Hi, can you please tell me the syllabus for mathematics and statistics, for both main and preliminary exams held by upsc for ips, And which are the topics covered in general studies for the same exam and please guide me which are the books i need to refer to get prepared very well to write ips exam ?
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There are two types of written examination in UPSC.
UPSC Prelim exam and UPSC Mains exam. You will appear in UPSC Prelim exam first in which Objective type Questions are asked from General English, General Studies etc.
For UPSC Mains you have to choose Subjects. There are total 51 Optional Subjects in which 23 are from main subjects and 28 Language Subjects like Hindi, English, Bengali etc.
The Preliminary Examination will consist of two papers of Objective type (multiple choice questions) and carry a maximum of 400 marks
The Main Examination will consist of a written examination and an Interview Test. The written examination will consist of 9 papers of conventional essay type.
Syllabus for prelim exam: Current events of national and international importance
History of India and Indian National Movement
Indian and World Geography - Physical, Social, Economic Geography of India and the World
Indian Polity and Governance - Constitution, Political System, Panchayati Raj, Public Policy, Rights Issues, etc
Economic and Social Development - Sustainable Development, Poverty, Inclusion, Demographics, Social Sector initiatives, etc.
General issues on Environmental Ecology, Bio-diversity and Climate Change - that do not require subject specialization
For mains exam you have to choose the subjects.
Syllabus of Mathematics
Paper-I
(1) Linear Algebra:
Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation.
Algebra of Matrices; Row and column reduction, Echelon form, congruence�s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.
(2) Calculus:
Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian.
Riemann's definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.
(3) Analytic Geometry:
Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.
(4) Ordinary Differential Equations:
Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut's equation, singular solution.
Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution.
Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters.
Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.
(5) Dynamics & Statics:
Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler's laws, orbits under central forces.
Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.
(6) Vector Analysis:
Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations.
Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet�s formulae.
Gauss and Stokes� theorems, Green�s identities.
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.
Syllabus of General Studies:
Paper-I
(1) History of Modern India and Indian Culture
The History of Modern India will cover history of the Country from about the middle of nineteenth century and would also include questions on important personalities who shaped the freedom movement and social reforms. The part relating to Indian culture will cover all aspects of Indian culture from the ancient to modern times as well as principal features of literature, arts and architecture.
(2) Geogrphy of India
In this part, questions will be on the physical, economic and social geography of India.
(3) Constitution of India and Indian Polity
This part will include questions on the Constitution of India as well as all constitutional, legal, administrative and other issues emerging from the politico-administrative system prevalent in the country.
(4) Current National issues and topics of social relevance
(i) The Indian economy and issues relating to planning, mobilization of resources, growth, development and employment.
(ii) Issues arising from the social and economic exclusion of large sections from the benefits of development.
(iii) Other issues relating to the development and management of human resource.
(iv) Health issues including the management of Public Health, Health education and ethical concerns regarding health-care, medical research and pharmaceuticals.
(v) Law enforcement, internal security and related issues such as the preservation of communal harmony.
(vi) Issues relating to good governance and accountability to the citizens including the maintenance of human rights, and of probity in public life.
(vii) Environmental issues, ecological preservation, conservation of natural resources and national heritage.
Paper-II
(1) India and the World
� Foreign Affairs with special emphasis on India�s relations with neighbouring countries and in the region.
� Security and defence related matters.
� Nuclear policy, issues, and conflicts.
� The Indian Diaspora and its contribution to India and the world.
(2) India�s Economic Interaction with the World
questions will be on economic and trade issues such as foreign trade, foreign investment; economic and diplomacy issues relating to oil, gas and energy flows; the role and functions of I.M.F., World Bank, W.T.O., WIPO etc. which influence India�s economic interaction with other countries and international institutions.
(3) Developments in the Field of Science & Technology, IT and space
questions will test the candidate's awareness of the developments in the field of science and technology, information technology, space and basic ideas about computers, robotics, nanotechnology, biotechnology and related issues regarding intellectual property rights.
(4) International Affairs and Institutions
questions on important events in world affairs and on international institutions.
(5) Statistical analysis, graphs and diagrams
This part will test the candidate's ability to draw conclusions from information presented in statistical, graphical or diagrammatical form and to interpret them.
For recommended books of UPSC visit http://www.upscportal.com/civilservices/order-books
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