Mathematics - Department of Higher Education

mPp f’k{kk foHkkx] ee-iz- 'kklu ch-,llh@ch-,- d{kkvksa ds fy;s ,dy Á’ui= Á.kkyh lsesLVj ds vuqlkj ikB~;Øe dsUnzh; v/;;u e.My }kjk vuq'kaflr rFkk e-iz- ds jkT;iky }kjk vuqeksfnr Department of Higher Education , Govt. of M.P. B.Sc./ B.A. Single Paper System Semester wise syllabus As Recommended by central Board of studies and Approved by the Governor of M.P.

Name of Paper

Theory

Minimum Passing

(M.M.)

C.C.E. (M.M.)

Marks in Theory

Minimum Passing Marks in C.C.E.

Practical

8

-----

Minimum Passing

Total

MM Marks

Compulsory

Calculus, Differential Equation ,and Mechanics

dyu] vody lehdj.k] ,o

125

42

25

-----

150

;kaf=dh Note: There are three sections in the question paper. All questions from each section will be compulsory. Section –A (20 marks.) will contain 10 objective type questions , two from each unit, with the weightage of 2 marks. Section –B (35 marks.) will contain 5 short answer type questions (each having internal choice), one from each unit having 7 marks. Section –C (70 marks.) will contain 5 long answer type questions (each having internal choice), one from each unit, having 14 marks. There should be at least 9 teaching periods per week.

mPp f’k{kk foHkkx] ee-iz- 'kklu ch-,llh-@ch-,- d{kkvksa ds fy;s ,dy Á’ui= Á.kkyh lsesLVj ds vuqlkj ikB~;Øe dsUnzh; v/;;u e.My }kjk vuq'kaflr rFkk e-iz- ds jkT;iky }kjk vuqeksfnr Department of Higher Education , Govt. of M.P. B.Sc./ B.A. Single Paper System Semester wise syllabus As Recommended by central Board of studies and Approved by the Governor of M.P.

Lk=~ @ Session : 2012-13 vf/kdre vad@Max. Marks : 125 Class/ d{kk

:

B.Sc. /B.A.

Semester/ lsesLVj

:

III

Title of subject Group / fo"k; lewg dk 'kh"kZd

:

Mathematics

Title / 'kh"kZd

:

Calculus, Differential Equation and Mechanics.

Compulsory / vfuok;Z ;k Optional /oSdfYid

:

Compulsory

: Particulars/ fooj.k :

Unit -1

Definition of a sequence. Theorems on limits of sequences. Bounded and monotonic sequences. Cauchy’s convergence criterion . Series of non-negative terms. Comparison test, Cauchy’s integral test, Ratio test. Raabe’s test ,logarithmic test. Leibnitz’s theorem. Absolute and conditional convergence.

.

bdkbZ&1

Unit -2

bdkbZ&2

Unit -3

vuqØe dh ifjHkk"kk] vuqØeksa dh lhekvksa ij ize; s ] ifjc) ,oa ,dfn"V vuqØe] dWk’kh ds vfHklj.k dk ekunaMA v_.kkRed inksa dh Js.kh] rqyuk ijh{k.k] dkW’kh dk lekdy ijh{k.k] vuqikr ijh{k.k] jkWch dk ijh{k.k] y?kqxf.kdh; ijh{k.kA fycuht dk ize; s A fujis{k ,oa lkis{k vfHklj.k A Continuity of functions of one variable , sequential continuity. Properties of continuous functions. Uniform continuity. Chain rule of differentiability. Mean value theorems and their geometrical interpretations. Darboux’s intermediate value theorem for derivatives. Limit and continuity of functions of two variables.

