Maths syllabus for UPSC(IAS) PRELIMINARY Note: UPSC exam consists of Preliminary
and Main. The Prelim consists of TWO papers ( ie Paper I and Paper II)
. Paper I is GENERAL STUDIES. It is
for 150 marks. Paper II : MATHEMATICS It is for
300 marks. (Ofcourse, instead of Maths you can choose some other subject
such as physics,chemistry,etc) Both the above prelim papers are
objective( ie multiple choice questions) Now let us see the Maths syllabus for Prelim 1. Algebra : Elements of Set Theory; Algebra of Real and Complex numbers
including Demovire's theorem; Polynomials and Polynomial equations, relation
between Coefficients and Roots, symmetric functions of roots; Elements
of Group Theory; Sub-Group, Cyclic groups, Permutation, Groups and their
elementary properties.
Rings, Integral Domains and Fields and their elementary properties. 2. Vector Spaces and Matrices : Vector Space, Linear Dependence and Independence.
Sub-spaces. Basis and Dimensions, Finite Dimensional Vector Spaces. Linear
Transformation of a Finite Dimensional Vector Space, Matrix Representation.
Singular and Nonsingular Transformations. Rank and Nullity. Matrices : Addition, Multiplication, Determinants of a Matrix, Properties
of Determinants of order, Inverse of a Matrix, Cramer's rule. 3. Geometry and Vectors : Analytic Geometry of straight lines and conics
in Cartesian and Polar coordinates; Three Dimensional geometry for planes,
straight lines, sphere, cone and cylinder. Addition, Subtraction and Products
of Vectors and Simple applications to Geometry. 4. Calculus : Functions, Sequences, Series, Limits, Continuity, Derivatives.
Application of Derivatives : Rates of change, Tangents, Normals, Maxima,
Minima, Rolle's Theorem, Mean Value Theorems of Lagrange and Cauchy, Asymptotes,
Curvature. Methods of finding indefinite integrals, Definite Integrals,
Fundamental Theorem of integrals Calculus. Application of definite integrals
to area, Length of a plane curve, Volume and Surfaces of revolution. 5. Ordinary Differential Equations : Order and Degree of a Differential
Equation, First order differential Equations, Singular solution, Geometrical
interpretation, Second order equations with constant coefficients. 6. Mechanics : Concepts of particles-Lamina; Rigid Body; Displacements;
force; Mass; weight; Motion; Velocity; Speed; Acceleration; Parallelogram
of forces; Parallelogram of velocity, acceleration; resultant; equilibrium
of coplanar forces; Moments; Couples; Friction; Centre of mass, Gravity;
Laws of motion; Motion of a particle in a straight line; simple Harmonic
Motion; Motion under conservative forces; Motion under gravity; Projectile;
Escape velocity; Motion of artificial satellites. 7. Elements of Computer Programming : Binary system, Octal and Hexadecimal
systems. Conversion to and from Decimal systems. Codes, Bits, Bytes and
Words. Memory of a computer, Arithmetic and Logical operations on numbers.
Precisions. AND, OR, XOR, NOT and Shift Not Shit operators, Algorithms
and Flow Charts.
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