Civil Service Management Main Exam Paper Two Syllabus
PAPER-II
SECTION-A
1. Algebra:Groups,subgroups,cyclic groups,cosets,Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups,Cayley’s theorem
Rings,subrings and ideals,homomorphisms of rings; Integral domains,principla ideal domains Euclidean domains and unique factorization domains;Fields,quotient fields
2. Real Analysis: Real number system as an ordered field with least upper bound property; Sequences limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series.
Continuity and uniform continuity of functions, properties of continuous functions on compact sets.
Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and inerrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.
3. Complex Analysis :Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; Singularities Laurent’s series; Cauchy’s residue theorem; Contour integration
4. Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution, Graphical method and simple’s method of solutions; Duality
Transportation and assignment problems.
5 Partial differential equations: Family of surface in three dimensions and formulations of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form;Wquation of a vibrating string ,heat equation,Laplce equation and their solutions
6. Numerical Analysis and Computer Programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection,Regula-Falsi and Newton-Raphson methods; Solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss- Seidel (iterative)methods. Newton’s (forward and backward)interpolation, Lagrange’s interpolation
numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula
Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods
Computer Programming: Binary system; Arithmetic and logical operations on number; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers
Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean integers
Algorithms and flow charts for solving numerical analysis problems
7 Mechanics and Fluid Dynamics: Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions
Equation of continuity; Euler’s equation of motion for inviscid flow’ Streamn-lines ,path of a particle potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion ;Navier-Stokes equation for a viscous fluid
PAPER-II
SECTION-A
1. Algebra:Groups,subgroups,cyclic groups,cosets,Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups,Cayley’s theorem
Rings,subrings and ideals,homomorphisms of rings; Integral domains,principla ideal domains Euclidean domains and unique factorization domains;Fields,quotient fields
2. Real Analysis: Real number system as an ordered field with least upper bound property; Sequences limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series.
Continuity and uniform continuity of functions, properties of continuous functions on compact sets.
Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and inerrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.
3. Complex Analysis :Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; Singularities Laurent’s series; Cauchy’s residue theorem; Contour integration
4. Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution, Graphical method and simple’s method of solutions; Duality
Transportation and assignment problems.
5 Partial differential equations: Family of surface in three dimensions and formulations of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form;Wquation of a vibrating string ,heat equation,Laplce equation and their solutions
6. Numerical Analysis and Computer Programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection,Regula-Falsi and Newton-Raphson methods; Solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss- Seidel (iterative)methods. Newton’s (forward and backward)interpolation, Lagrange’s interpolation
numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula
Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods
Computer Programming: Binary system; Arithmetic and logical operations on number; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers
Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean integers
Algorithms and flow charts for solving numerical analysis problems
7 Mechanics and Fluid Dynamics: Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions
Equation of continuity; Euler’s equation of motion for inviscid flow’ Streamn-lines ,path of a particle potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion ;Navier-Stokes equation for a viscous fluid
No comments:
Post a Comment