,d pj ds Qyuksa dk lkarR;] vuqØe.kh; lkarR;] larr Qyuksa ds xq.k/keZ] ,dleku lkrR;A vodyuh;rk dk J`[a kyk dk fu;e] ek/;eku ize; s ,oa mudk T;kferh; vFkZ] vodyu ds fy, MkWjckDl dk ek/;eku ize; s A nks pjksa ds Qyuks dh lhek ,oa lkrR;A Series Solution of Differential Equations-Power series Method, Bessel’s Equation Bessel’s function and its properties, recurrence and generating relations. Legendre’s

Equation, Legendre’s function and its properties, recurrence and generating relations.

vody lehdj.kksa dh Js.kh] gy&?kkr Js.kh fof/k] csly dk lehdj.k] csly dk Qyu ,oa mlds xq.k/keZ] iqujkxeu ,oa tud lac/a kA yhtsUMj dk lehdj.k] yhtsUMj dk Qyu ,oa mlds xq.k/keZ] iqujkxeu ,oa tud lac/a kA

bdkbZ&3

Laplace transformations, Linearity of the Laplace transformation, Existence theorem of Laplace transforms, Laplace transforms of derivatives and integrals. Shifting theorem . Differentiation and integration of transforms. Inverse Laplace transforms, Convolution theorem. Applications of Laplace transformation in solving linear differential equations with constant coefficients.

Unit -4

ykIykl :ikarj.k] ykIykl :ikarj.kkas dh ykafcdrk] ykIykl :ikarj.kkasa dk vfLrRo ize; s ] vodyksa ,oa lekdyksa ds ykIykl :ikarj.k] laoyu ize; s A:ikarj.kksa dk vodyu ,oa lekdyu] izfrykse ykIykl :ikraj.k] laoyu vpj xq.kaakdksa ds jSf[kd vody lehdj.kksa dks gy djus esa ykIykl :ikarj.kks ds vuqiz;ksxA

bdkbZ&4

Unit -5

Analytical conditions of equilibrium of Coplanar forces. Catenary. Forces in three dimensions. Velocities and accelerations along Radial and transverse direction

bdkbZ&5

leryh; cyks ds larqyu dk fo’ys"k.kkRed izfrca/kA jaTtqdk f=foeh; cy] f=Tth; ,oa vuqizLFk fn’kk ds vuqfn’k osx ,oa Roj.k A

Text Books : 1. 2. 3. 4. 5. 6. 7

R.R. Goldberg, Real Analysis, I.B.H. Publishing Co. New Delhi, 1970. Gorakh Prasad, Integral Calculus, Pothishala Pvt. Ltd. Allahabad. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & sons, 1999. R.V. Churchill, Fourier series and boundary value problem. S.L. Loney, Statics, Macmillan & Co. London S.L. Loney, An Elementary Treatise on the Dynamics of a Particle and of Rigid Bodies, Cambridge Uni. Press 1956. e-iz- fgUnh xzFa k vdkneh dh iqLrdsa A

Reference Books: 1. 2. 3. 4. 5.

T.M. Apostol Mathematical Analysis Narosa Publishing House New Delhi 1985. Murray R.Spiegel, Theory and Problems of Advanced Calculus, Schaum Publishing Co. New York. N. Piskunov, Differential and Integral Calculus, Peace Publishers, Moscow. S.C. Malik, Mathematical Analysis, Wiley Eastern Ltd. New Delhi. R.S. Verma, A Text Book on Statics, Pothishala Pvt. Ltd., Allahabad

mPp f’k{kk foHkkx] ee-iz- 'kklu ch-,llh@ch-,- d{kkvksa ds fy;s ,dy Á’ui= Á.kkyh lsesLVj ds vuqlkj ikB~;Øe dsUnzh; v/;;u e.My }kjk vuq'kaflr rFkk e-iz- ds jkT;iky }kjk vuqeksfnr Department of Higher Education, Govt. of M.P. B.Sc./ B.A. Single Paper System Semester wise syllabus As Recommended by central Board of studies and Approved by the Governor of M.P.

Name of Paper

Theory

Mini Passing

(M.M.)

Marks in Theory.

125

42

C.C.E.

Mini Passing Marks in C.C.E.

25

8

Practical Mini Passing MM M.

