B.Sc./B.A. SEMESTER - I- 2011-2012. MATHEMATICS. Name of ..... 2000. 4.
Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons 1999. 5.
COURSE STRUCTURE B.Sc./B.A. SEMESTER - I- 2011-2012 MATHEMATICS
Name of the Papers
Theory (M.M.)
Mini. Passing M.
C.C.E.
Mini.
Practical MM
Minimum
Passing
Passing
M.
M.
Total
Compulsory/ vfuok;Z
Paper 1.Algebra , Trigonometry & Geometry chtxf.kr ] f=dks.kfefr ,oa T;kfefr
105
35
45
15
-------
-------
150
Note : There should be three sanction in question paper all questions will be compulsory Section - A will contain five objective questions one from each unit each having 3 marks. Section - B will contain 5 Short answer type questions (each having internal choice) One from each unit having 6 marks Section – C will contain 5 Long answer type questions (each having internal choice) One from each unit having 12 marks There should be at least nine periods (Minimum 40 minutes each) per week per paper.
Department of Higher Education, Govt. of M.P. Under Graduate Semester wise Syllabus as recommended by Central Board of Studies and approved by the Governor of M.P.
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Session ¼l=½ 2011&201 2011&2012 &2012 Class / d{kk
% B.Sc./B.A.
Semester / lsesLVj
%I % Mathematics
Title of Subject /Group
fo"k; @lewg dk 'kh"kZd Paper No. / iz'ui=
% xf.kr
dz dzekad
% I (Algebra, Trigonometry & Geometry) (cht cht xf.kr] f=dks.kfefr ,oa T;kfefr½
Compulsory / vfuok;Z
;k
Optional / oSdfYid
Max. Marks vf/kdre
vad
vfuok;Z
%
Compulsory / vfuok;Z
% 150
Unit-1
Rank of a matrix. Eigen values, eigen vectors.Characteristic equation of a matrix. Cayley Hamilton theorem and its use in finding inverse of marix. Application of matrix to a system of linear ( both homogenous and non - homogenous) equations. Theorems on consistency and inconsistency of a system of linear equations. Solving the linear equations with three unknowns. Relation between the roots and coefficients of a general polynomial equation in one variable. Transformation of equations, Descarte’s rule of signs.
bdkbZ & 1
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Unit-2
De Moivre’s theorem and its application. Direct and inverse circular and hyperbolic functions, Expansion of trignometrical function. Gregory’s Series, Summation of Series,
bdkbZ & 2
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Unit-3
Definition and basic properties of group. Order of an element of a group. Subgroups, algebra of subgroups. Cyclic groups, and their simple properties. Coset decomposition and related theorems. Lagrange’s theorem andits consequences, Normal sub groups, quotient groups.
bdkbZ & 3
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Unit-4
Homomorphism and isomorphism of groups, kernel of Homomorphism of groups and fundamental theorem of Homomorphism of groups Permutation groups (even and odd permutations) Alternating groups An, Cayley’s theorem. Introduction to rings, subrings, integral domains and fields, simple properties and examples.
bdkbZ & 4
Unit-5
lewgks dh lekdkfjrk ,oa rqY;kdkfjrk] lekdkfjrk dh vf"V] lewgks dh lekdkfjrk dk ewyHkwr ize; s A Øep; lewg ¼le ,oa fo"ke Øep; ½ ,dkarj lewg An, dSyh dk ize; s oy;] mioy;] iw.kakZdah; izakar ,oa {ks= dk ifjp; ljy xq.k/keZ ,oa mnkgj.k General equation of second degree. Tracing of conics. Equation of cone with given base, generators of cone, condition for three mutually perpendicular generators, Right circular cone. Equation of Cylinder and its properties. Right circular cylinder, enveloping cylinder and their properties Central conicoids, Paraboloids. Plane sections of Conicoids.
