Goyal's Mathgoyalsmath.com/BA-BSC-Part1.pdf · Goyal's Math @ B.Sc.-Ist year (Ist Semester) MAT}IEM.dTICS FOR SESSION (2013_ Ltt, 2014_tS, 20tS_16) PAPER-II: CALCULUS Maxirnum Marks:

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Nlaxirnum Marlrs: 50

I\{inimum Pass lVlark z 35 "/oTime allowed: 3 Hrs.

Lectures to be delivered: S periods (of 45 rhinutes

E.Sc.-Ist )rear ( Ist Semester)

MATIIEIIIA.TICS

FoR sEssroN ( ?pL312014_8, 201s-16)

PAPER-I: DIFFERENTIAL EQUATIONS

duration) per week

.--;r"f5qi 12

University Exam: 40

Internal Assessment: l0

Instructions for paper-setters \-t-:

The question paper will consist of tlree sections A, B ancl c. Each of sections A anrl B r.vill havefour questions from the respective sections of the syllabus and section c will consist of onecompulsory question having teu short auswel' type questions covering tire enr.ire syllabusunifonnly. AII questions will cany equal mnrks

'Instructions for the candidates

Candidates are required to attempt five qtrestir.rns in all selectilg tr.vo questions fronr each seclionfl and B and compulsory question of seotir-',n (1. All questions will carry equal marl<s.

Section - A^

First ordet' clifferential equations : orclei aird degtee of a cliffer.ential equation, separablediffere,tial equations,.I{omogenbous ilifferentiai equations, equations r:educible.to llo6ogeno,sdilferential equations Exact differential equations. Linear clifferential eq*ations a.d equati,.,nsretlucible to linear differential equations. :;' .

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Ashwani Goyal’s Tutorial

Copyright © 2013 GoyalsMath.com .All rights reserved.

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I{igher order differential eguations : Solution of Linear homogeneous and non-homogeneousgi$rEFEntiel cquatisnE sf highE[ BroE[ lxith GBBuaRt o0efnEiEmE ano urlm uadablE E0EfflciEnE"

Wronskian, method of Variation of Parameters, method of Undetermined Coefficients.

Section - B

Differential operator method. Linear non-homogeneous differential equations with variable

coelfrcients, Eu)er's Cauchy method.

Sedes solution of Differential equation: Regular point, ordiary point, power Series method,

forbinious method, Bessel, Legendre arrd hypergeometric eqtgtiaon..B6ssel,,.Le$endre and

liypergeometric functions and their properties. Couvergerice, recurrence relations, orthogonality,

Rodrigue's fonnula.

BOOKS RECOMMENDED

1' H.T.H. Piaggio : An Elementry Tleatise on Differential equations . : Barman Press.

2 R K. Jain and S.R.K. Iyengar:Advanced Engineering Mathernatics,Narosa publishing House.

3. Zafar Ahsan: Differential Equations and Their Applications, Prentice-Hall of India Pvt. Ltd.,i

New Delhi-Second edition

I. N. Sneddon : Elements of Partial Differentiat Equations, Mc Graw Hill Book Co.

Rai Singhania : Ordinary and Parlial Differeritial Ecluations" , S.Chand &Company,New

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Delhi,

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@B.Sc.-Ist year (Ist Semester)

MAT}IEM.dTICS

FOR SESSION (2013_ Ltt, 2014_tS, 20tS_16)

PAPER-II: CALCULUS

Maxirnum Marks: 50

Minimum pass Mark :35 o/o

Time allowed: 3 Hrs.

Lectures to be derivered: 5 periods (of 45 min,t'es duration) n". .,o""rl

. Instructions for paper_oetters

The question paper will consist of tfuee sections A, B and c. Each of sections A and B w,r havefour questions from the respective sections of the syrrabus ;;.;;;;;;,"nsist of onecompulsory question having ten shortu,iformly.eriqu"rtio*ffi;;"*;J]t tvn" questions covering the entire svllabus

Instructions for the candidates

candidates are required to-attempt five questions in all selecting two questions fi.om each sectionA and B and compursorv qr*i",i"r s".ri";-c. ;ii qrlrr,"r, wil camy equar mar.ks

Section_A

successive differentiation Asymptotes, Murtiple points, Tests for concavity and convexity,poi.ts of i,flexion' Tracing of curves in ca'tesian, ,"rrr",rt" and polar forms. curvature,radius crf curuature, centre of curvature.