Total

Compulsory

Advanced Calculus, Partial Differential Equations, Complex and Abstract Algebra.

mPPk dyu] vkf'kad vody lehdj.k] lfEeJ fo’ys"k.k

,o

-----

-----

150

vewrZ chtxf.kr

Note: There are three sections in the question paper. All questions from each section will be compulsory. Section –A (20 marks.) will contain 10 objective type questions , two from each unit, with the weightage of 2 marks. Section –B (35 marks.) will contain 5 short answer type questions (each having internal choice), one from each unit having 7 marks. Section –C (70 marks.) will contain 5 long answer type questions (each having internal choice), one from each unit, having 14 marks. There should be at least 9 teaching periods per week.



:

B.Sc. /B.A.

Semester/ lsesLVj

:

IV


:

Mathematics

Title / 'kh"kZd

:

Advanced Calculus, Partial Differential Equations, Complex Analysis and Abstract Algebra.


:

Compulsory


Unit -1

Partial differentiation. Change of variables. Euler’s Theorem on homogeneous function, Taylor’s theorem for functions of two variables. Jacobians, Envelopes, Evolutes.

bdkbZ&1

vkaf'kd vodyu] pjksa dk ifjorZu] le?kkr Qyuksa ij vk;yj dk ize; s ] nks pjksa ds Qyuksa ds fy, Vsyj dk ize; s Atsdksfc;u] vUokyksih] dsUnzt A

Unit -2

Maxima, minima and saddle points of functions of two variables. Beta and Gamma functions. Double and triple integrals. Dirichlet’s integrals.

bdkbZ&2 Unit -3

nks pjksa ds Qyuksa dk mfPp"B] fufEu"B ,oa lsMy fcUnqA chVk ,oa xkek QyuA f}’k% ,oa f=&lekdyu] fMfjDys dk lekdyA Partial Differential equations of the first order. Lagrange’s solution. Some special types of equations which can be solved easily by methods other than general methods. Charpit’s general method of solution, Partial differential equations of second and higher orders. Homogeneous and non- Homogeneous equations with constant coefficients. Partial differential equations reducible to equations with constant coefficients.

bdkbZ bdkbZ&3

Unit -4

izFke dksfV ds vkaf’kd vody lehdj.k] ysxzkt a dk gy] dqN fof’k"V izdkj ds lehdj.k ftUgsa O;kid fof/k ds vykok ljy fof/k ls gy fd;k tk ldsA gy ds fy, pkjfiV dh O;kid fof/k] f}rh; ,oa mPprj dksfV ds vkaf’kd vody lehdj.k] vpj xq.kakdksa ds le?kkrh; ,oa vle?kkrh; lehdj.k] vkaf’kd vody lehdj.k tks vpj xq.kkadksa okys lehdj.kksa esa ifjorZuh; gSA Complex numbers as ordered pairs. Geometric representation of Complex numbers, Continuity and differentiability of Complex functions. Analytical function, Cauchy Riemann equation, Harmonic function, Mobius transformations, fixed point, cross ratio.

bdkbZ&4

dzfer ;qXe ds :Ik esa lfEeJ la[;k;s]a lfEeJ la[;kvksa dh T;kferh; O;k[;k] lfEeJ Qyuksa dk lkarR; ,oa vodyuh;rkA oS’ysf"kd Qyu] dkS’kh jheku lehdj.k] izlaoknh Qyu] eksfc;l :ikarj.k] fLFkj fcUnq] fr;Zd vuqikrA

Unit -5

Group-Automorphisms, inner automorphism. Group of Automorphism, Conjugacy relation and centraliser. Normaliser. Counting principle and the class equation of a finite group. Cauchy’s theorem for finite abelian groups and non abelian groups. Ring homomorphism. Ideals and Quotient Rings

bdkbZ&5

Lewg&Lokdkfjrk ¼Lole:irk½] vakrj Lokdkfjrk] Lokdkfjrkvksa dk lewg] la;qXerk lac/a k ,oa dsUnzh;dkjd] izlkekU;d] x.kuk fl)kar ,oa ifjfer lewg dk oxZ lehdj.kA ifjfer vkcsyh ,oa vu&vkcsyh lewgksa ds fy;s dkS’kh ize; s A oy; lekdkfjrk] xq.ktkoyh ,oa foHkkx oy;]