bdkbZ & 5
f}?kkr dk lkekU; lehdj.k] 'kkadoksa dk vuqj[s k.kA fn, x, vk/kkj ds 'kadq dk lehdj.k] 'kadq ds tud] rhu ijLij yEcor tudksa gsrq 'krZ] yaco`Rrh; 'kadq
csyu dk lehdj.k ,oa mlds xq.k/keZ] yaco`Rrh; csyu] vUoyksfi; csyu ,oa mlds xq.k/keZA dsUnzh; 'kkadot ijoYk;t 'kkadoksa dh leryh; dkVA
Texts Books : 1. S.L. Loney – Plane Trigonometry Part II 2. K.B. Datta – Matrix and Linear Algebra Prentice Hall of India Pvt. New Delhi 2000 3. Chandrika Prasad – A Text Book on Algebra and Theory of Equations, Pothishala Pvt. Ltd. Allahabad 4. I. N. Herstein – Topics in Algebra, Wiley Eastern Ltd. New Delhi 1977 5. N. Saran & R.S. Gupta : Analytical Geometry of Three dimensions. Pothishala Pvt. Ltd. Allahabad 6. S.L. Loney, Elements of Coordinate Geometry, Macmillan and Co. London. Reference Books: 1. P. B. Bhattacharya, S. K. Jain and S.R. Nagpaul, First Courses in Linear Algebra, Wiley Eastern, New Delhi. 1983. 2. S. K. Jain, A. Gunewardena and P. B. Bhattacharya, Basic Linear Algebra with MATLAB, Key CollegePpublishing, 2001. Allahabad 3. H.S. Hall and S.R. Knight, Higher Algebra, H.M. publication, 1994. 4. R.S. Verma and K.S. Shukla, Text Book on Trigonometry Pothishala Pvt. Ltd. 5. P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul, Basic Abstract Algebra, Wiley Eastern, New Delhi, 1997. 6. I. S. L.uther and I.B. S. Passi, Alegebra Vol- I , II, Narosa Publishing House.
7. P.K. Jain & Khalil Ahmad, A text book of Analytical Geometry of Two Dimensions, Wiley Eastern Ltd. 1994 8. P.K. Jain & Khalil Ahmad, A text book of Analytical Geometry of Three Dimensions, Wiley Eastern Ltd. 1999 9. R.J.T. Bell : Elementary Treatise on Coordinate Geometry of Three dimensions, Macmillan India Ltd. 1994. 10.ee-iz- fgUnh xzFa k vdkneh dh iqLrdsa A
COURSE STRUCTURE B.Sc./B.A. SEMESTER - II- 2011-2012 MATHEMATICS
Theory (M.M.)
Name of the Papers
Mini. Passing M.
C.C.E.
Mini.
Practical MM
Minimum
Passing
Passing
M.
M.
Total
Compulsory/ vfuok;Z
Paper 1. Calculus , Differential Equations & Calculus
Vector 105
Izk'ui=
I
35
45
15
--
--
150
dyu] vody
lehdj.k
& lfn'k
dyu
Note : There should be three sanction in question paper all questions will be compulsory Section - A will contain five objective questions one from each unit each having 3 marks. Section - B will contain 5 Short answer type questions (each having internal choice) One from each unit having 6 marks Section – C will contain 5 Long answer type questions (each having internal choice) One from each unit having 12 marks There should be at least nine periods (Minimum 40 minutes each) per week per paper.
mPp f'k{kk foHkkx] ee-iz- 'kklu Lukrd d{kkvksa ds fy;s lsesLVj vuqlkj ikB~;dze dsna zh; v/;;u e.My }kjk vuq'kaflr rFkk ee- iz- ds jkT;iky }kjk vuqeksfnr
Session ¼l=½ 2011&2012
Class / d{kk
% B.Sc./B.A.
