Maths All Combined

8/13/2019 Maths All Combined

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MA 101 Mathematics-I L T P C

First Semester ( All Branch ) 3 1 0 8

Differential Calcls !

Successive differentiation, Leibnitzs theorem & its application. Indeterminate forms,

L. Hospitals Rules. Rolles Theorem, Lagranges ean value theorem, Ta!lors &

aclaurins theorems "ith Lagranges form of remainder for a function of one variable.

#urvature, radius & centre of curvature for #artesian and polar curves.. $artial

differentiation, change of variables, %ulers theorem & acobian.

Inte"ral Calcls !

Reduction 'ormulae. (s!mptotes for #artesian and polar curves. #urve tracing. (rea &

length of plane curves. )olume & surface area of solids of revolution *for #artesian and

polar curves+.

Differential #$ati%n

Solution of ordinar! differential e-uations of first order & of first degree Homogeneous

e-uation, %act differential e-uation, Integrating factors, Leibnitzs linear e-uation,

/ernoullis e-uation.

0ifferential e-uation of first order but of higher degree, #lairauts e-uation. 0ifferential

e-uations of second & higher order "ith constant coefficients. Homogeneous Linear

e-uations.

&eference B%%'s!

1. 0ifferential #alculus 0as & u2her3ee 4.5. 0hur & Sons $vt. Ltd.

6. Integral #alculus 0as & u2her3ee 4.5. 0hur & Sons $vt. Ltd.

7. %lementar! %ngineering athematics /.S. 8re"al 9hanna $ublisher

:. %ngineering athematics;II Santi 5ara!an S. #hand & #o.


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MA 10 Mathematics-II L T P C Sec%n Semester ( All Branch ) 3 1 0 8

Matrices !

Ran2 of a matri , %lementar! transformations, #onsistenc! and solutions of a s!stem of

linear e-uations b! matri methods .%igen values & eigen vectors. #ale!;Hamiltons

theorem & its applications.

S%li "e%metr* !

Straight lines. Shortest distance bet"een s2e" lines . Sphere , cone, c!linder and

conicoid .

Infinite + F%rier Series!#onvergence of infinite series & simple tests of convergence . 'ourier series in an!

interval .Half range sine & cosine series .

C%m,le Anal*sis

'unction of a comple variable, (nal!tic functions , #auch!;Reimann e-uations, #omple

line integral , #auch!s theorem , #auch!s Integral formula. Singularities and residues,

#auch!s Residue theorem and its application to evaluate real integrals.

Differential calcls !

Ta!lors & aclaurins theorems "ith Lagranges form of remainder for a function of t"o

variables, %pansions of functions of t"o variables . %rrors & approimations. %treme

values of functions of t"o & more variables

.

.

&eference B%%'s!

1. atrices 'ran2 (!res c 8ra" Hills

6. Solid 8eometr! Santi 5ara!an S. #hand & #o.

7. Laplace Transforms .R.Spiegel c 8ra" Hills

:. Higher %ngineering athematics /.S. 8re"al 9hanna $ublisher


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MA 01 Mathematics-III L T P C

Thir Semester ( All Branch ) 3 1 0 8

Inte"ral + .ect%r Calcls !

0ouble & triple integrals, /eta & 8amma functions . 0ifferentiation of vector functions of

scalar variables. 8radient of a scalar field , 0ivergence & #url of a vector field and their

properties, directional derivatives. Line & surface integrals. 8reens theorem , Sto2es

theorem & 8auss theorem both in vector & #artesian forms * statement onl!+ "ith

simple applications.

Inte"ral transf%rms !

La,lace transf%rm Transform of elementar! functions , Inverse Laplace transforms.

Solution of ordinar! differential e-uation using Laplace transform.

F%rier transf%rms 0efinition, 'ourier sine and cosine transforms, properties, relation

bet"een 'ourier and Laplace transforms.

/-transf%rm! 0efinition, standard z;transforms, properties, initial and final value

theorems, convolution theorem. Inverse z;transform, application to difference e-uation.

Partial Differential #$ati%n!

'ormation of partial differential e-uations *$0%+, Solution of $0% b! direct integration.

