RAS PRE MATHEMATICS SYALLBUS

Mathematics (Code No. 20)
Algebra : Sets, relations, equivalence relations, Natural numbers, Integers, Rational
numbers, Real and Complex numbers, division algorithm, greatest common division
polynomials, division algorithm, derivations, Integral, rational real and complex roots of
a polynomial, Relation between roots and Coefficients, repeated roots, elementary
symmetric functions, Groups, rings, fields and their elementary properties.
Matrices : Addition and multiplication, elementary row and column operation, rank
determinants, inverse, solutions of systems of linear equations.
Calculus : Real numbers, order completeness property, standard functions, limits,
continuity, properties of continuous functions in closed intervals, differentiability, Mean
value Theorem, Taylors Theorem, Maxima and Minima, Application to curves tangent
normal properties, Curvatute, asymptotes, double points, points of inflection and tracing.
Definition of a definite integral of continuous function as the limit of a sum,
fundamental theorem of integral Calculus, methods of integration, rectification
quadrature, volume and surfaces of solids of revolution.
Partial differentiation and its application.
Simple test of convergence of series of positive terms, alternating series and absolute
convergence.
Differential Equations : First order differential equations, Singular solutions,
geometrical interpretations, linear differential equations with constant coefficients.
Geometry : Analytic Geometry of straight lines and conics referred to Cartesian and
polar Coordinates; three dimensional geometry for planes, straight lines, sphere, Cone
and Cylinder.
Mechanics : Concept of particle, lamina, rigid body, displacement, force, mass,
weight, concept of scalar and vector quantities, Vector Algebra, Combination and
equilibrium of coplanar forces, Newton's Laws of motion, motion of a particle in a
straight line; Simple Harmonic motion, projectile, circular motion, motion under central
forces (inverse square law), escape velocity.