Semester / lsesLVj
% II % Mathematics
Title of Subject /Group
fo"k; @lewg dk 'kh"kZd
% xf.kr
Paper No. / iz'ui=
% I (Calculus , Differential
dzekad
Equations & Calculus)
Vector
¼dyu] vody lehdj.k
&
lfn'k
dyu ½ Compulsory / vfuok;Z
;k
Optional / oSdfYid
Max. Marks vf/kdre
vad
vfuok;Z
%
Compulsory / vfuok;Z
% 150
Unit-1
Concept of Partial differentiation, Successive differentiation, Leibnitz theorem, Maclaurin and Taylor series expansions Asymptotes and Curvature Tests for concavity and convexity Points of inflexion. Multiple points Tracing of curves in cartesian and polar co-ordinates
bdkbZ & 1
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Unit-2
Integration of irrational algebraic functions and transcendental functions. Reduction formulae. Definite Integrals. Quadrature, Rectification, Volumes and Surfaces of solids of revolution of curves.
bdkbZ & 2
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Unit-3
Linear equations and equations reducible to the linear form, Exact differential equation First order higher degree equations for x, y, p, Clairaut’s form and singular solutions. Linear differential equations with constant coefficients.
bdkbZ & 3
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Unit-4
Homogenous linear ordinary differential equations, linear differential equations of second order. Transformation of the equation by changing the dependent variable and the independent variableMethod of variation of parameters, Ordinary simultaneous differential
bdkbZ & 4
Unit-5
equations.
lkekU; le?kkr jSf[kd vody lehdj.k] f}?kkr jSf[kd vody lehdj.k] ijra= ,oa Lora= pjksa dks cny dj lehdj.k dk :ikarj.kA izkpy fopj.k dh fof/k] lk/kkj.k ;qxin vody lehdj.kA
Vector differentiation. Gradient, Divergence and Curl. Vector integration, Theorem of Gauss (without proof ) and problems based on it. Theorem of Green (without proof ) and problems based on it. Stoke’s theorem(without proof ) and problems based on it.
bdkbZ & 5
lfn’k vodyu] xzfs M;aV] Mk;OgtZsal ,oa dyZA lfn’k lekdyu] xkWl dh ize; s ¼fcuk miifRr½ ,oa ml ij vk/kkfjr iz’uA xzhu dk ize; s ¼fcuk miifRr½ ,oa ml ij vk/kkfjr iz’uA LVksd dk ize; s ¼fcuk miifRr½ ,oa ml ij vk/kkfjr iz’uA
Texts Books : 1. Gorakh Prasad – Differential Calculus, Pothishala pvt. Ltd. Allahabad 2. Gorakh Prasad – Integral Calculus, Pothishala pvt. Ltd. Allahabad 3. D.A. Murray : Introductory Course in Differential Equations, Orient Long man, India 1967. 4. N. Saran & S.N. Nigam – Introduction to Vector Analyss, Pothishala Pvt. Ltd., Allahabad
Reference Books: 1. Gabriel Klambauer, Mathematical Analysis Marcel Dekkar, Inc. New York, 1975. 2. Murray R. Spiegel, Theory & problems of Advanced Calculus.Schaum’s outline series, Schaum Publishing Co. NewYark. 3. P.K. Jain and S. K. Kaushik, An introduction of Real Analysis, S.Chand & Co. New Delhi 2000. 4. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons 1999. 5. G. F. Simmons, Differential Equations, Tata Mcgraw Hill, 1972. 6. E.A. Codington, An introduction to ordinary differential equations, Prentice Hall of India 1961. 7. H.T.H. Piaggio, Elementary Treatise on Differential equations and their applications, C.B.S. Publisher and Distributors, Delhi 1985. 8 W.E. Boyce and P.C. Diprima, Elementary Differential equations & Boundary Value problems, John Wiley 1986. 9. Murray R. Spiegel, Vector Analysis, Schaum Publishing Co. New York. 10. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons 1999. 11. Shanti Narayan, A text book of Vector Calculus, S. Chand & Co., New 12.ee-iz- fgUnh xzFa k vdkneh dh iqLrdsa A
