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Here you will find IAS Mathematics Syllabus 2023.

PAPER - I

(1) Linear Algebra:-

Vector spaces over R and C, linear dependence and in dependence, 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, meanvalue 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 incartesian 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 seriesrepresentation 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.

Indian Institute of Management (IIM), Ahmedabad is listed amongst the top three business schools in India, which is known for offering excellent education to those students who aspire to become an entrepreneur or aim of achieving higher position in the field of business management.

Indian Institute of Management (IIM) Ahmedabad Courses Offered

Address : Vastrapur, Ahmedabad - 380015, Gujarat, India. Tel : +91-79-66323456 / 26308357 Fax: +91-79-26306896

Indian Institute of Management (IIM), Bangalore is amongst the well recognized business schools in India.

Indian Institute of Management (IIM) Bangalore Courses Offered

Address : Bannerghatta Road, Bangalore, India Pin Code : 560 076 Ph : +91-80-26582450 / 26993996 Fax Number: +91-80-26584050 / 26584004 / 26584181 / 26581602

Indian Institute of Management (IIM), Kolkata is one of the oldest and best management institutes in India that was established in the year 1961 by Government of West Bengal.

Indian Institute of Management (IIM) Kolkata Courses Offered

Address : Diamond Harbour Road Joka, Kolkata (Calcutta) - 700104 West Bengal INDIA

Indian Institute of Management (IIM) Indore is the sixth Indian Institute of Management, which came into existence in year 1996.

Indian Institute of Management (IIM) Indore Courses Offered

Address : Prabandh Shikhar Rau - Pithampur Road Indore - 453556 Madhya Pradesh, INDIA Tel: + 91-731-2439666 Fax: + 91-731-2439800
IIM kozhikode
Kozhikode

The Government of India has established 13 Indian Institutes of Management in different states in order cater the escalating demand for the degree.

IIM kozhikode Courses Offered

Address : IIMK Campus P. O., Kozhikode, Kerala, India, PIN - 673 570 Ph : +91-495-2809100 Fax: +91-495-2803010-11

Institute of Management Technology (IMT) - Ghaziabad, was established in 1980 by well-known industrialist Shri.

Institute of Management Technology (IMT) Ghaziabad Courses Offered

Address : Raj Nagar Post Box No. 137 Ghaziabad Pin - 201001, India Ph : +91 0120 3002200 Fax : +91 0120 2827895 Email : info@imt.edu

Indian Institute of  Foreign Trade (IIFT) is a business management institute in New Delhi, which was set up by the Government of India in the year 1963.

Indian Institute of Foreign Trade (IIFT) Courses Offered

Address : IIFT Bhawan, B-21, Qutab Institutional Area, New Delhi, Delhi, India Ph : 011- 26965124, 011-26965051 Email : ldmago@iift.ac.in

Indian Institute of Forest Management is an autonomous institution in Bhopal that strives to develop and equip students with essential skills in the field of forest management.

Indian Institute of Forest Management Bhopal Courses Offered

Address : Po Box 357, Nehru Nagar, Bhopal, Madhya Pradesh, India Contact No : 0755-2775716, 2773799 Email: director@iifm.ac.in

Indian Institute of Social Welfare and  Business Management is one of the premier and leading management institutes in Kolkata, established in the year 1953.

Indian Institute of Social Welfare and Business Management Courses Offered

Address : College Square West Kolkata-700 073 EPABX :+91- 33 - 2241 3756 / 5792 / 8694/8695 Fax : +91- 33 - 2241 3975 E-mail : iiswbm@iiswbm.edu

Indira Institute of Management is affiliated to University of Pune and Recognized by A.

Indira Institute of Management Pune Courses Offered

Address : 85/5-A, “TAPASYA”, New Pune-Mumbai Highway, Tathwade, Pune – 411 033 Tel. No. (020) 66739862, 22933279 – 84, 66759400. Fax No. (020) 22934126, Toll-Free No. 18002094332 Email : info@indiraiimp.edu.in

Institute for Financial Management and Research Chennai is a business institute in Chennai, established in the year 1970.

Institute for Financial Management and Research Chennai Courses Offered

Address : No. 24, Kothari Road Nungambakkam, Chennai – 600 034 Phone : +91 44 28303400

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