Text Books : 1. 2. 3. 4. 5. 6

Gorakh Prasad, Differential Calculus, Pothishala Pvt. Ltd. Allahabad. Gorakh Prasad, Integral Calculus, Pothishala Pvt. Ltd. Allahabad. I.N. Sneddon, Elemets of partial Differential equatiins Mc graw Hill, Co. 1988 Shanti Narayan, Theory of Functions of a Complex Variable, S. Chand & Co., New Delhi. I. N. Herstein Topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975. e-iz- fgUnh xzFa k vdkneh dh iqLrdsa A

Reference Books: 1. T.M. Apostol, Mathematical Analysis Narosa Publishing House, New Delhi 1985 2. Murray R. Spiegel, Theory and Problems of Advanced Calculus, Schaum Publishing o., New York 3. N. Piskunov , Differential and Integral Calculus, Peace Publishers, Moscow. 4. S.C. Malik, Mathematical Analysis, Wiley Eastern Ltd., New Delhi. 5. N. Jacobson, Basis Algebra, Vols, I & II. W.H. Freeman, 1980 (also published by Hindustan Publishing Company.) 6. Shanti Narayan, A Text Book of Modern Abstract Algebra, S. Chand & Co. New Delhi


Name of Paper

Theory

Minimum Passing

C.C.E.

(M.M.) Marks in Theory

Minimum Passing Marks in

Practical

Minimum Passing

Total

MM Marks

C.C.E.

Compulsory

Real Analysis, Linear Algebra and Discrete Mathematics

okLrfod fo’ys"k.k] jSf[kd chtxf.kr] ,oa

125

42

25

8

-----

-----

150

fofoDr xf.kr

Note: There are three sections in the question paper. All questions from each section will be compulsory. Section –A (20 marks.) will contain 10 objective type questions , two from each unit, with the weightage of 2 marks. Section –B (35 marks.) will contain 5 short answer type questions (each having internal choice), one from each unit with a weightage of 7 marks. Section –C (70 marks.) will contain 5 long answer type questions (each having internal choice), one from each unit, with a weightage of 14 marks. There should be at least 9 teaching periods per week.

mPp f’k{kk foHkkx] ee-iz- 'kklu ch-,llh-@ch-,- d{kkvksa ds fy;s ,dy Á’ui= Á.kkyh lsesLVj ds vuqlkj ikB~;Øe dsUnzh; v/;;u e.My }kjk vuq'kaflr rFkk e-iz- ds jkT;iky }kjk vuqeksfnr Department of Higher Education , Govt. of M.P. B.Sc./ B.A. Single Paper System Semester wise syllabus As Recommended by central Board of studies and Approved by the Governor of M.P.


:

B.Sc. /B.A.

Semester/ lsesLVj

:

V


:

Mathematics

Title / 'kh"kZd

:

Real Analysis, Linear Algebra and Discrete Mathematics


:

Compulsory


Unit -1 bdkbZ&1

Unit -2 bdkbZ&2 Unit -3

Riemann integral, Integrability of continuous and monotonic functions, The fundamental theorem of integral calculus, Mean value theorems of integral calculus, Partial derivatives and differentiability of real-valued functions of two variables.

jheku lekdy] lrr ,oa ,dfn"V Qyuksa dh lekdyuh;rk] lekdyu dk ewyHkwr ize; s ] lekdyuks ds ek/;eku ize; s ] nks pjksa ds okLrfod eku Qyuksa ds vkaf’kd vodyt ,oa vodyuh;rk A Schwarz and Young's theorem, Implicit function theorem, Fourier series of half and full intervals, Improper integrals and their convergence, Comparison test, Abel’s and Dirichlet’s tests, Frullani’s integral, Integral as a function of a parameter.

