### B.A./B. Sc. Semester-I

PAPER I TRIGONOMETRY and MATRICES
I. Separation into real and imaginary parts, Logarithmic of complex quantities, Hyperbolic functions with
their inverses.

II. Gregory’s series, Summation of trigonometric series.

III. Rank of a matrix, Invariance of rank under elementary transformations, Adjoint of matrices, Inverse
of matrices, Reduction to normal form.

IV. Solutions of linear homogeneous and non-homogeneous equations with number of equations and
unknowns upto four, Solutions of a system of linear equations using matrices.

Books Recommended

1.S.L.Loney: Plane Trigonometry(Part I,II) , Arihant Publications.

2.M.D.Raisinghania, H.C.Sexena& H. K.Dass : Trigonometry, S. Chand & Company Pvt. Ltd. 2002.

3.A.I. Kostrikin, Introduction to Algebra, Springer Verlag, 1984.

4. Richard Bronson, Theory and Problems of Matrix Operations, Tata McGraw Hill,1989.

PAPER II DIFFERENTIAL CALCULUS
I. Successive differentiation, Leibnitz’s theorem, Partial differentiation, Euler’s theorem on
homogeneous functions.

II. Tangents and normal, Curvature,Asymptotes.

III. Singular points, Maxima and minima.

IV. Tracing of curves, Parametric representation of curves and tracing of parametric curves, Polar
coordinates and tracing of curves in polar coordinates.

Books Recommended:
1. M. Ray: Differential Calculus, Shiva Lal Agarwal and Co.,Agra.

2. Gorakh Prasad: Differential Calculus, Pothishala publication,Allahabad.

### B.A./B. Sc. Semester-II

PAPER I GROUP THEORY
I Sets, Operations on sets, Realtions, Equavalence relations and partition Functions.

II Algebraic structures, Group, Example of groups, Subgroups, Permutationgroup.

III Order of an element,Cyclic group,Coset decomposition,Lagrange’s theorem and its consequences.

IV Quotient group, Homomorphism, Isomorphism, Cayley’s theorem, Normalizer and center of agroup.

Books Recommended

1. John B. Fraleigh, A First Course in Abstract Algebra, 7th Ed., Pearson,2002.

2. Joseph A Gallian, Contemporary Abstract Algebra, 4th Ed., Narosa, 1999.

PAPER II INTEGRAL CALCULUS

I. Integration of rational and irrational functions, Properties of definite integrals.

II. Gamma-Beta functions, Reduction formulae for integrals of rational, Trigonometric,
Exponential and Logarithmic functions and of their combination.

III. Areas and lengths of curves in the plane.

IV. Volumes and surfaces of solids of revolution, Double and triple integrals.

Books Recommended
1. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi,2005.

2. H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) P. Ltd.,2002.

### B.A./B. Sc. Semester-III

PAPER I ADVANCED ALGEBRA
I. Normal subgroups and their properties, Simple group.

II. Rings, various types of rings, Subrings, Properties of rings.

III. Ideals, Principal ideal ring,Quotient rings, Characteristics of a ring.

IV. Integral domain,Field,Skew field;Examples and its characterizations,

### Books Recommended

1. John B. Fraleigh, A First Course in Abstract Algebra, 7th Ed., Pearson,2002.

2. Joseph A Gallian, Contemporary Abstract Algebra, 4th Ed., Narosa, 1999.

3. Khanna & Bhambhari, A course in Abstract Algebra, 4th ED, Vikash Publication 2006.

### PAPER II DIFFERENTIAL EQUATIONS

I. First order exact differential equations, Integrating factors, Rules to find an integrating
factor, First order higher degree equations solvable for x, y, p, methods for solving
higher-order differential equations, Basic theory of linear differential equations,
Wronskian, and its properties.

II. Solving a differential equation by reducing its order, Linear homogenous equations with
constant coefficients, Linear non-homogenous equations, The method of variation of
parameters.

III. The Cauchy-Euler equation, Simultaneous differential equations, Total differential
equations.

IV. Order and degree of partial differential equations, Concept of linear and non-linear partial
differential equations, Formation of first order partial differential equations, Linear partial
differential equation of first order, Lagrange’s method, Charpit’s method.

### Books Recommended

1. Shepley L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons,1984.

2. I. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, International Edition,1967.

B.A./B.Sc. Semester IV

PAPER I LINEAR ALGEBRA
I. Vector spaces,Subspaces,Algebra of subspaces, Quotient spaces, Linear combination of
vectors, Linear span, Linear independence, Basis and dimension, Dimension of
subspaces.

II. Linear transformations,Null space,Range, Rank and nullity of a linear transformation,
Matrix representation of a linear transformation, Algebra of linear transformations.
III. Dual Space,Dual basis,Double dual,Characteristic polynomial,Eigenvalues and eigen
vectors.

IV. Isomorphisms,Isomorphism theorems,Invertibility and isomorphisms,Change of
coordinate matrix.

### Books Recommended

1. Stephen H.Friedberg,Arnold J.Insel,Lawrence E.Spence,Linear Algebra,4thEd.,Prentice-Hall of
India Pvt. Ltd., New Delhi,2004.