Lagranges linear e-uation . 5on;linear $0% of first order. ethod of separation of

variables. Heat, >ave & Laplaces e-uations *T"o dimensional $olar & #artesian #o;

ordinates+.

&eference B%%'s!

1.)ector (nal!sis 'ran2 (!res c 8ra" Hills

6.(dvanced athematical (nal!sis ali2 & (rrora S. #hand & #o.

7. (dvanced 0ifferential %-uations .0.Rai Singhani!a S. #hand & #o.

:. #omple (nal!sis. .R.Spiegel. Schuams out line Series


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MA 0 Pr%ailit* The%r* + St%chastic Pr%cesses L TP C

Thir Semester ( #T + CS Branch ) 3 10 8

Pr%ailit* !Introduction, 3oint probabilit!, conditional probabilit! , total probabilit!, /a!es theorem ,multiple events, independent events.

&an%m .ariale!

Introduction, discrete and continuous random variables, distribution function , mass ? densit!function , /inomial, $oisson , 4niform, %ponential, 8aussian and 8amma random variables,conditional distribution and densit! function, function of a random variable .

/ivariate distributions, 3oint distribution and densit!, marginal distribution and densit!functions, conditional distribution and densit!, statistical independence, distribution anddensit! of a sum of random variables.

,erati%n %n %ne &an%m 2ariale!

%pected value of a random variable , conditional epected value , moments about theorigin , central moments , moment generating function, variance , s2e"ness and9urtosis,covariance, correlation and regression, monotonic and non;monotonictransformation of a random variable *both discrete and continuous+.

St%chastic Pr%cesses!

0efinition of a stochastic process , classification of states, Random "al2, ar2ov chains,poisson process, >iener process ,stationar! and independence, distribution and densit!functions, statistical independence,9olmogorov e-uations, first order stationar! processes,second order and "ide sense stationar!, time averages and ergodicit! , correlation functions,covariance function.

S,ectral characteristics %f ran%m ,r%cesses!

$o"er densit! spectrum and its properties, band"idth of the po"er densit! spectrum,relationship bet"een po"er spectrum and autocorrelation function, cross po"er spectraldensit! and its properties.

%ise!

>hite 5oise , shot noise, thermal noise, noise e-uivalent band"idth.

&eference B%%'s!1. (n Introduction to $robabilit! Theor! and its (pplications *)ol. 1 & II+;> 'eller *ohn>ile! & Sons+.

6. $robabilit! , Random )ariables & Stochastic processes $apoulis c8ra" Hill7. $robabilit! & Stochastic processes #.>.Helstrom cillan, 5e" @or2 for engineers:. $robabilit! & Random processes (.Leon;8arcia (ddison >isle! for electrical engineers 'eller *ohn>ile! & Sons+.


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MA 203 Discrete Mathematics L T P

C

F%rth Semester ( CS Branch ) 3 1

0 8

B%%lean al"era!- /inar! relation , e-uivalence relation , $artial order

relations, $B;set, Totall! ordered set, aimal and inimal elements. >ell

ordered set. Lattice, bounded lattices, sublattice, distributive lattice, modular

lattice, irreducible elements, complemented lattice.

/oolean (lgebra, /oolean functions & epression , minimization of /oolean

functions & epressions.*(lgebraic method and 9arnaugh map method+

Logic gates ; Introduction, 0esign of digital circuits and application of

/oolean algebra in s"itching circuits.

Graph theory:-. Introduction, Basic definition, incidence and degree, adjacency,

paths and cycles, matrix representation of graphs( directed and non-directed).

Digraphs. Trees.

Mathematical L%"ic!

Statement Calcls- sentential c%nnecti2es4 Trth tales4 L%"ical

e$i2alence4 Decti%n the%rem5

Preicate Calcls- S*m%li6in" e2er*a* lan"a"e54 2aliit* an

c%nse$ence5

M%ern Al"era!

(lgebraic structures, Semi group, onoid, 8roup, #!clic group, Subgroup,

5ormal subgroup, Cuotient group, Homomorphism of groups.