LoktZ ,oa ;ax ds ize; s ]vLi"V Qyu ize; s ] v)Z ,oa iw.kZ varjky dh Qwfj;s Js.kh] fo"ke lekdy ,oa mudk vfHklj.k] rqyuk ijh{k.k] vkcsy ,oa fMfjDys dk ijh{k.k] Qzqykuh lekdy] izkpfyd Qyuksa ds :Ik esa lekdy A Definition and examples of vector spaces, subspaces, Sum and direct sum of subspaces. Linear span, Linear dependence, independence and their basic properties. Basis, Finite dimensional vector spaces, Existence theorem for basis, Invariance of the number of elements of a basis set, Dimension, Dimension of sums of vector subspaces.

bdkbZ&3

lfn’k lef"V dh ifjHkk"kk ,oa mnkgj.k] milef"V] milef"V;ksa dk ;ksx ,oa lh/kk ;ksx A jSf[kd foLr`fr] jSf[kd vkfJrrk] Lora=rk ,oa muds ewy xq.k/keZA vk/kkj] ifjfer foeh; lfn’k lef"V;kW]a vk/kkj dk vfLrRo ize; s ] vk/kkj leqPp; esa vo;oksa dh la[;k dh vifjoZru’khyrk A foek] lfn’k milef"V;ksa ds ;ksx dh foek A

Unit -4

Linear transformations and their representation as matrices, The Algebra of linear transformations, The rank- nullity theorem, Eigen values and eigen vectors of a linear transformation, Diagonalisation. Quotient space and its dimension.

bdkbZ&4

jSf[kd :ikarj.k ,oa mudk vkO;wg fu:i.k] jSf[kd :ikarj.kksa dk cht xf.kr] tkfr 'kwU;rk ize; s ] jSf[kd :ikarj.kksa ds vk;xu eku ,oa vk;xu lfn’k] fod.khZdj.k foHkkx lef"V

,oa mldh foekA

Unit -5

Binary Relations, Equivalence Relations, Partitions and Partial Order Relation . Graphs, Multigraphs, Weighted Graphs, Paths and Circuits, Shortest Paths. Trees and their properties.

bdkbZ&5

f}pj lac/a k] rqY;rk lac/a k] foHkktu ,oa vkaf'kd dze lac/a k dh xzkQ] cgqxzkQ] Hkkfjr xzkQ] iFk ,oa ifjiFk] y?kqre iFk] o`{k ,oa mlds xq.k/keZ A

Text Books : 1. R.R Goldberg, Real Analysis, Oxford & IBH Publishing Co., New Delhi, 1970. 2. Shanti Narayan, Theory of Functions of a Complex Variable, S. Chand & Co., New Delhi. 3. K. Hoffman and R. Kunze, Linear Algebra, 2nd Edition. Prentice Hall Englewood Cliffs,New Jersey.1971. 4. C.L. Liu,Elements of Discrete Mathematics, (Second Edition), McGraw Hill, International Edition, Computer Science scries 1986. 6. Narsingh Deo : Graph Theory, McGraw Hill. 7. e-iz- fgUnh xzFa k vdkneh dh iqLrdsa A

Reference Book:1. 2. 3.

5. 6. 7. 8. 9. 10. 11. 12. 13.

T.M Apostol, Mathematical Analysis. Norosa Publishing House. New Delhi, 1 S. Lang. Undergraduate Analysis, Springer-Veriag, New York, 1983. D. Somasundaram and B. Choudhary, A first Course in Mathematical Analysis. Narosa Publishing House, New Delhi 199 /. Shanti Narayan, A Course of Mathematical Analysis. S. Chand & Co. Delhi. RK. Jain and S.K. Kaushik, An introduction to Real Analysis, S. Chand & Co., New Delhi. 2000. R. V. Churchill & J.W. Brown, Complex Variables and Applications, 5th Edition, McGraw-Hili New. York. 1990 Mark; J. Ablowitz & A. S. Fokas. Complex Variables : Introduction and Applications, Cambridge University Press, South Asian Edition, 1998 Ponnuswamy : Complex Analysis, Narosa Publishing Co. Babu Ram, Discrete Mathematics, Vinayak Publication. K.B. Datta. Matrix and Linear Algebra, Prentice hall of India Pvt Ltd., New Delhi, 2000. S.K. Jain, A. Gunawardena & P.B. Bhattacharya. Basic Linear Algebra with MATLAB Key college Publishing (Springer-Verlag) 2001 S. Kumarsaran, Linear Algebra, A Geometric Approach Prentice – Hall of India, 2000

