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MATRICES AND DETERMINANTS
VECTOR ALGEBRA
COMPLEX NUMBERS
ANALYTICAL GEOMETRY
DIFFERENTIAL CALCULUS - part1
DIFFERENTIAL CALCULUS - PART II
INTEGRAL CALCULUS
DIFFERENTIAL EQUATIONS
DISCRETE MATHEMATICS
PROBABILITY DISTRIBUTIONS
Adjoint, Inverse - Properties, Computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a Matrix − Elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, Non-homogeneous equations, homogeneous linear system, rank method.
Scalar Product - Angle between two vectors, properties of scalar product, applications of dot products. Vector Product − Right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors − Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines − Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points (derivations are not required). angle between two lines. Skew lines − Shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points. Planes − Equation of a plane (derivations are not required), passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere − Equation of the sphere (derivations are not required) whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.
Complex number system, Conjugate − properties, ordered pair representation. Modulus − properties, geometrical representation, meaning, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications. Roots of a complex number − nth roots, cube roots, fourth roots.
Definition of a Conic - General equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola - Standard equation of a parabola (derivation and tracing the parabola are not required), other standard parabolas, the process of shifting the origin, general form of the standard equation, some practical problems. Ellipse - Standard equation of the ellipse (derivation and tracing the ellipse are not required), x^2?a^2 + y^2?b^2 =1,(a>b), Other standard form of the ellipse, general forms, some practical problems, Hyperbola - standard equation (derivation and tracing the hyperbola are not required), x^2?a^2 - y^2?b^2 =1,(a>b), Other form of the hyperbola, parametric form of conics, chords. Tangents and Normals - Cartesian form and Parametric form, equation of chord of contact of tangents from a point (x1, y1), Asymptotes, Rectangular hyperbola - standard equation of a rectangular hyperbola.
Derivative as a rate measure − rate of change − velocity − acceleration − related rates − Derivative as a measure of slope − tangent, normal and angle between curves. Maxima and Minima. Mean value theorem − Rolle’s Theorem − Lagrange Mean Value Thorem − Taylor’s and Maclaurin’s series, I’ Hopital’s Rule, stationary points − increasing, decreasing, maxima, minima, concavity convexity, points of inflexion.
Errors and approximations − absolute, relative, percentage errors, curve tracing, partial derivatives − Euler’s theorem.
Properties of definite integrals, reduction formulae for sinn x and cosn x (only results), Area, length, volume and surface area.
Formation of differential equations, order and degree, solving differential equations (1st order) - variable separable homogeneous, linear equations. Second order linear equations with constant coefficients f(x) = e^mx, sin mx, cos mx, x, x^2 .
Mathematical Logic - Logical statements, connectives, truth tables, Tautologies, Binary Operations - Semi groups - monoids, groups (Problems and simple properties only), order of a group, order of an element.
Random Variable, Probability density function, distribution function, mathematical expectation, variance, Discrete Distributions - Binomial, Poisson, Continuous Distribution - Normal distribution
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