Ring, Integral domain, 'ield. )ector space , Linear dependence &

independence . /asis & 0imension.

Recurrence relations & 8enerating functions.

&eference B%%'s!

1. Set Theor! and Logic R.R Stoll. S. #hand.&

#o.


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6. 0iscrete athematical Structures 8. S. Rao 5e" age

International

7.0iscrete athematics and Structures S. /algupta Lami

$ublications

:. odern (lgebra Herstein 5e" age

International


7/14

MA 07 Mathematics-I. L T

P C

F%rth Semester ( C# + M# Branch ) 1

0

Statistics !

easures of central tendenc!, dispersion, moments, s2e"ness & 2urtosis.

$robabilit! densit! function, distribution function, /inomial, $oisson & 5ormal

distributions.

#urve fitting; ethod of Least s-uares, fitting of straight line & parabola.

#orrelation & Regression; determination of correlation & regression

coefficients & determination of lines of regression.

merical Anal*sis!

'inite differences, Interpolation & etrapolation. 5e"tons for"ard & bac2"ard

formulae, Lagranges formula & 5e"tons divided difference formula for

une-ual intervals.*statements & applications of the formulae onl!+

5umerical differentiation & integration, Trapezoidal rule, Simpsons 1?7 rd &

7?Dthrules.

5umerical solution of transcendental & algebraic e-uations; ethod of

Iteration & 5e"ton;Raphson method.

S%lti%n %f s*stem %f linear e$ati%ns !

8aussian elimination method, 8auss Seidal method, L4 decomposition &

#holes2! decomposition.& their application in solving s!stem of linear

e-uations, matri inversion b! 8auss;ordan method .

&eference B%%'s !

15 5umerical athematical (nal!sis ames / Scarborough Bford &

I/H $ublishing

6. 5umerical (nal!sis /.S. 8re"al 9hanna

$ublishers

7. 'inite 0ifferences H.#. Seena S. #hand

& #o.


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& 5umerical (nal!sis

:. $robabilit! & Statistics .R. Spiegel c 8ra"

Hill


9/14

1. $robabilit! & Statistics .R. Spiegel c 8ra" Hill

6. athematical Statistics 9apoor & Seena S.#hand.

MA 301 merical Meth%s + L TP C

C%m,tati%ns Fifth Semester ( #T + CS Branch ) 10

merical Anal*sis!

'inite differences, Interpolation & etrapolation. 5e"tons for"ard & bac2"ard

formulae, Lagranges formula & 5e"tons divided difference formula forune-ual intervals.*statements & applications of the formulae onl!+, evaluationof functions , minimization & maimization of functions .

5umerical differentiation & integration, 5e"tons general -uadrature formula,Trapezoidal rule, Simpsons 1?7rd & 7?Dthrules.

merical s%lti%n %f transcenental + al"eraic e$ati%ns!; ethod ofIteration & 5e"ton;Raphson method.

merical S%lti%n %f a s*stem %f linear e$ati%ns !

8aussian elimination method "ith pivoting strategies , 8auss;ordan method

& 8auss;Seidel method. L4 decomposition & #holes2! decomposition.&

their application in solving s!stem of linear e-uations. atri inversion b!

8auss;ordan method .

merical s%lti%n %f %rinar* ifferential e$ati%ns :ith initial 2ale!

Ta!lors series method , %ulers & modified %ulers method , Runge;9uttamethod of :thorder.

&eference B%%'s !

1. 5umerical athematical (nal!sis ames / Scarborough Bford &I/H $ublishing

6. 5umerical (nal!sis /.S. 8re"al 9hanna$ublishers


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7. 'inite 0ifferences H.#. Seena S.#hand & #o. & 5umerical (nal!sis.

:. %ngineering athematics /ali & I!engar Lami

$ublications Ltd.

MA 771 M%ern Al"era L T PC

#i"hth Semester (#lecti2e ;III4 ,en ) 3 0 0

P%sets + Lattices !

$artial order relations, $o;set, Lattices & /oolean algebra.


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MA 77 Fncti%nal Anal*sis L T PC

#i"hth Semester (#lecti2e ;III4 ,en) 3 0 0

Matric S,ace !