mPp f’k{kk foHkkx] ee-iz- 'kklu ch-,llh@ch-,- d{kkvksa ds fy;s ,dy Á’ui= Á.kkyh lsesLVj ds vuqlkj ikB~;Øe dsUnzh; v/;;u e.My }kjk vuq'kaflr rFkk e-iz- ds jkT;iky }kjk vuqeksfnr Department of Higher Education , Govt. of M.P. B.Sc./ B.A. Single Paper System Semester wise syllabus As Recommended by central Board of studies and Approved by the Governor of M.P. Name of Paper

Theory

Mini Passing

(M.M.)

Marks in Theory

125

42

C.C.E.

Mini Passing Marks in CCE

Practical

8

----

MM

Mini Passing

Total

M.

Compulsory

Metric Spaces and Numerical Analysis And

25

----

150

Optional

Note: There are three sections in the question paper. All questions from each section will be compulsory. Section –A (20 marks.) will contain 10 objective type questions , two from each unit, with the weightage of 2 marks. Section –B (35 marks.) will contain 5 short answer type questions (each having internal choice), one from each unit having 7 marks. Section –C (70 marks.) will contain 5 long answer type questions (each having internal choice), one from each unit, having 14 marks. There should be at least 9 teaching periods per week.

mPp f’k{kk foHkkx] ee-iz- 'kklu ch-,llh@ch-,- d{kkvksa ds fy;s ,dy Á”ui= Á.kkyh lsesLVj ds vuqlkj ikB~;Øe dsUnzh; v/;;u e.My }kjk vuq'kaflr rFkk e-iz- ds jkT;iky }kjk vuqeksfnr Department of Higher Education , Govt. of M.P. B.Sc./ B.A. Single Paper System Semester wise syllabus As Recommended by central Board of studies and Approved by the Governor of M.P.

Lk=~ @ Session : 2013-14

vf/kdre vad@Max. Marks : 125

Class/ d{kk

:

B.Sc. /B.A.

Semester/ lsesLVj

:

VI


:

Mathematics

Title / 'kh"kZd

:

Metric Spaces, Numerical Analysis and optional


:

Compulsory (V unit optional)


Unit -1

bdkbZ&1

Unit -2

Definition and examples of metric spaces. Neighbourhoods. Limit points. Interior points. Open and closed sets. Closure and interior. Boundary points. Subspace of a metric space. Cauchy sequences. Completeness, Cantor's intersection theorem, Contraction principle. Real numbers as a complete ordered field. Dense subsets. Baire Category theorem. Separable, first and second countable spaces.

nwjhd lef"V dh ifjHkk"kk ,oa mnkgj.k] lkehI;] lhek fcUnq] var% fcUnq] foo`Rr ,oa lao`r leqPp;] laoj.kd ,oa vH;arj] ifjlhek fcUnq] nwjhd lef"V dh mi lef"VA dkS’kh vuqdze] iw.kZrk] dsUVj dk loZfu"B ize; s ] ladqpu fl)kar] iw.kZ dzfer {ks= ds :Ik esa okLrfod la[;k;s]a l?ku leqPp;] cs;j dk laoxZ ize; s A fo?kVh;] izFke ,oa f}rh; x.kuh; lef"VA Continuous functions. Extension theorem. Uniform continuity. Compactness, Sequential compactness. Totally bounded spaces, Finite intersection property. Continuous functions and compact sets. Connectedness

bdkbZ&2 Unit -3

larr Qyu] foLrkj ize; s ] ,dleku lkarR;A lagrrk] vuqdze.kh; lagrrk] iw.kZ ifjc) lef"V]ifjfer loZfu"B izx.q kA larr Qyu ,oa lagr leqPp;] lac)rkA Solution of Equations: Bisection. Secant, Regula Falsi. Newton, Method. Roots of second degree Polynomials, Interpolation, Lagrange interpolation, Divided Differences, Interpolation formulae using Differences, Numerical Quadrature, Newton-Cote's Formulae, Gauss Quadrature Formulae.