3

University Exam: 40

Internal Assessment; 10

Section-B

Integration of hyperbolic eind inverse hyperbolicdefinite integral to find quadrature, length of an

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nfunctibns, Reduction Formulae, application ofarc, Improper integrals and their convergence,

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Books Recommended:l; Calculus and /rnalylie Georneky, Tlrornas and Finneg Ninth$dition.z. Mathematic"l Ar"iiJr, il;iii1J,iotrr"

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B.Sc .-Ist year (Ist Semester)

MATHEIvIATnCs

F OR sESSroN ( 2073_74, 2014-15,2015-16)

PAPER-II: CO0RDINATE GEOMETRY

Maximum.Marks: 50

Mirrimum pass Marks :35 yoTime allowed: 3 Hrs.

Universify Exam: 40

Inter nal Assessment: 10

Lectures to be delivered: 5 periods (of 45 minufes,duration) r_ffi

Instructions for paper_settersThe question paper will consist of tluee sectio,s

^, ; "ra:. Each of secrions A and B w,r have

::,r#1*ilJT";:"'-T',;:.i,"* ";;;ffi ancr section c w,r consistoroneu,ifonnlv; AIt quesrions will carry

"rJ#il:t t*" questions coveting the enti'e ,",;;;

Instructions for the candidatesCandidates are reouired tn a++-*-. cA ;il;;il:ffiXi::iJ"d"::,il1t#:'.|ll"i:,,,.11 a, serecting.rwo quesrions rrom eacrr sectionItron C. All question, *itt

"urry "Orri*rrO,Transfounation of axis srri*i-^ ^r , . Section-A

*: :*k H;:",;::#; ;:***m::, x i. #f" :: :ff Hr:Parabola: Pole and Dolar ^oi* ^r.

;J:.:: _ ;;,i ff :,fl ;:,::-::: ffi il::, H.,";.# :ff l :" ;:H:;

Ellipse: properties of ellipse, paramekic,"l:"-::: : !'crrord joining rrvo points on erlipse. r,."::::""T:iTJ#;:T;ffi:.,,,#:::,r:.,::ffi::

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uud conjugate diameter (-^-^__, ^Hyperbora: ,roo"n: "1':*n Points and ih geornetricar properties.

rrvperbora, -,*i;J:[ffi:]|',"; J::::::- .,u";;", parametric rspresenration ornornrals' - ': ' --'4ugate hyperbola, rectangular hyperbolq tangents and

Pvt. Ltd.

hf; tI :$ioElementarY rreatise

"" ;;ordinate Geomeky of Three Dimesions, Macmillanr- I t -, , .,.. -,r., .

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Sectiorr -BHomogeneous and non-homogeneous partial differential equations with constant coefficients.

One dimention Wave and Heat Equation. Two climentionatr Laplace equation by separation of

variable method and D'Alernbert's solution of wave e{uation.

BOOKS RECOMMENDED

1. H.T.H. Piaggio .: An Elementry iieatise on Differential equations, Barman Press.

2. R.K.Jain and S.R.K.Iyengar : Advanced Engineering Matlrematics,NarosaPublishing House.

3. Zafar Ahsan: Differential Equations. and Their Applications, f,rdntice-Hatl of In{!a Pvt. Ltd.New Delhi-second edition

4. I. N. Sneddon : Elements of Partial Differential Equations; Mc Graw Hill Book Co.

5 Rai Singhania: Ordinary'and'Partial Differential Equations" , S.Chand &Company,NewDelhi

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B.Sc -Ist year (IInrI Senrester)

MATIIE]VIATICS

FoR sEssION ( 201s_74, ztotl_ts,20r5_16)

pApER_V: Algebra_X

I\{aximum l4arks: 50Mininrum pass Marks :35 yoTirne allowed: 3 Hrs.

