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UPSC Civil Services Main Examination 2014 Syllabus: Mathematics Paper-II

(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, principal 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 integrability 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 simplex method of solutions; Duality.
Transportation and assignment problems.
(5)  Partial differential equations: Family of surfaces in three dimensions and formulation 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; Equation of a vibrating string, heat equation, Laplace 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 numbers; 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 algebra, normal forms.
 Representation of unsigned integers, signed integers and reals, double precision reals and long 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; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

UPSC Civil Services Examination 2014 Syllabus of more subjects browse from the links below:

UPSC Civil Services Main Examination 2014 Syllabus: Zoology Paper-II
UPSC Civil Services Examination 2014 Syllabus: Zoology Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Statistics Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Statistics Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Sociology-II
UPSC Civil Services Main Examination 2014 Syllabus: Sociology Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Public Administration Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Public Administration Paper-I
UPSC Civil Services Main Examination 2014 Syllabus Psychology-II
UPSC Civil Services Main Examination 2014 Syllabus: Psychology Paper-I
UPSC Civil Services Main Examination 2014 Syllabus Political Science and International Relations Paper-I
UPSC Civil Services Examination 2014 Syllabus: Political Science and International Relations (PS&IR) Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Physics Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Physics Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Philosophy Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Philosophy Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Medical Science-II
UPSC Civil Services Main Examination 2014 Syllabus: Medical Science Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Mechanical Engineering Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Mechanical Engineering Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Mathematics Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Mathematics Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Management Paper-II
UPSC Civil Services Examination 2014 Syllabus: Management Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Urdu Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Urdu Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Telugu Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Telugu Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Tamil Paper-II
UPSC Civil Services Examination 2014 Syllabus: Tamil Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Sindhi Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Sindhi Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Sindhi Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Santhali Paper-II
UPSC Civil Services Examination 2014 Syllabus: Santhali Paper-I
UPSC Civil Services Examination 2014 Syllabus: Sanskrit Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Sanskrit Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Punjabi Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Punjabi Paper-I
UPSC Civil Services Main Examination Syllabus: Oriya Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Oriya Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Nepali Paper-II
UPSC Civil Services Main Examination 2014: Nepali Paper-I
UPSC Civil Services Main Examination 2014 Syllabus Marathi Paper-II
UPSC Civil Services Main Examination 2014 Syllabus Marathi Paper-I
UPSC Civil Services Main Examination 2014 Syllabus Manipuri Paper-II
UPSC Civil Services Examination 2014 Syllabus Manipuri Paper-I
UPSC Civil Services Examination 2014 Syllabus: Malyalam Paper-II
UPSC Civil Services Main Examination 2014 Syllabus Malayalam Paper-I
UPSC Civil Services Main Examination 2014 Syllabus Maithili-II
UPSC Civil Services Main Examination 2014 Syllabus Maithili-I
UPSC Civil Services Main Examination 2014 Syllabus Konkani-II
UPSC Civil Services Main Examination 2014 Syllabus Konkani-I
UPSC Civil Services Main Examination 2014 Syllabus Kashmiri-II
UPSC Civil Service Main Examination 2014 Syllabus Kashmiri-I
UPSC Civil Services Main Examination 2014 Syllabus Kannada-II
UPSC Civil Services Main Examination 2014 Syllabus Kannada-I
UPSC Civil Services Main Examination 2014 Syllabus Hindi-II
UPSC Civil Services Main Examination 2014 Syllabus Hindi-I
UPSC Civil Services Main Examination 2014 Syllabus Gugarati-II
UPSC Civil Services Main Examination 2014 Syllabus Gujarati Paper I
UPSC Civil Services Main Examination 2014 Syllabus English-II
UPSC Civil Services Examination 2014 Syllabus English - I
UPSC Civil Services Main Examination 2014 Syllabus: Dogri-II
UPSC Civil Services Main Examination 2014 Syllabus Dogri Paper-I
UPSC Civil Services Main Examination 2014 Syllabus: Bodo-II
UPSC Civil Services Main Examination 2014 Syllabus: Bodo-I
UPSC Civil Services Main Examination 2014 Syllabus: Bengali Paper-II
UPSC Civil Services Main Examination 2014 Syllabus: Bengali Paper I
UPSC Civil Services Main Exam 2014 Syllabus: Assamese-II
UPSC Civil Services Main Exam 2014 Syllabus: Assamese-I
UPSC Civil Services Main Examination 2014 Syllabus: Law-II
UPSC Civil Services Main Examination 2014 Syllabus: Law-I
UPSC Civil Services Main Examination 2014 Syllabus: History-II
UPSC Civil Services Main Examination 2014 Syllabus: History-I
UPSC Civil Services Main Examination 2014 Syllabus: Geology-II
UPSC Civil Services Main Examination 2014 Syllabus: Geology-I
UPSC Civil Services Main Examination 2014 Syllabus: Geography-II
UPSC Civil Service Main Exam Syllabus 2014: Geography-I
UPSC Civil Services Main Examination 2014 Syllabus Electrical Engineering-II
UPSC Civil Services Main Examination 2014 Syllabus Electrical Engineering-I
UPSC Civil Services Main Exam 2014 Syllabus Paper VII: Economics-II
UPSC Civil Services Main Exam 2014 Syllabus: Paper VI: Economics-I
UPSC Civil Services Main Examination 2014 Syllabus Paper VII: Commerce and Accountancy-II
UPSC Civil Services Main Examination 2014 Syllabus Paper VI: Commerce and Accountancy-I
UPSC Civil Services Main Examination 2014 Syllabus Paper VII: Civil Engineering-II
UPSC Civil Services Main Examination 2014 Syllabus Paper VI: Civil Engineering-I
UPSC Civil Services Main Examination 2014 Syllabus Paper VII: Chemistry-II
UPSC Civil Services Main Examination Syllabus Paper VI: Chemistry-I
UPSC Civil Services Main Examination 2014 Syllabus Paper VII: Botany-II
UPSC Civil Services Main Examination 2014 Syllabus Paper VI: Botany-I
UPSC Civil Services Main Examination 2014 Syllabus Paper VII: Anthropology-II
UPSC Civil Services Main Examination 2014: Syllabus Paper VI: Anthropology-I
UPSC Civil Services Main Examination 2014 Syllabus Paper VII
UPSC Civil Services Main Examination 2014: Syllabus Paper VI
UPSC Civil Services Main Examination 2014: Syllabus Paper VII: Agriculture-II
UPSC Civil Services Main Examination 2014: Syllabus Paper VI: Agriculture-I
UPSC Civil Services Main Examination 2014 Syllabus: Paper-V: General Studies-IV
UPSC Civil Services Main Examination 2014 Syllabus: Paper-IV: General Studies-III
UPSC Civil Services Main Examination 2014 Syllabus: Paper-III: General Studies-II
UPSC Civil Services Main Examination 2014 Syllabus: Paper-II: General Studies-I
UPSC Civil Services Main Examination 2014 Syllabus: Paper-I: Essay
UPSC Civil Services Main Examination 2014 Syllabus: Indian Language and English

More Useful Articles about UPSC Civil Services Examination 2014

UPSC Civil Services Examination 2014
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Level of Question Papers in Civil Service Main Examination 2014
Criteria of Negative Marking in UPSC Civil Services Examination 2014
UPSC Civil Services Preliminary Exam Syllabus 2014
Download E-Admit Card: UPSC Civil Services Preliminary Examination 2014

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