Mathematics Syllabus for Chattisgarh GroupI Services
The Mathematics Syllabus for Chhattisgarh State Civil Services Preliminary Exam2011 is given below. The examination will be held on 6 May 2012 (Sunday) by the Chhattisgarh Public Service Commission. Acquaint yourself with the breakup of Mathematics syllabus into various sections.
PaperI

AlgebraGroups, semigroups, Lagranges theorem. Cyclic groups, Normal subgroups Quotient groups, conjugate elements and subgroups rings subrings, Integral domain, Fields and polynomial rings. Vector spaces, Linear independence bases Dimensions of a finitely generated space. Lineartransformation. Matrices and their operations. Row & column reduction Echelon form, Rank and nullity of a linear transfoamation. System of linear equations.

Differential CalculusConvergence of sequences and series; Limit and continuity of functions. Differentiability, Mean Value theorem. Taylor's theorem. Expansion in Taylor's and Maclauries Series, Maxima and Minima, successive differentiation. Leibnitz's theorem. Functions. Of several variables Partial derivatives, transformation. Eular's theorem. Jacobian.

Integral CalculusIntegration of rational, irrational and transcendental functions. Definite integrals; Double and tripe integrals, Beta and Gamma functions.

Differential EquationsOrdinary differential equations of first and higher degree Homogeneous equations of first degree Integrating factors; Linear differential equations with constant coefficients. Complimentary functions and perticular integrais, Linear differential equations with variable coefficients.

Vector AnalysisAlgebra of vectors, Double and triple products (Scalar and Vectors), Differentiation of vectors, Directional direvatives Gradient divergence and curl and their elementary properties. Integratioin of vector functions along curves.

StatisticsStatistical population and random sample Collection, and presentation of data measures of locaton dispersion Moments and shepard's corrections, cummulants. Measures of skewness and kurtosis.
PaperII

Analytical GeometryDirection cosines, plane and straight line, sphere cone and cylinder. Tangent planes and normal lines.

Advanced CalculusTangents and Normals. Asymptotes Curvature and Tracing of conics. Determination of areas, lengths surfaces and volumes (Cartesian and polar curves)

Real AnalysisLeast upper bound and greatest lower bounds of sets; limit point of a set Bolzanoweirstrass theorem. Open and closed sets and their porperties, Metric spaces. Cauchy sequences and complete metric spares. Compact sets and HeineBorel theorem.

Boolean AlgebraDifinition and properties. Demorgan's Laws. Switching circuits. Boolean fuctions conjunctive and disjunctive forms.

MechanicsEquilibrium of three forces, friction. Newton's second law of motion, impulsive force. Kinetic energy of particles angular velocity, tragential and normal velocity and accleration projectiles on horizontal and inclined planes Colliston of elastic bodies, Direct and bolique impacts.

Partial Differential EquationsPartial differential equations of first order, Standards forms, Linear partial differential equations of higher degree with constant coefficients. Laplace, diffusion and vibration equation. Simple cases of solutions of