' tr ectures to be delivered: S periods (of 45 minutes

University Exam: 40Internal Assessment: I0

duration) per week

InstrurThe question paper ' '

-ctions for paper-setters

ffi*'TJ:;:i""':;T:':;:"""""s A' B a,d c

l:':"".tio,s A a,d B wirrrrave

u n i rorn' r v a,il."ili'ffi --; ;:* ff;;

ff l'

,,H:: :ffi #' ;;:: ffi ;:

Instructions for the candidates

;ilttffi ::ffi xi:::,ff I,",iliJ*'J":ffi,J,3:Iir;Hil;il:::i.:,,"nsnorn,irr cauy .or;i;;i:each secrion

Secfiotr _ r{Ilermitian, Skew_I{

nratrices. Inverse "rt]]""'"t

orthogonal ancl Unitary nrar

column *r"rr, o* a mafuix using Gar t,":-u, .Elen1g111alr

operatfo, on

th.e characterr*,.

"r."ank,

colurr, *ru, -"t Jotdan Nfethod'

Diagonariza,,on,

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",rirrr,^,_J,ir"."1,":::::.",.,*"1'"";3: ,ffi,;,:: ve*or-s n'c

ru. consister,r; ";; :l:.]t'

fbr speciar t.r,ire or. nrarrice.s,

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polynourial, thnformation ofBiquadratic equations and,their:

and inverse circular ,,functions,

li I :::ltl:.;:

@Seetion-B

Relations between roots r and,,:doefficiens of a general

equation.Descartesn mle qf,qi ,#orutien of cubic "f,uutionr,

solution. De Moiwe's theorem and its application, Dhecthyperbolic and'logarithmic func,tions. summation of series...

lo

Boohs Recommendedl1. Linear Algebra by Scharn outline Series.2. Trisonol"t l uv s-L,i"""t. ililik,i una

"o*p*v London.:3, TextrBook of Algebra by Chandrika prasad.

! -.... ,:,. .., . _r.t i.t i,

.. :. *,.,rrajii--;j:r..-.j ..! |]' .rij..:,nr ::.,1: 'l]1. .',. '];

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B.Sc -Ist Year (IInd Semester)

MATHEI\{ATICS

FOR SESSION ( 2013-14, 2014-15,2015-16)

PAPER-VI: Analytic Geometry

per week

University Exarn: 40

Internal Assessment: 10

Maximum Marks: 50

Minimum Pass Marks z3S oh ' '

Time allowed: 3 Hrs.i

Lectures to be delivered: 5 periods (of 45 minutes duration)

Instructiong for paper_setters

The question paper will consist of three sections A, B and C. Each of sections A and B will havefour questions fi'om the respective sections of the syllabus and section c will consist of onecompulsory question having ten shoft allswer type questions covering the eltire syllabusunifonnly. All questions will carry equal rnarks.

Instrucfions for the canclidates

Candidates are required to attempt five questions in all selecting two questions fiom each sectiouA and B and cbmpulsory question of section c. All qr".tr"r.-*ill carry equal marks.Section - A

The plane: General fonn, Normal form, Intercept form, Reduction of the general form to noruralform

' Equation of plane through thlee points, Angle between two planes, parallel plan6i

Perperrdicular distance'of a point from the planes, Pair of the planes, Area of a triangle a,dVolunre of a tetrahedroh. iThe straight line: Equation of a line in ge,eral form, symmetric form, two point form,

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Goyal

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Goyal

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Documents

Goyal's Mathgoyalsmath.com/BA-BSC-Part1.pdf · Goyal's Math @ B.Sc.-Ist year (Ist Semester) MAT}IEM.dTICS FOR SESSION (2013_ Ltt, 2014_tS, 20tS_16) PAPER-II: CALCULUS Maxirnum Marks: