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TNPSC CSSSE Syllabus 2021

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Brief Info of TNPSC CSSSE 2021 Syllabus

TNPSC Combined Statistical Service Exam Pattern 2021

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Subject Wise Tamil Nadu PSC CSSSE Syllabus 2021

Algebra and Trigonometry

• Theory of Equations: Polynomial equations; Symmetric functions of roots in terms of coefficient; Imaginary and irrational roots; Sum of rth powers of roots; Reciprocal equations; Transformations of equations.
• Descrates’ rule of signs: Approximate solutions of roots of polynomials by Newton – Raphson Method – Horner’s method; Cardan’s method of solution of a cubic polynomial.
• Expansions of sin x, cos x, tan x in terms of x; sin nx, cos nx, tan nx, sin nx, cos nx , tan nx, hyperbolic and inverse hyperbolic functions – simple problems.
• Summation of Series: Binomial, Summation of finite series using method of differences – simple problems, Exponential and Logarithmic series theorems.

UNIT II: Calculus, Coordinate Geometry Of 2 Dimensions And Differential Geometry

• nth derivative; Leibnitz’s theorem and its applications; Partial differentiation. Total differentials; Jacobians; Maxima and Minima of functions of 2 and 3 independent variables – necessary and sufficient conditions; Lagrange’s method – simple problems on these concepts.
• Methods of finding asymptotes of rational algebraic curves with special cases. Beta and Gamma functions, properties and simple problems. Double Integrals; triple integrals; change of order of integration; applications to area, surface are volume.
• Conics – Parabola, ellipse, hyperbola and rectangular hyperbola – pole, polar, co-normal points, con-cyclic points, conjugate diameters, asymptotes and conjugate hyperbola.
• Curvature; radius of curvature in Cartesian coordinates; equation of a straight line, circle and conic; polar coordinates; radius of curvature in polar coordinates; p-r equations; evolutes; envelopes.
• Methods of integration; Properties of definite integrals; Reduction formulae – Simple problems.

UNIT III – Differential Equations and Laplace Transforms

• First order but of higher degree equations – solvable for p, solvable for x, solvable for y, clairaut’s form – simple problems.
• Second order differential equations with constant coefficients with particular integrals for eax, xm , eax sin mx, eax cos mx
• Method of variation of parameters; Total differential equations, simple problems.

UNIT IV – Vector Calculus, Fourier Series and Fourier Transforms

• Vector Differentiation: Gradient, divergence, curl, directional derivative, unit normal to a surface.
• Fourier Series: Expansions of periodic function of period 2π ; expansion of even and odd functions; half range series.
• Vector integration: line, surface and volume integrals; theorems of Gauss, Stokes and Green – simple problems.
• Fourier Transform: Infinite Fourier transform (Complex form, no derivation); sine and cosine transforms; simple properties of Fourier Transforms; Convolution theorem; Parseval’s identity.

UNIT V – Algebraic Structures

• Groups: Subgroups, cyclic groups and properties of cyclic groups – simple problems; Normal subgroups; Lagrange’s Theorem; Homomorphism; Automorphism ; Cayley’s Theorem, Permutation groups.
• Vector Spaces: Definition and examples, linear dependence and independence, dual spaces, inner product spaces.
• Linear Transformations: Algebra of linear transformations, matrices, canonical forms, characteristic roots, triangular forms.
• Rings: Definition and examples, Integral domain, Ideals and quotient Rings, Prime ideal and maximum ideal; homomorphism of rings, the field and quotients of an integral domain, Euclidean Rings.

UNIT VI – Real Analysis

• Sets and Functions: Sets and elements; Operations on sets; functions; real valued functions; equivalence; countability; real numbers; least upper bounds.
• Series of Real Numbers: Convergence and divergence; series with non-negative numbers; alternating series; conditional convergence and absolute convergence; tests for absolute convergence; series whose terms form a non-increasing sequence; the class I 2
• Sequences of Real Numbers: Definition of a sequence and subsequence; operations on convergent sequences; limit of a sequence; convergent sequences; bounded sequences; monotone sequences; divergent sequences; operations on divergent sequences; limit superior and limit inferior; Cauchy sequences.
• Limits and metric spaces: Limit of a function on a real line; metric spaces; limits in metric spaces.

UNIT VII – Complex Analysis

• Complex numbers: Point at infinity , Stereographic projection
• Mappings by elementary functions: linear functions, the function 1/z, linear fractional transformations , the functions w=zn , w=ez , special linear fractional transformations.
• Analytic functions: Functions of a complex variable , mappings, limits , theorems of limits, continuity, derivatives, differentiation formula, Cauchy-Riemann equations, sufficient conditions Cauchy-Riemann equations in polar form, analytic functions, harmonic functions.
• Integrals: definite integrals, contours , line integrals, Cauchy-Goursat theorem, derivatives of analytic functions, Cauchy integral formula, maximum moduli of functions.

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UNIT VIII – Dynamics and Statics

• DYNAMICS: kinematics of a particle, velocity, acceleration, relative velocity, angular velocity, equation of motion, rectilinear motion under constant acceleration, Newton’s laws of motion, simple harmonic motion.
• Central forces : Central orbit as plane curve, p-r equation of a central orbit, finding law of force and speed for a given central orbit, finding the central orbit for a given law of force.
• Projectiles : Time of flight, horizontal range, range in an inclined plane. Impulse and impulsive motion, direct and oblique impact-simple problems, collision of two smooth spheres.
• Moment of inertia : Moment of inertia of simple bodies, theorems of parallel and perpendicular axes, circular lamina, circular ring, right circular cone, moment of inertia of triangular lamina, sphere (hollow and solid).

UNIT IX – Operations Research

• Linear programming – formulation – graphical solution – simplex method
• Sequencing problem – n jobs through 2 machines – n jobs through 3 machines – two jobs through m machines – n jobs through m machines.
• PERT and CPM: project network diagram – Critical path (crashing excluded) – PERT computations.
• Big-M method – Two-phase method-duality- primal-dual relation – dual simplex method – revised simplex method – Sensitivity analysis. Transportation problem – assignment problem.

UNIT IX – Mathematical Statistics

• Statistics – Definition – functions – applications – complete enumeration – sampling methods – measures of central tendency – measures of dispersion – skewness- kurtosis.
• Random Variables (Discrete and continuous), Distribution function – Expected values & moments – Moment generating function – probability generating function – Examples. Characteristic function– Cumulants, Chebychev’s inequality– Uniqueness and inversion theorems – Simple problems.
• Sample space – Events, Definition of probability (Classical, Statistical & Axiomatic ) – Independence – Conditional probability – Addition and multiplication laws of probability –Bayes theorem – simple problems.

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