% - Allied - Mathematics for Statistics II


Matri, theory - definition and types of matrices= Scalar= &lementary= Symmetric= Skewsymmetric= 2ermitian= Skew - 2ermitian= independent and unitary matrices - algebraicoperations on matrices and their properties - elementary transformations of matrices -determinant of matri, - definition of a row rank - column rank and rank of a matri, -determination of a rank of a matri,.

In5erse of a s'uare matri, - computation of the in5erse of the s'uare matri, - solution of lineare'uations - 2omogenous and non-homogeneous systems of e'uations - solutions space -

consistency and general solutions !ramer


13/21

Semester % - Paper I* - Algebraic Structures I


"roups 9-

/ormal subgroups; 2omomorphisms; Automorphisms; !ayley


14/21

Series of +eal /umbers 9-

!on5ergence and di5ergence; series with non-negati5e numbers; alternating series; conditionalcon5ergence and absolute con5ergence; tests for absolute con5ergence; series whose termsform a non-increasing se'uence; the class :#.

(imits and metric spaces 9-

(imit of a function on a real line; metric spaces; limits in metric spaces.

+eference Book 9-

:. Treatment as in LMethods of +eal AnalysisL 9 +ichard. +. "oldberg 4,ford and IB2Pubhshing !o.8

!h : - full.

!h # - Sections #.: - #.:6.

!h ) - Section ).: - ).7= ).= ).E= ).:6.

!h 7 - full

Semester % - Paper *I - $ynamics


>inematics9

kinematics of a particle= 5elocity= acceleration= relati5e 5elocity= angular 5elocity= /ewton


15/21

Moment of inertia of simple bodies= theorems of parallel and perpendicular a,es= moment ofinertia of triangular lamina= circular lamina= circular ring= right circular cone= sphere 4hollowand solid8

+eference Books9

:. Mechanics-P.$uraipandian and others= S.chand and co.

#. $ynamics->.%iswanatha naik and M.S.>asi= &merald publishers.

). $ynamics-A.%. $harmapadam= S.%iswanathan publishers.

Semester %I - Paper *III - Algebraic Structures


!redits9 7

%ector Spaces9

$efinition and e,amples= linear dependence and independence=dual spaces=inner product spaces

(inear Transformations9

Algebra of linear transformations= characteristic roots= matrices= canonical forms= triangularforms. Treatment and content as in LTopics In AlgebraL-l./.2erstein-3iley &astern ltd.

chapter 7-sections 7.:= 7.#= 7.)= 7.7.chapter -sections .:= .#= .)= .7.

+eference Books9

:. 0ni5ersity Algebra-/.S."opalakrishnan-/ew age international publications=3iley &asternltd.

#. irst course in Algebra-ohn B. raleigh=Addison 3esle.

). Te,t Book of Algebra-+.Balakrishnan and /.+amabadran=%ikas publishing !o.

7. Algebra-S.Arumugam /ew gamma publishing house=Palayarnkotta(

Semester %I - Paper *I% - +eal Analysis II


!redits9 7


16/21

!ontinuous functions on Metric Spaces

unctions continuous at a point on the real line=reformulation=functions continuous on a metricspace= open sets= closed sets= discontinuous functions on the real line.

!onnectedness completeness and compactness

More about open sets= connected sets=bounded sets and totally bounded sets= complete metricspaces= compact metric spaces= continuous functions on a compact metric space= continuity ofin5erse functions= uniform continuity.

!alculus

sets of measure Cero= definition of the +iemann integral= e,istence of the +iemannIntegral4statement only8 properties of +iemann integral= deri5ati5es= +olle


17/21

unctions of a comple, 5ariable= mappings= limits=theorems of limits without proof= continuity=deri5ati5es= differentiation formula=!auchy-+iemann e'uations= sufficient conditions= !auchy-+iemann e'uations in Polar form= analytic functions= harmonic functions.

Mappings by elementary functions9

linear functions=the function :O= linear fractional transformations= the functions w J Cn=wJe,p4O8= special linear fractional transformations.

Integrals9

definite integrals= contours= line integrals= !auchy-"oursat theorem4without proof8= !auchyintegral formula= deri5ati5es of analytic functions= ma,imum moduli of functions.

Series9

con5ergence of se'uences and series 4theorems without proofs8= Taylor


18/21

Book for +&&+&/!&9

:. $ifferential &'uations and !alculus of %ariations - (.&ls golts

#. $ifferential &'uations - $iwan and Agashe

). /umerical Analysis - Sear borough

Semester % - Application riented Subect I - Astronomy I

Spherical trignometry - celestial sphere and $iurnal motion-The &arth. Oones of earth=5ariations of $ay and night= $ip and Tuei light-Astronomical +efraction - "eocentric Paralla,->eplerumara5elu.

Semester % - Application riented Subect I - $iscrete Mathematics

Integers= Sets= Integers di5isibility of Integers= Mathematical induction= +epresentation ofPositi5e integers Boolean algebra and it.Sen and B.!.!hakraborthy boks and allied pri5ate (td.= >olkata

!hapter :!hapter 4omit .7 and .8!hapter E and

+eference Books9

:. $iscrete mathematics for computer scientists and mathematicians by .(. Mertt= Abraham>endel and T.P.Baker prentice-hall= India.

#. $iscrete mathematics for computer scientists by ohn Truss-Addison wesley.

). &lements of discrete mathematics= !.(.(iu= /ew 1ork Mcgraw-2ill= :?EE.

7. $iscrete mathematical structures with applications to computer science= .T.Tremblay and+.P. Manohar= /ew 1ork= Mcgraw-2ill= :?E@.

@. $iscrete mathematical structures= Bernard >olman= +obert !.Busby= Shron +oss= )rdedition=:??= Prentice hall of India= /ew $elhi.


19/21


20/21

Temperature= distribution in rectangular plates.(aplaceumara 5elu D Susheela >umara5elu.

Semester % - Application riented Subect I - "raph Theory I

"raphs= subgraphs= degree of a 5erte,= isomorphism of graphs=independent sets and co5erings=intersection graphs and line graphs= adacency and incidence matrices= operation on graphs=degree se'uence and graphic se'uences - simple problems.

!onnectedness= walks= trails= paths= components= bridge= block= connecti5ity - simple problems.&ulerian and hamiltonian graphs= trees - simple problems.

!ontent and treatment as in I/%ITATI/ T "+AP2 T2&+1 by S. Arumugam and S.+amachandran= /ew "amma Publishing 2ouse= Palayam >ottai.

!hapters9 :=# 4omit #.@8= )=7= @=.

+eference Books9

:. A first book at graph theory by ohn clark and $erek Allan 2olton=Allied publishes.

#. "raph theory by S.>umara5elu and Susheela >umara5elu= publishers authors !o.:#=!hidambara /agar= /agarkoil - #? 66#.


21/21

Semester %I - Application riented Subect II - "raph Theory II

Planarity; definition and properties= charaterisation of planar graphs= colourability= chromaticnumber and inde,= the fi5e colour theorem= four colour problem= chromatic polynomialsdirected graphs; definition and basic properties= paths and connectedness= digraphs and

matrices= tournaments= some application connector problem= shortest path problem= one waytraffic system; tra5elling sales man problem.

RTreatment as in in5itation to graph theory by S.Arumugam and S. +amachandran= chapters E4omit E.)8 = ?= :6.: to :6.@

Matching; Ma,imal matching= augmenting path= Bergiumara5elu

110873574 bsc maths subjects

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