bdkbZ&3

Unit -4

bdkbZ&4

Unit -5

lehdj.kksa ds gy % f}Hkktu] lhdsUa V] jsX;qyk QkYlh rFkk U;qVu fof/kA f}rh; ?kkr cgqinksa ds ewy A vUrZo’s ku % ykxjkat vUrZo’s ku foHkkftr vUrj] vUrj ds mi;ksx ls vUrZo’s ku lw= ]la[;kRed {ks=dyu U;qVu dksV~Zl lw=] xkml {ks=dyu lw= A Linear Equations: Direct Methods for Solving Systems of Linear Equations (Guass elimination, LU Decomposition. Cholesky Decomposition), Iterative methods (Jacobi. Gauss - Seidel Reduction Methods). Ordinary Differential Equations: Euler Method, Singlestep Methods, Runge-Kutta's Method, Multi-step Methods, Milne-Simpson Method. Methods Based on Numerical Integration, Methods Based on numerical Differentiation.

jSf[kd lehdj.k % jSf[kd lehdj.kksa ds fudk; dks gy djus dh izR;{k fof/k;ka (xkml foyksiu] ,y ;w fo;kstu] pksysLdh fo;kstu) iqujko`rh fof/k;ka (tsdksch] xkml flMsy ) lk/kkj.k vody lehdj.k% vk;yj fof/k] ,dy pj.k fof/k] #ax dqVV~ k fof/k] cgqpj.k fof/k] feyus flEilu fof/k] la[;kRed lekdyu ij vk/kkfjr fof/k;ka] la[;kRed vodyu ij vk/kkfjr fof/k;ka A ELEMENTARY STATITICS Measures of dispersion-range, inter quartile range, Mean deviation, Standard deviation, moments, skewness and kurtosis. Probability, Continuous probability, probability density function and its applications (for finding the mean, mode, median and standard deviation of various continuous probability distributions) Mathematical expectation, expectation of sum and product of random variables. Theoretical distribution- binomial, Poisson distributions and their properties and use, Moment generating functions.

bdkbZ -5

fo{ksi.k dh ekis%a ifjlj] vUr% prqFkZd ifjlj ] ek?; fopyu] ekud fopyu] vk?kw.kZ ] fo"kerk rFkk ddqnrk] izkf;drk] lrr izkf;drk] izkf;drk ?kuRo Qyu rFkk muds vuqi; z ksx ( lrr izkf;drk caVu ds fy;s ek?;] cgqyd]ekf?;dk rFkk ekud fopyu Kkr djus ds fy;s ) xf.krh; izR;’kk ];kn`fPNd pjksa ds ;ksx ,oa xq.ku dh izR;k’kkA lS)kafrd caVu&f}in]ikW;t+u caVu rFkk mlds xq.k/keZ ,oa mi;ksx] vk?kw.kZ tud Qyu

OR Unit -5

PRINCIPLES OF COMPUTER SCIENCE Data Storage of bits Ram Memory. Mass srorage. Coding Information of Storage. The Binary System Storing integers fractions, communication errors. Data Manipulation - The Central Processing Unit The Stored Program concept. Programme Execution,. Anthmetic/Logic Instruction. Computer-Peripheral Communication. Operation System : The Evolution of Operating System.(Dos, Window) Operating System Architecture. Coordinating the Machine's Activities. Other Architectures.