0efinition and %amples of metric space . Bpen Sphere, Bpen Set & #losedSet. #onvergence of se-uences, #auch! se-uence, #omplete etric Spaces,Se-uentiall! #ompact etric Space, #ontinuous mappings.

T%,%l%"ical S,ace !

0efinition and eamples, Trivial and non;trivial topolog!, #ofinite topolog!,4sual Topolog! "ith special reference to R. #ontinuit! and homeomorphism.

Fncti%nal Anal*sis !Linear space, subspace, basis, dimension, normed linear space, /anach space,continuous linear transformation, #on3ugate space, Inner product spaces, Hillbestspace, Brthogenalit!, orthonormal sets, #auch!s Sch"artzs ine-ualit!, /essels ine-ualit!.

Linear operators, Self ad3oint operator, normal and unitar! operators, $ro3ections,Spectrum of an operator. The spectral theorem.

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF&eference B%%'s!

1. Introduction to Topolog! and

odern (nal!sis

Simmon 8.'. Tata c8ra" Hill

6. 'unctional (nal!sis /.9. Lahiri >orld $ress $vt. Ltd.7. 8eneral Topolog! Lipschutz Schaum Butline Series, c8ra"

Hill /oo2 #ompan!.


12/14

MA 443 Mathematical Modeling L T P C #i"hth Semester (#lecti2e ;III4 ,en ) 3 00 athematical modelling techni-ues, classification "ith simple illustration.

athematical modelling through ordinar! differential e-uations.

odelling through difference e-uations.

odelling through partial differential e-uations.

odelling through integral and differential ; difference e-uations.

odelling through calculus of variations and d!namic programming.

odelling through mathematical programming, maimum principle and

maimum entrop! principle.

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&eference B%%'s!

1. athematical odelling .5. 9apur 5e" age International6. (dvanced %ngineering

athematics

%. 9re!szig 5e" age International

7. Higher %ngineering athematics /.S. 8re"al 9hanna $ublishers

:. Bperations Research, ethodsand $ractice

ile! %astern

acmillan India

Limited


13/14

MA 777 ,erati%n &esearch L T PC #i"hth Semester (#lecti2e ;III4 ,en ) 3 0 0

Intr%cti%n t% ,erati%n &esearch (5&)!eaning of B.R. $rinciples of odelling. 'eatures and $hases of B.R.

Linear Pr%"rammin"!Introduction, 'ormulation of Linear $rogramming $roblems *L.$.$+, 8raphicalsolution procedure. Idea of #onve set & conve combination of t"o points,'undamental Theorem of L.$.$. *proof not re-uired +. Solutions of L.$.$. Simpleethod . /ig; methods.

Trans,%rtati%n Pr%lems(T5P)!Introduction. athematical formulation. 0efinitions of /alanced, 4nbalanced T. $.Rules to find initial /asic feasible Solution */.'.S+ of a T.$.; 5orth >est #orner Rule,)ogels approimation ethod. Solution algorithm of T.$. Solution techni-ue forunbalancedT. $. Resolution of degenerac!. %amples.

Assi"nment Pr%lems(A5P)!Introduction , athematical 'ormulation. Reduction theorem * proof not re-uired+.0efinitions of /alanced and 4nbalanced (.$. Hungarian (lgorithm for solving (.$.Solution techni-ue for unbalanced (.$. %amples.

Se$encin" Pr%lems!Introduction. 0efinition. Solution of Se-uencing problems. $rocessing n 3obs through6 machines, 6 3obs through m machines * 8raphical method+, $rocessing n 3obsthrough m machines.Inte"er Pr%"rammin" Pr%lems(I5P5P)!Introduction. $ure and mied integer programming problems. 8omor!s #utting$lane techni-ue for solving I.$.$. %amples.

&eference B%%'!

1.Bperations Research 9anti S"arup Sultan #hand &Sons

6.Bperations Research S.0. Sharma 9hanna$ublishers7.Bperations Research .9. Sharma acillan IndiaLtd:.Bperations Research Hira and 8upta Sultan #hand &Sons


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Maths All Combined

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