2. DavidC.Lay,LinearAlgebra and its Applications,3rdEd.,Pearson Education Asia,
Indian Reprint, 2007.

3. S. Lang, Introduction to Linear Algebra, 2nd Ed., Springer, 2005
PAPER II MECHANICS

I. Conditions of equilibrium of a particle and of coplanar forces acting on a rigid
body, Laws of friction, Problems of equilibrium under forces including friction.

II. Centre of gravity, Work and potential energy.

III. Newton’s laws of motion,Motion under constant acceleration,Motion under inverse
square law, Velocity and acceleration, Simple harmonic motion.

IV. Angular velocity and angular acceleration,Velocity and acceleration of a particle along a
curve: Radial and transverse components (plane curve), Tangential and normal
components (spacecurve).

### Books Recommended

1. A.S. Ramsay: Statics, CBS Publishers and Distributors (Indian Reprint),1998.

2. A.P.Roberts:Statics and Dynamics with Background in Mathematics,Cambridge University Press,
2003.

### B.A./B. Sc. Semester-V

PAPER I REAL ANALYSIS
I. Finite and infinite sets, Examples of countable and uncountable sets, Real line, Bounded
sets, Suprema and infima, Completeness property of R, Archimedean property of R,
Intervals, Concept of cluster points and statement of Bolzano-Weierstrass theorem.

II. Real Sequence, Bounded sequence, Cauchy convergence criterion for
sequences.Cauchy’s theorem on limits, Order preservation and squeeze theorem,
Monotone sequences and their convergence, Monotone convergence theorem
withoutproof.

III. Infinite series, Cauchy convergence criterion for series, Positive term series, Geometric
series, Comparison test, Convergence of p-series, Root test, Ratio test, Alternating series,
Leibnitz’s test (Tests of convergence without proof), Definition and examples of absolute
and conditional convergence.

IV. Rolle’s theorem, Mean Value theorems, Taylor’s theorem with Lagrange’s and Cauchy’s
forms of remainder, Taylor’s series, Maclaurin’s series of sin x, cos x, ex
, log(l+x),
(1+x)m
.

Books Recommended
1. T. M. Apostol, Calculus (Vol. I), John Wiley and Sons (Asia) P. Ltd.,2002.

2. R.G. Bartle and D. R Sherbert, Introduction to Real Analysis, John Wiley and Sons (Asia), P. Ltd.,
2000.

3. K.A. Ross, Elementary Analysis- The Theory of Calculus Series- Undergraduate Texts in
Mathematics, Springer Verlag, 2003.

PAPER I COMPLEX ANALYSIS
I. Limits, Limits involving the point at infinity, Continuity, Properties of complex numbers,
Regions in the complex plane, Functions of complex variable, Mappings,
Derivatives,Differentiation formulas, Cauchy-Riemann equations, Sufficient conditions
for differentiability.

II. Analytic functions, Examples of analytic functions, Exponential function, Logarithmic
function, Trigonometric function, Derivatives offunctions.

III. Definite integrals of functions, Contours, Contour integrals and its examples, Upper
bounds for moduli of contour integrals, Cauchy- Goursat theorem, Cauchy integral
formula.

IV. Liouville’s theorem and Taylor and Laurent series and itsexamples.

### Books Recommended

1. James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, 8th Ed.,McGraw
– Hill International Edition, 2009.

2. Joseph Bak and DonaldJ.Newman,Complex analysis,2ndEd.,UndergraduateTexts in
Mathematics, Springer-Verlag New York, Inc., New York,1997.

### B.A./B. Sc. Semester-VI

PAPER I LINEAR PROGRAMMING
I. Linear programming problems, Graphical approach for solving some LPP, Convex sets,
Supporting and separating hyper planes.

II. Theory of simplex method, Optimality and unboundedness, The simplex algorithm,
Simplex method in tableau format, Introduction to artificial variables.

III. Two-phase method, Big-M method and their comparison.

IV. Duality, formulation of the dual problem, Primal-dual relationships, Economic
interpretation of thedual.

Books Recommended

1. Mokhtar S. Bazaraa, John J. Jarvis and Hanif D. Sherali, Linear Programming and Network
Flows, 2nd Ed., John Wiley and Sons, India,2004.

2. F.S.HillierandG.J.Lieberman,Introduction to Operations Research,8thEd.,TataMcGrawHill,
Singapore, 2004.

3. Hamdy A. Taha, Operations Research, An Introduction, 8th Ed., Prentice-Hall India,2006.
PAPER II NUMERICAL ANALYSIS

I. Algorithms,Convergence,Bisection method,False position method,Fixed point iteration
method, Newton’s method, Secant method, LU decomposition, Gauss-Jacobi, GaussSiedel methods.

II. Lagrange and Newton interpolation: Linear and higher order, Finite difference operators.

III. Numerical differentiation:Forward difference,Backward difference and central
difference.

IV. Numerical integration: Trapezoidal rule, Simpson’s rule.

Recommended Books

1. B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson Education, India,2007.

2. M.K.Jain,S.R.K.IyengarandR.K.Jain,NumericalMethodsforScientific and Engineering
Computation, 5th Ed., New age International Publisher, India, 2007

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