bdkbZ -5

chVksa dk MsMkLVksjt s ] jse Le`frA o`gn Hk.Mkj.kA Hk.Mkj.k dh dwVd`r lwpukA ck;ujh flLVe A iw.kkZd a ] fHkUukad dk Hk.Mkj.k] lapkj.k =qfV;kaA MkVk esfuiwy’s ku&lsUVªy izkslfs lax ;wfuV] Hk.Mkfjr izkx s zke vfHk/kkj.kkA izkx s zke dk lapkyuA xf.krh;@rkfdZd funsZ’kA dEI;wVj&lg midj.k ¼isjhQsjYl½ ds e/; lapkjA vkijsfVax flLVe% dk mn~Hko ¼DOS, Windows½ vkijsfVax flLVe vkfdZVDs pj dEI;wVj e’khu dh xfrfof/k;ksa dk leUo;uA vU; vkfdZVDs pj

OR

Unit -5

METHEMATICAL MODELING The process of Applied Mathematics. Setting up first order differential equations. Qualitative solution sketching. Stability of solutions. Difference and differential equation models of growth and decay. Single species population model, Exponential and logistic population models.

bdkbZ -5

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Compulsory Text Books : 1. R.R Goldberg, Real Analysis, Oxford & IBH Publishing Co., New Delhi, 1970. 2. G.F. Simmons. Introduction to Topology and Modem Analysis. McGraw-Hill, 1963. e-iz- fgUnh xzFa k vdkneh dh iqLrdsa A

3.

4. V Raja raman Programing C, Prentice Hall cf India, 1994. 5. C E Frooerg. Introduction to Numerical Analysis, (Second Edition L Addison-Wesley - 1979, Reference Books: 1.

T.M Apostol, Mathematical Analysis. Norosa Publishing House. New Delhi, 1 985

2.

S. Lang. Undergraduate Analysis, Springer-Veriag, New York, 1983.

3.

D. Somasundaram and B. Choudhary, A first Course in Mathematical Analysis. Narosa Publishing House, New Delhi 1997.

4.

Shanti Narayan, A Course of Mathematical Analysis. S. Chand & Co. Delhi.

5.

RK. Jain and S.K. Kaushik, An introduction to Real Analysis, S. Chand & Co., New Delhi 2000.

6.

P.K. Jain and K. Ahmed Metric Spaces, Narosa Publishing House, New Delhi, 1996.

7.

S. Lang, Undergraduate Analysis, Springer-Verlag, New York 1983.

8.

E.T. Copson, Metric Spaces, Cambridge University Press, 1968

9.

Henry, Mullish and Herbert, L. Copper, Spirit of C: An Introduction to Modern Programming, Jaico Publishers.

10

M K Jain, S.R.K. Iyengar, R. K. Jain. Numerical Methods Problems and Solutions, New Age International (P)Ltd. 1996.

11.

E. Balaguruswamy- Numerical Method Tata Mc Graw_ Hill Pub.Com. New Yark.

Optional

1. Elementary Statistics Text Book 1.

Statistics by M. Ray

2.

Mathematical Statistics by J.N. Kapoor, H.C. Saxena (S. Chand)

3

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References Book: 1.

Fundamentals of Mathematical Statistics, Kapoor and Gupta

2. Principles of Computer Science Text Book : 1.

J. Glen Brokkshear, Computer Science: An Overview, Addition- Wesley.

2.

Stanley B. Lippman, josee Jojoie. C++ Primer)3rd Edition), Addision- Wesley Total at least ten practicals.

3


3.

Mathematical Modeling

Text Books: 1.

Kapoor, J.N. : Mathematical models in Biology and Medicine. EWp (1985)

2.

SAXENA V.P. : Bio-Mathematics an introduction, M.P. Hindu Growth Arademy 1993

3.

Martin Braun C.S. Coleman, DA Drew (Eds) Differential Equation Models.

4.

Steven J.B. Lucas W.P., Straffin B.D. (Eds.) Political and Related Models, Vol. 2

5.


Reference Books : 1.

Cullen Linen. Models in Biology.

2.

Rubinow, SI : Introduction to Mathematical Biologv. John Wiley and Sons 1975.

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